Material Library Users Guide

Material Library
User’s Guide
Material Library User’s Guide
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Part number: CM021201

C o n t e n t s
Chapter 1: Introduction
The Material Library Environment 6

About the Material Library . . . . . . . . . . . . . . . . . . . 6
Where Do I Access the Documentation and Application Libraries? . . . . 7
Chapter 2: Using the Material Library
Working with Materials 12

The Material Browser Window . . . . . . . . . . . . . . . . . 12
The Add Material Window . . . . . . . . . . . . . . . . . . . 17
Materials . . . . . . . . . . . . . . . . . . . . . . . . . . 20
The Settings Window for Material . . . . . . . . . . . . . . . . 21
Property Groups . . . . . . . . . . . . . . . . . . . . . . . 28
Material Link . . . . . . . . . . . . . . . . . . . . . . . . 32
Switch for Materials . . . . . . . . . . . . . . . . . . . . . . 33
Layered Material . . . . . . . . . . . . . . . . . . . . . . . 34
Layered Material Link . . . . . . . . . . . . . . . . . . . . . 40
Layered Material Stack. . . . . . . . . . . . . . . . . . . . . 44
Layered Material Link (Subnode) . . . . . . . . . . . . . . . . . 48
Single-Layer Materials . . . . . . . . . . . . . . . . . . . . . 50
Material Properties 51
Viewing Material Property Information . . . . . . . . . . . . . . 51
Functions Default Values in the Material Library . . . . . . . . . . . 52
Available Material Library Material Properties . . . . . . . . . . . . 53
Checking the Validity of Properties in the Material Library . . . . . . . 54
Other Material Properties Reference 59

About Model Inputs. . . . . . . . . . . . . . . . . . . . . . 59
About the Output Material Properties. . . . . . . . . . . . . . . 60
Acoustics Material Properties . . . . . . . . . . . . . . . . . . 63
CONTENTS |3
Electrochemistry Material Properties . . . . . . . . . . . . . . . 64
Electromagnetic Models . . . . . . . . . . . . . . . . . . . . 65
Equilibrium Discharge . . . . . . . . . . . . . . . . . . . . . 67
Gas Models . . . . . . . . . . . . . . . . . . . . . . . . . 67
Geometric Properties (Shell) . . . . . . . . . . . . . . . . . . 67
Magnetostrictive Models . . . . . . . . . . . . . . . . . . . . 68
Piezoelectric Models . . . . . . . . . . . . . . . . . . . . . 69
Piezoresistive Models . . . . . . . . . . . . . . . . . . . . . 69
Semiconductors Material Properties . . . . . . . . . . . . . . . 70
Solid Mechanics Material Properties. . . . . . . . . . . . . . . . 75
Solid Mechanics Material Properties: Nonlinear Structural Materials
Module . . . . . . . . . . . . . . . . . . . . . . . . . 78
Solid Mechanics Material Properties: Fatigue Module . . . . . . . . . 83
Solid Mechanics Material Properties: Geomechanics Material Model . . . 84
Thermal Expansion Material Properties . . . . . . . . . . . . . . 85
External Material Properties . . . . . . . . . . . . . . . . . . 86
Using Functions 87
Adding a Function to the Material . . . . . . . . . . . . . . . . 87
Defining an Analytic Function . . . . . . . . . . . . . . . . . . 88
4 | CONTENTS
1
Introduction
Welcome to the Material Library, an add-on product that provides predefined

material data, primarily as piecewise polynomial functions of temperature. The
Material Library contains more than 30,000 property functions; these functions
specify various material properties of over 3800 materials.
The Material Library is ideal for multiphysics couplings such as electrical-thermal

analysis and structural-thermal analysis because most of the properties are available
as functions of temperature.
5
T he M a te r i a l Li b rary E n v i ron men t
When working with the Material Library, it is the same as working with any other
material database. Below are descriptions about the predefined material databases, the
Material Library folders, and the windows and pages you work in to add any material
to your model.
See Materials in the COMSOL Multiphysics Reference Manual for an

overview of working with material properties, material databases, and the
Material Browser.
About the Material Library

The Material Library stores the material data in folders. A search engine on the Material
Browser makes it easy to find materials to add to models — you can search by name,
UNS number, or DIN number.
The following is some basic information about the available material properties
contained in the Material Library.
• The Material Library incorporates mechanical, thermal, and electrical properties

primarily for solid materials.
• The material properties are described as a function of some variable, typically
temperature, and focus on elastic and thermal properties.
• Where applicable, data is given for a material’s solid, liquid, and vapor phases. A
material can also contain data for multiple orientations or variations.
• The properties are analytic functions over a given interval of the argument.
• Smoothing is used to interpolate the values of the properties between different
intervals. You can choose the smoothing settings in order to obtain continuous first
and second derivatives of the property functions.
• Materials can be copied to a User-Defined Library where you can add and edit
properties. You can also plot and inspect the definition of a function.
• The material property data in the Material Library is based on the Material Property
Database (MPDB) from JAHM Software, Inc.
• For all properties contained in the Material Library, you can view the literature
reference, notes, and reference temperature (where applicable) by first selecting a
6 | CHAPTER 1: INTRODUCTION
material property and then on the Material Browser, under Properties, click a specific
property. Then information, when available, displays under Property reference.
• Working with Materials

• The Material Browser Window
• The Add Material Window
Where Do I Access the Documentation and Application Libraries?

A number of internet resources have more information about COMSOL, including
licensing and technical information. The electronic documentation, topic-based (or
context-based) help, and the application libraries are all accessed through the
COMSOL Desktop.
If you are reading the documentation as a PDF file on your computer,

the blue links do not work to open an application or content
referenced in a different guide. However, if you are using the Help
system in COMSOL Multiphysics, these links work to open other
modules, application examples, and documentation sets.
THE DOCUMENTATION AND ONLINE HELP

The COMSOL Multiphysics Reference Manual describes the core physics interfaces
and functionality included with the COMSOL Multiphysics license. This book also has
instructions about how to use COMSOL Multiphysics and how to access the
electronic Documentation and Help content.
Opening Topic-Based Help

The Help window is useful as it is connected to the features in the COMSOL Desktop.
To learn more about a node in the Model Builder, or a window on the Desktop, click
to highlight a node or window, then press F1 to open the Help window, which then
THE MATERIAL LIBRARY ENVIRONMENT | 7

displays information about that feature (or click a node in the Model Builder followed
by the Help button ( ). This is called topic-based (or context) help.
To open the Help window:
• In the Model Builder, Application Builder, or Physics Builder click a node or

window and then press F1.
• On any toolbar (for example, Home, Definitions, or Geometry), hover the
mouse over a button (for example, Add Physics or Build All) and then
press F1.
• From the File menu, click Help ( ).
• In the upper-right corner of the COMSOL Desktop, click the Help ( )
button.
To open the Help window:
• In the Model Builder or Physics Builder click a node or window and then
press F1.
• On the main toolbar, click the Help ( ) button.
• From the main menu, select Help>Help.
Opening the Documentation Window
To open the Documentation window:
• Press Ctrl+F1.
• From the File menu select Help>Documentation ( ).
To open the Documentation window:
• Press Ctrl+F1.
• On the main toolbar, click the Documentation ( ) button.
• From the main menu, select Help>Documentation.
THE APPLICATION LIBRARIES WINDOW
Each model or application includes documentation with the theoretical background
and step-by-step instructions to create a model or application. The models and
applications are available in COMSOL Multiphysics as MPH files that you can open
for further investigation. You can use the step-by-step instructions and the actual
models as templates for your own modeling. In most models, SI units are used to
describe the relevant properties, parameters, and dimensions, but other unit systems
are available.
Once the Application Libraries window is opened, you can search by name or browse
under a module folder name. Click to view a summary of the model or application and
its properties, including options to open it or its associated PDF document.
The Application Libraries Window in the COMSOL Multiphysics

Reference Manual.
Opening the Application Libraries Window

To open the Application Libraries window ( ):
• From the Home toolbar, Windows menu, click ( ) Applications

Libraries.
• From the File menu select Application Libraries.
To include the latest versions of model examples, from the File>Help

menu, select ( ) Update COMSOL Application Library.
Select Application Libraries from the main File> or Windows> menus.
To include the latest versions of model examples, from the Help menu
select ( ) Update COMSOL Application Library.
CONTACTING COMSOL BY EMAIL

For general product information, contact COMSOL at info@comsol.com.
COMSOL ACCESS AND TECHNICAL SUPPORT

To receive technical support from COMSOL for the COMSOL products, please
contact your local COMSOL representative or send your questions to
THE MATERIAL LIBRARY ENVIRONMENT | 9

support@comsol.com. An automatic notification and a case number are sent to you by
email. You can also access technical support, software updates, license information, and
other resources by registering for a COMSOL Access account.
COMSOL ONLINE RESOURCES
COMSOL website www.comsol.com

Contact COMSOL www.comsol.com/contact
COMSOL Access www.comsol.com/access
Support Center www.comsol.com/support
Product Download www.comsol.com/product-download
Product Updates www.comsol.com/support/updates
COMSOL Blog www.comsol.com/blogs
Discussion Forum www.comsol.com/community
Events www.comsol.com/events
COMSOL Video Gallery www.comsol.com/video
Support Knowledge Base www.comsol.com/support/knowledgebase
2
Using the Material Library
This chapter describes the material properties in the Material Library and how to
use them in your COMSOL Multiphysics® models. It also contains information
about using functions to define material properties.
In this chapter:
• Working with Materials

• Material Properties
• Other Material Properties Reference
• Using Functions
11
Working with Materials
The Material Browser Window
The Material Browser window ( ) contains a number of databases with a broad
collection of elastic, solid mechanics, electromagnetic, fluid, chemical, thermal,
piezoelectric, and piezoresistive properties of materials. The number of material
databases depends on which COMSOL products your license includes. Use the
Material Browser to find predefined materials and add them to the Model Builder, or
create a custom material library.
To open the Material Browser :
• On the Materials toolbar, click Browse Materials.

• Right-click the Materials node ( ), and then select Browse Materials.
• From the Home toolbar, select Windows>Material Browser.
To open the Material Browser :
• On the Model Toolbar, click Browse Materials.

• Right-click the Materials node ( ), and then select Browse Materials.
• Select Windows>Material Browser.
The Material Browser is similar to The Add Material Window but it includes detailed
property information about each material. From this window you can also create a new
material library and import a material library. See Adding Materials to a Component
for information about adding materials to your model’s components (geometries).
Click Done ( ) to close the Material Browser and add the materials in the Added to
model list to the model. Click Cancel ( ), press Escape, or click in the main toolbar
to exit the Material Browser without adding any materials.
Right-click a material library in the Material Browser and choose Reload Selected ( )
to clear all cached data for that library and force the COMSOL Multiphysics software
to reload the content from the file system. This operation is useful, for example, if the
library is a user-defined library that has been edited since the COMSOL Multiphysics
session started and needs to be reloaded to display the latest contents.
12 | CHAPTER 2: USING THE MATERIAL LIBRARY

You can browse all of the available material databases or search for specific materials.
There is also a Recent Materials folder where you find the most recently used
materials. Search a specific material by name (or, for the Material Library product, by
UNS number or DIN number, which are listed in the Material Browser when
available).
When browsing the material databases, in particular the Material Library, some
materials include additional information — UNS number, DIN number, and
composition.
As in Figure 2-1, the following information is included in the window to the right of
the material tree. Navigate in the material tree and click a material to display the
information.
Material availability is based on the type of COMSOL Multiphysics

license. For example, if you have the MEMS Module, you have the
Built-In, Liquids and Gases, MEMS, and Piezoelectric material libraries.
PROPERTIES
While browsing the databases, predefined material properties for the selected material
are listed in a table in the columns Property, Expression, Unit, and the Property group to
which the material property belongs. If Property group is empty, the material property
is a Basic property.
Under Property reference, for the materials in the Material Library product, reference
information about a material’s properties appears when you click a property above.
INPUTS
For some materials, predefined function inputs are listed in a table in the columns
Input, Variable, and Unit. Inputs appear for material properties defined using functions
that require the input. Typical inputs are temperature and pressure, for temperature-
and pressure-dependent material properties, respectively.
CREATE A NEW MATERIAL LIBRARY OR IMPORT A MATERIAL LIBRARY

Click the New Material Library button ( ) to open the New Material Library dialog
box. You can also right-click a material and select Add to New Library ( ) to create a
new material library and add that material to the new library. Go to Creating a New
Material Library and Adding and Editing Materials in the COMSOL Multiphysics
Reference Manual.
WORKING WITH MATERIALS | 13

Click the Import Material Library button ( ) to open the Choose Material Library
dialog box. Go to Importing a Material Library in the COMSOL Multiphysics
Reference Manual.
Figure 2-1: The Material Browser details a material’s properties after selection. In this
example, the properties of Oxygen are listed to the right of the Material Browser folders.

MATERIAL LIBRARY FOLDERS
TABLE 2-1: MATERIAL LIBRARY FOLDERS
FOLDER
Elements
Iron Alloys
Nickel Alloys
Aluminum Alloys
Copper Alloys
Magnesium Alloys
Titanium Alloys
Simple Oxides
Complex Oxides/Silicates
Carbides
Cermets
Tool Steels
Carbons
Thermal Insulators
Intermetallics
Refractory Metal Alloys
Thermal Barrier Coatings
Nylons and PA/PI (polyamides)
PAI (polyamide-imide)
PPA (polyphthalamides)
Polyethers and Polyesters
PEI (polyetherimide)
PARA (polyarylamide)
Acetal (polyoxymethylene)
PVDF (poly(vinylidene fluoride))
EVA (ethylene-vinyl acetate)
Miscellaneous Polymers
Miscellaneous Polymer Composites
Elastomers
Epoxies

FOLDER
Minerals, Rocks, and Soils

Woods
PP (polypropylenes)
PET (polyethylene terephthalate)
PBT (polybutylene terephthalate)
ECTFE (polyethylene chlorotrifluoroethylene)
m-PPE and PPE/PA
PAEK and PEEK (polyaryletherketone)
PSU (polysulfone)
PES/PESU (polyethersulfone)
PPSU/PPSF (polyphenysulfone)
Controlled Expansion Alloys
Precious Metal Alloys
Thermocouple Alloys
Semiconductors and Optical Materials
Organics and Hydrocarbons
Other Materials
Solders, Low Melting, and Dental
Cobalt Alloys
Resistance Alloys
Magnetic Alloys
Metal Matrix Composites
Ceramic Matrix Composites
Salts (single component)
Salts (multicomponent)
Salts (binary mixtures)
Salts (ternary mixtures)
Fuel Cell, Battery, and Electro-ceramics
Silicides
Borides
Glasses and Metallic Glasses

FOLDER
Nitrides
Cast Irons
Mold Materials
The Add Material Window

The Add Material window is similar to The Material Browser Window. It has the same
material libraries available but does not include the detailed properties about each
material. The number of material libraries depends on which COMSOL Multiphysics
products your license includes. This window is a quick way to add materials to models.
To open the Add Material window :
• From the Materials toolbar, click Add Material.

• Right-click the Materials node ( ) and select Add Material from Library.
As in Figure 2-2you can browse all the available material databases or search for specific
materials. There is also a Recent Materials folder where you find the most recently used
materials. Search a specific material by name (or, for the Material Library product, by
UNS number or DIN number).

Figure 2-2: The Add Material window. In this example, the liquid phase of Oxygen is
selected and can be added to the Material node in the local Component or as a global
material in the Model Builder.
ADDING MATERIALS TO A COMPONENT

You can add materials to Component nodes using either the Add Material or Material
Browser windows. In either window, use the Search field to find materials by name,
UNS number, or DIN number. Or click any of the folders and subfolders to locate and
add a specific material. To add a material to the current component, click the Add to
Component button, right-click the material and choose Add to Component, or, in the
Add Material window, press Enter. In the Add Material window you can also add a
material to global Materials list and to the current selection. In the Material Browser
window, you can also add the material to the global Materials list and to an existing
user-defined or new material library.

For example, click the arrow to the left of Elements to expand that folder, and then click
Oxygen.
In the Add Material window, all the materials are listed with a description
of the phase and orientation/type next to the primary name (for example,
Oxygen [liquid], Oxygen [vapor]. This is different in the Material Browser,
where you select these options from the Phase or Orientation/variation
lists.
Using the Add Material Window

1 Open the Add Material window (see The Add Material Window).
2 In the Add Material window, select a material by phase (liquid, vapor, gas, or solid)
and orientation/variation, when available.
3 Click the Add to Global Materials or Add to Component buttons, or right-click the
material and select the same options from the context menu. If there is more than
one Component node in the model tree, add the material to the applicable geometry.
- Click the Add to Global Materials button to add it under the global Materials node.
- Click the Add to Component button to add the material to the active component
in the Model Builder and then make it an active material in the domains (or other
geometric entities) where it is selected. You can also select any of the components
in the model to add it to its Materials node, or select Add to Switch 1, for example,
to add it under a Switch node for materials under the global Materials node.
Right-click the Material node to rename it, for example, using the name of the
material it represents.
Using the Material Browser Window

1 Open the Material Browser window (see The Material Browser Window).
2 In the Material Browser, select options from the Phase and Orientation/variation lists,
when available (only included for some materials in the Material Library product).
In this window you can review the material Properties and Input sections. See
Viewing Material Property Information for information about viewing information
about, for example, references for a specific material property.
3 Click the Add to Component button ( ) under the list of materials to add the
selected material to the current model component. Alternatively, click the Add To
button ( ) to add the material to the global Materials node (choose Global
Materials), to any available model component, or to an existing or new user-defined
material library. You can also right-click the selected material node to add that

material to a model component or user-defined material library. Materials that you
have selected to add to any of the model components appear in the Added to model
list.
4 Click Done ( ) to add the materials to the model tree in the Model Builder and close
the Material Browser. If it is the first material in that model component, the material
in the Model Builder becomes the default material; otherwise, the material is initially
not used anywhere but becomes the active material in the domains (or other
geometric entities) that you pick to add to that material’s selection list.
Materials
Use the nodes under Materials ( ) to add predefined or user-defined materials, to
specify material properties using model inputs, functions, values, and expressions as
needed, or to create a custom material library. Also see Material Link, Switch for
Materials, Working with External Materials, and About the Material Databases in the
COMSOL Multiphysics Reference Manual.
You can right-click the Materials node and select Add Materials from Library to add a
material using The Add Material Window or select Browse Materials to open The
Material Browser Window for more thorough information about the available
materials in the material libraries. Yous can also select Blank Material to add a Material
node with no predefined material properties.
MATERIAL OVERVIEW
This section provides an overview of the materials in the Component node and where
they are used. You can also add materials under Global Definitions. To access such global
materials in a model component, use a Material Link.
The Material column lists the current materials in the Component using the materials’
node labels from the model tree according to the settings defined in Displaying Node
Names, Tags, and Types in the Model Builder.
The Selection column lists the geometric entities selected for the material (the domains,
boundaries, or edges where the material is defined).
ERRORS RELATING TO THE MATERIAL NODES

If a material property in a physics interface takes its value from a material and no
material is defined for the same geometric selection, a stop sign ( ) displays in the
leftmost column and the Material column contains Entities needing a material. The
Selection column contains the geometric entities in which a material definition is

missing. The Materials node also indicates when there is a material error (see
Figure 2-3). For example, if some property is deleted but needed in a part of the
geometry, then the icon indicates where the error is located.
Figure 2-3: An example of a Materials node error.
The Settings Window for Material

The Settings window for Material ( ) summarizes the predefined or user-defined
material properties for a material. This is where you can add or change material
properties to fit your model and assign the material to all types of geometric entities:
domains (most common), boundaries, edges (3D models only), or points. Also see
Material Link and Switch for Materials.
After adding a material (see The Add Material Window and The Material Browser
Window), click the Material node (for example, Material 1 or Copper) in the Model
Builder. The Settings window for Material opens.
A standard Material node in the global component can turn into a layered material by
adding a Shell property group. After that, it can be linked by a Layered Material Link.

Figure 2-4: Click the Copper node to open the Settings window for Material for the node.
GEOMETRIC ENTITY SELECTION

Assign the material to some or all entities on a specific Geometric entity level — Domain,
Boundary, Edge (3D only), or Point — on the geometry in the Graphics window (the
geometry in the model).
By default, the first material in the Component is active in all domains (or
all boundaries or edges if the Component only contains surfaces or
edges). By assigning other materials to some or all domains, the first
material is overridden and remains active only in domains where no other
material, added below it in the Materials branch, is active.
If the Component contains features on different geometric entity levels,

such as solid mechanics in domains coupled to beams on edges, and the
features use the same material, you need to add two Material nodes with
the same material, one defined in the domains, and the other defined on
the edges.

OVERRIDE
This section shows if the material, in some or all parts of the geometry where it is
active, is overridden by another material added underneath it in the Materials branch,
or if it overrides another material above it.
The Overridden by list shows the names of the materials that override this material. The
Selection list in the Geometric Entity section displays (overridden) for the geometric
entities in which this material is overridden.
The Overrides list shows the names of the materials that this material overrides.
• Physics Exclusive and Contributing Node Types

• Physics and Variables Selection
• Physics Node Status
ORIENTATION AND POSITION
This section only appears in Material nodes that are single layer material.
See Single-Layer Materials.
Select a Coordinate system defining the principal directions of the laminate. Only
Boundary System coordinate systems can be selected.
Choose a Position — Midplane on boundary, Downside on boundary, Upside on boundary,

or User defined. This controls the possible offset of the material from the geometrical
boundary on which the mesh exists (the reference surface). For User defined, enter a
value for the Relative midplane offset. The value 1 corresponds to Downside on boundary,
and the value −1 corresponds to Upside on boundary. Values may be outside the range
−1 to 1, in which case the reference surface is outside the laminate.
The Position setting is only used by physics features where the physical behavior
depends of the actual location, such as structural shells.
By clicking the Layer Cross Section Preview ( ) button, you get a preview plot of the
single layer material, including the location of the reference surface. This plot looks
similar to Figure 2-10, but there is only a single layer.
MATERIAL PROPERTIES
You can add material properties to the material if they are not already included. To do
so, browse the available material property categories (Basic Properties, Acoustics, and so

on), and select a material property or a collection of material properties in one of the
property groups or material models that appear under the main level of material
property categories. Right-click the material property or property group and select Add
to Material, or click the Add to Material button ( ) to add the material property or
group of properties to the material.
Review the properties listed in the Material Contents table before adding
new material properties.
For example, under Acoustics>Viscous Model select Bulk viscosity (muB) and right-click
to Add to Material or click the Add to Material button ( ). If you add a material model
like the Viscous Model with more than one property, all of its material properties are
added to the Material Contents table. In this example, a Viscous model node is added to
the Model Builder and its associated properties are added to the Material Contents table.
To delete a property group, right-click the property group node (in the
Model Builder) and select Delete ( ). The Basic property group cannot be
deleted.
A Note About Adding Basic Material Properties

Material properties can be added to the Basic group or to any User-Defined Property
Group from two locations — the Settings windows for Material and Property Group.
• When material properties are added from the Basic node’s or a user-defined group
node’s Settings window for Property Group, they are listed under Output Properties
and Model Inputs in that Settings window.
• When material properties are added from the Settings window for Material, the
available material properties are listed under Material Properties and are added to the
list under Material Contents with the property group listed. The list under Material
Contents also contains material properties added from a subnode with a Settings
window for Property Group.
Material Type
The Material type setting decides how materials behave and how material properties are
interpreted when the mesh is deformed. Select Solid for materials whose properties
change as functions of material strain, material orientation, and other variables
evaluated in a material reference configuration (material frame). Select Nonsolid for
materials whose properties are defined only as functions of the current local state at

each point in the spatial frame and for which no unique material reference
configuration can be defined.
Simply put, Solid materials associate material properties with specific pieces of the
material, and the properties follow the material as it moves around. In particular, a
solid material may be inherently anisotropic, meaning that its axes rotate together with
the material. The Nonsolid choice, in contrast, applies typically to liquids and gases
whose properties are associated with fixed points in space and insensitive to local
rotation of the material. Such materials are inherently isotropic when studied in
isolation but can exhibit anisotropy induced by external fields. In practice, this means
that any anisotropic tensor properties in a nonsolid material must be functions of some
external vector field.
MATERIAL CONTENTS
This section lists all of the material properties that are defined for the material or
required by the physics in the model. The table lists the Property, Variable, Value, and
Unit for the material property as well as the Property group to which the material
property belongs. The Property group corresponds to the subnodes in the Model Builder
with the same name. If required, edit the values or expression for the property’s Value.
The left column provides visual cues about the status of each property:
• A stop sign ( ) indicates that an entry in the Value column is required. It means
that the material property is required by a physics feature in the model but is
undefined. When you enter a value in the Value column, the material property is
added to its property group.
• A warning sign ( ) indicates that the material property has been added to the
material but is still undefined. An entry is only required if the material property is to
be used in the model.
• A green check mark ( ) indicates that the property has a Value and is currently
being used in the physics of the model.
• A synchronize symbol ( ) indicates that the property is computed and
synchronized using the given values for other material properties from which it can
be computed.
• Properties with no indication in the left column are defined but not currently used
by any physics in the model.
You can change the value for any property that is not synchronized by editing its value
directly in the Value column, or, for a selected property, click the Edit button ( ) to
enter a value in the window that opens. If the property can be anisotropic, you can

choose to enter the values in one of these forms: Isotropic, Diagonal, Symmetric, or Full.
The Variable column lists the variable names corresponding to the degree of
anisotropy. For example, for a symmetric electrical conductivity, it contains {sigma11,
sigma12, sigma22, sigma13, sigma23, sigma 33}; sigmaij = sigmaji. For an isotropic
electrical conductivity, it contains sigma_iso; sigmaii = sigma_iso, sigmaij = 0, where
sigma_iso is the name of the variable for the isotropic electrical conductivity (available
as, for example, mat1.def.sigma_iso).
APPEARANCE
The settings in this section make it possible to control or change the default appearance
of a material in the Graphics window when working in the materials or physics parts of
the model tree.
In 3D components, the material is rendered including color and texture

when Scene Light is active. In 2D models and in 3D components, when
Scene Light is turned off, only a change of color is visible.
The Family list provides quick settings approximating the appearance of a number of
common materials — Air, Aluminum, Brick, Concrete, Copper, Gold, Iron, Lead,
Magnesium, Plastic, Steel, Titanium, and Water. Select Custom to make further
adjustments of the specific settings for colors, texture, reflectance, and so on. The
default custom settings are inherited from the material selected last from the Family list.
Specular Color, Diffuse Color, and Ambient Color

For each of these properties, click the Color button to assign a Custom specular color or
select a standard color from the list: Black, Blue, Cyan, Gray, Green, Magenta, Red, White,
or Yellow.
The combination of Specular color, Diffuse color, and Ambient color gives a 3D object its
overall color:
• Specular color is the color of the light of a specular reflection (specular reflection is
the type of reflection that is characteristic of light reflected from a shiny surface).
• Diffuse color represents the true color of an object; it is perceived as the color of the
object itself rather than a reflection of the light. The diffuse color gets darker as the
surface points away from the light (shading). As with Ambient color, if there is a

texture, this is multiplied by the colors in the texture, otherwise it is as if it has a
white texture.
• Ambient color is the color of all the light that surrounds an object; it is the color seen
when an object is in low light. This color is what the object reflects when illuminated
by ambient light rather than direct light. Ambient color creates the effect of having
light hit the object equally from all directions. As with Diffuse color, if there is a
texture, this is multiplied by the colors in the texture; otherwise, it is as if it has a
white texture.
For examples of specular, diffuse, and ambient light, which are related to
these definitions, see About the 3D View Light Sources and Attributes in
the COMSOL Multiphysics Reference Manual.
Noise
The Noise check box is selected by default, with the default Normal vector noise scale
and Normal vector noise frequency taken from the material. Enter other values as
needed, or click to clear the Noise check box.
• Noise is a texture that disturbs the normals when calculating lighting on the surface.
This causes the surface to look rough and textured.
• Normal vector noise scale is the power of the noise texture. A high value creates a
stronger texture of the surface. A value between 0–1 is suitable.
• Normal vector noise frequency is the size of the noise disturbances. A small value
creates smaller features on the texture. A value between 0–10 is suitable.
Diffuse and Ambient Color Opacity

The default Diffuse and ambient color opacity is 1.
Lighting Model
The default Lighting model — Blinn-Phong or Cook-Torrance — is based on the material.
Select Simple instead as needed.
The different lighting models provide a set of techniques used to calculate the
reflection of light from surfaces to create the appropriate shading. For example, a
specular highlight is the bright spot of light that appears on shiny objects when
illuminated. Specular highlights are important in 3D computer graphics because they
provide a strong visual cue for the shape of an object and its location with respect to
light sources in the scene.

For Blinn-Phong, the default Specular exponent is 64. The specular exponent determines
the size of the specular highlight. Typical values for this property range from 1 to 500,
with normal objects having values in the range 5 to 20. This model is particularly useful
for representing shiny materials.
For Cook-Torrance, the default Reflectance at normal incidence and Surface roughness are
taken from the material. The Cook-Torrance lighting model accounts for wavelength
and color shifting and is a general model for rough surfaces. It is targeted at metals and
plastics, although it can also represent many other materials.
• Reflectance at normal incidence is the amount of incoming light (0–1) from the
normal direction (of the surface) that is reflected.
• Surface roughness is a value that describes microreflectance on the surface. Higher
values create a rougher look of the surface with fewer highlights. A value from 0–1
is suitable.
Property Groups
The Settings window for Property Group is where output properties and model inputs
are added, local properties are defined, and expressions for material properties are
entered in a specific property group such as Basic. The property groups are subnodes
to a material node. The Settings window for Property Group is displayed when you click
the property group node (for example, Basic) under the material node (typically with
the material’s name — Aluminum, for example) in the Model Builder.

Figure 2-5: An example of a Basic Settings window for Property Group.
A property group under a material creates the following variables:

TABLE 2-2: VARIABLES GENERATED FROM A PROPERTY GROUP
TYPE VARIABLE NAME SCOPE SELECTION EXAMPLE
Basic Variable name root.material Material selection root.material.

property of physical rho
quantity
root.<comp>. Global selection root.comp1.
<mat>.<group> mat1.def.rho

TABLE 2-2: VARIABLES GENERATED FROM A PROPERTY GROUP
TYPE VARIABLE NAME SCOPE SELECTION EXAMPLE
Output Property name root.material Material selection root.material.

property .group linzRes.alpha
root.<comp>. Global selection root.comp1.

<mat>.<group> mat1.linzRes.
alpha
OUTPUT PROPERTIES
The predefined material properties in the property group appear in a table in the
Output Properties section.
It is only possible to add, move, and delete output properties from the
Basic material properties and with user-defined property groups.
Click the Add button ( ) to add another output property, which you choose from
one of the available physical quantities in the Physical Quantity dialog box that opens.
If required, edit the expressions in the list’s Expression column. Edit directly in the
table or in the Expression field underneath the table. You can insert predefined
expressions by clicking the Insert Expression button ( ) or clicking Ctrl+Space and
then choosing an expression from the list of predefined expressions. You can also click
the Edit button ( ), which opens a dialog box for easier specification of orthotropic
and anisotropic material properties (tensors), when applicable. Select Isotropic,
Diagonal, Symmetric, or Full when entering the data in the material property’s dialog
box. In the Expression column, use a syntax with curly braces such as
{k11, k21, k31, k12, k22, k32, k13, k23, k33} to enter anisotropic material
properties for a 3-by-3 tensor kij in the order k11, k21, k31, k12, k22, k32, k13, k23, and
k33. 1, 2, and 3 represent the first, second, and third direction in the active coordinate
system. In many cases (for example, when entering the elasticity matrix for structural
mechanics), the matrix must for physical reasons be symmetric. The upper diagonal
part of the matrix you enter will then be mirrored when forming the actual constitutive
matrix, and the lower diagonal part is ignored.
The Variable column lists the variable names depending on the type of anisotropy. For
an isotropic k, k_iso represents its single scalar value.
The Unit and Size columns provide information about the unit and size of the output
property. The size is 1x1 for a scalar value such as density and 3x3 for a tensor (matrix)
quantity such as electrical conductivity.

If desired, you can add information about the property, such as references for its value
or expression. To do so, click the Edit/Show Property Information button ( ) and
enter the property information in the dialog box that opens and then click OK. When
information is available for a property, and information symbol ( ) appears in the
Info column.
Use the Move up ( ), Move down ( ), and Delete ( ) buttons to organize the
table as needed.
MODEL INPUTS
The model inputs are physical quantities, such as temperature, that are used as inputs
in the expressions that define the output properties (for example, to describe a
temperature-dependent physical quantity). For example, adding Temperature as a
model input with the variable name T makes it possible to use an expression for the
heat capacity at constant pressure Cp, such as 300[J/(kg*K)]*T[1/K], which works
regardless of the name of the actual dependent variable for temperature in the model
that uses the temperature-dependent material. Without the model input, the
expression above only works with a temperature variable called T.
Click the Add button ( ) to add another model input, which you choose from one
of the available physical quantities in the Physical Quantity dialog box that opens.
Use the Move up ( ), Move down ( ), and Delete ( ) buttons to organize the
table as needed.
LOCAL PROPERTIES
Here you can enter a user-defined property by entering its variable name in the Name
column and its corresponding Expression and organizing the table as needed. You can
also enter a Description, which appears in the Property column in the Material Contents
section of the parent Material node. In that node, the Name entered here appears in the
Variable column. These local properties are useful for parameterizing functions that
describe material properties if they contain inputs other than those that are model
inputs (such as temperature and pressure). For example, a local property can be a

reference value at a certain temperature. Use the Move up ( ), Move down ( ), and
Delete ( ) buttons to organize the tables as needed.
You can use local properties to parameterize a material (for example, to

create a generic “template” material for a particular symmetry class of
anisotropic materials). You can then adjust the local property values for
each instance of the material.
About Automatic Adding of Property Groups to a Material

Material property groups are automatically added to the material node in the Model
Builder. You can also add additional predefined property groups or create a User-Defined
Property Group (on the Materials toolbar, click User-defined Property Group ( ) or
right-click the Material node). The available properties are collected in property groups
according to the physical context.
Each property group has a Settings window for Property Group. When a Model Builder
node is clicked (for example, Basic), the Settings window for Property Group displays
specific information about that property group. The physical properties for all property
groups are summarized in a Material Contents table on the Settings window for the
parent Material node.
Material Link
Add a Material Link node ( ) under a Materials node in a model component to add a
link to a material that you have added under the global Materials node ( ) and use it
as a material in that component’s geometry. The Material Link node’s Settings window
is similar to the Settings window for a material node (see The Settings Window for
Material), with the exception that there is no Material Properties sections. Instead, it
includes the following section:
LINK SETTINGS
From the Material list, select the global material that you want to link to:
• Any global material node, to use that material in the component.

• Any Switch node, if you want to run a material sweep.
• None, to not link to any global material.
Click the Go to Material button ( ) to move to the selected material node. Click the
Add Material from Library button ( ) to add a global material from the material

libraries or a new blank global material. The added material then becomes the one
selected in the Material list.
Switch for Materials

Use the Switch node ( ) to switch between materials during a solver sweep. You add
the materials as subnodes under the Switch node. Right-click to add a Blank Material or
select Add Material from Library to select materials from the libraries in the Add Material
window.
The switch for materials acts essentially as a switch statement in a programming

language; that is, it dynamically selects one of its underlying branches depending on a
parameter that can be controlled from the solvers, using a Material Sweep study. The
parameter name is constructed based on the tag of the Switch node, using the special
namespace matsw. For example, the parameter controlling a Switch node on the global
level will typically be matsw.sw1, while for a component-level Switch it will be
matsw.comp1.sw1.
During a material sweep, the sweep parameter takes consecutive integer values, starting
from one, indicating which material under the switch that should currently provide
material properties. You can use the parameter name in conditional expressions to
control also other aspects of the model. Conversely, it is possible to control a material
Switch also by manually defining the full switch parameter name in a Parameters node.
You can then choose the parameter to sweep over in a standard Parametric Sweep node
or assign it different (integer) values in different parameter Case nodes and sweep using
a Parameter switch sweep.
The Switch node’s Settings window contains the following sections:
MATERIAL CONTENTS
This section lists all of the material properties that are defined for the material or
required by the physics in the model on domains where the Switch node is the active
domain material. The table lists the Property, Name, Value, and Unit for the material
property as well as the Property group to which the material property belongs. The
Property group corresponds to the subnodes in the Model Builder with the same name.
If required, edit the values or expression for the property’s Value.

The list includes properties that are defined by any of the materials under the Switch
node. The left column provides visual cues about the status of each property:
• A stop sign ( ) indicates that some subnode is missing a required Value. That is,
the material property is required by a physics feature in the model but is not defined
for all switch cases.
• A warning sign ( ) indicates that the material property has been added to some
material subnode but is still undefined.
• A green check mark ( ) indicates that the property has a Value in all subnodes and
is currently being used in the physics of the model.
APPEARANCE
The settings in this section make it possible to control or change the default appearance
of the material switch in the Graphics window when working in the materials or physics
parts of the model tree. See The Settings Window for Material for more information.
Layered Material
In the Layered Material node ( ), you can specify the properties of a multilayer
laminate. It is used when defining the properties of the following features:
• The Layered Shell interface (requires the Composite Materials Module).

• Layered Linear Elastic Material in the Shell interface (requires the Composite
Materials Module).
• Thin Layer in the Heat Transfer in Solids interface.
• The Heat Transfer in Shells interface (requires the Heat Transfer Module).
• The Electric Currents, Layered Shell interface (requires the AC/DC Module).
A Layered Material node can be present in two locations in the Model Builder:
• The most common place is under Global Definitions>Materials. When you reference
a layered material from a physics interface, you do it indirectly through either a
Layered Material Link or a Layered Material Link (Subnode) under Materials in the
current component.
• It can also be a subnode under a Layered Material Stack node in a component.
LAYER DEFINITION
In this table you specify the properties of each layer.

Click the Add button ( ) to add another table row. Use the Move up ( ), Move
down ( ), and Delete ( ) buttons to organize the table as needed. To completely
reset the table to its default state, you can use the Reset to Default button ( ).
Conceptually, the layers are ordered from bottom to top of the laminate. Enter the
following data in the table:
Layer
Here you can assign a name to the layer for future reference. The default is a sequential
numbering: Layer 1, Layer 2, and so on.
Material
Select any available material. If the Layered Material node is located under Global
Definitions, the list contains only global materials. If the Layered Material node is used
as a subnode to a Layered Material Stack, also materials defined under Materials in the
component are available.
When you have a certain row in the table selected, you can access three shortcuts:
• Click the Blank Material ( ) button to add a new blank material under global
materials. The material is referenced in current row of the Material column.
• Click the Add Material from Library ( ) button to add a new material under global
materials from Material Libraries. The material is referenced in current row of the
Material column.
• Click the Go to Material ( ) button to jump to the definition of the material
selected on the current row.
When you add a new row to the table, the same material as on the previous row is
selected. This means that if you have many, not adjacent, layers with the same material,
it is more efficient to initially add all layers with that same material. Then you can go
back and change the material for some layers. Alternatively, you can reorder the layers
using the Move up ( ) and Move down ( ) buttons.
Rotation
If the material in the layer is orthotropic or anisotropic, enter the angle in degrees
(positive counterclockwise) from the first principal axis of the laminate to the first
principal axis of the layer. Even for an isotropic material, the orientation can matter for
result presentation, since it affects the interpretation of for example stress tensor
components.

Thickness
Enter the thickness of the layer (default unit: m). The thickness can be numeric value
or a scalar parameter.
Mesh elements
In the physics interfaces, the layered materials are handled through the concept of a
virtual extra dimension. For a layered material defined on a boundary, you can think
of that as an extra coordinate in the normal direction. Enter the number of elements
that you want in the extra dimension for the layer.
INTERFACE PROPERTY
In some physics features, not only the layers themselves but also the interfaces between
them are important. In such a case, you can assign materials to the interfaces in this
table. The number of interfaces is one more than the number of layers because the free
top and bottom surfaces of the laminate are also considered as interfaces.
In most cases, you do not need to enter anything in this section.
Interface
This is the interface name, for future reference. As a default, the interface name is
constructed from the names of the two adjacent layers. For the top and bottom
interfaces, the labels “up” and “down” are used for the two exterior sides.
You can rename the interfaces. This is, however, seldom needed.
Position
This column shows the location of the interface. The distance is counted from the
bottom of the laminate. The column is for information only, and cannot be modified.
Material
Select the material of the interface. You only need to assign materials to the interfaces
that are explicitly referenced by physics features. The default is to take the material
From layer. The interface material properties are then computed from the adjacent
layers’ material properties.

Figure 2-6 shows an example of the settings for a layered material. The layer names
have been entered manually, whereas the interfaces have retained their default names.
Figure 2-6: Settings for a material with three layers.
You can save the laminate definition to a text file by clicking the Save Layers to
File ( ) button. For the example above, the text file has the following contents:
Bottom mat1 0.0 1.2E-4 2

"Middle layer" mat2 45 2.3E-4 2
Top mat1 60 3.4E-4 2

To load a text file on this format, click the Load Layers from File ( ) button. For
complex laminates, it may be easier to start by creating the text file representation in a
text editor, than to enter the data in the GUI.
When loading a file, the second column containing the material tag is
ignored. The reason is that there is no way to ascertain that a material tag
like ‘mat2’ would point to the same material in another context. You can
even load a file where that column is absent.
You have two options for visualizing the laminate defined in the Layered Material node.
To see the thickness of each layer, click the Layer Cross Section Preview ( ) button.
This will give a plot like the one shown in Figure 2-7.
Figure 2-7: The layer cross section plot for a material with three layers.
To visualize the layer orientations, click the Layer Stack Preview ( ) button. In
Figure 2-8, an example of such a plot is shown. The x-axis corresponds to the principal
laminate direction, and the stripes indicate the principal direction of each layer.

Figure 2-8: The layer stack preview plot for a material with three layers.
PREVIEW PLOT SETTINGS

In this section, you can fine-tune the display in the preview plots.
In the Distance between the orientation lines text field, you can enter a value for the
spacing of the stripes showing the orientation of the principal orientation of the layer.
The layer itself is always drawn as a square with the unity side length. If you deselect
the corresponding check box, no orientation lines are drawn.
The value of the Thickness-to-width ratio is used by both types of preview plots.
• In a layer stack preview plot, it controls the height of the stack in the z direction.
For laminates with many layers, you may need to increase this value.
• In the layer cross section preview plot, it controls the height in the y direction. The
width is always unity.
Clear the Shows labels in cross section plot check box to remove the text labels showing
layer names and materials.

Layered Material Link
The Layered Material Link node ( ) provides a bridge from a Layered Material,
located under Global Definitions, to a physics feature residing in a component. A physics
feature designed to work with layered materials cannot directly reference a Layered
Material. The Layered Material Link node is located in the Layers submenu under a
Materials node.
LAYERED MATERIAL SETTINGS

Select a layered material from the Material list. You can also select a Switch for
Materials.
By clicking the Go to Material ( ) button, you can jump to the settings for the
selected material.
Click the Add Layered Material button ( ) to add another Layered Material or a Switch.
The added material then becomes the one selected in the Material list.
From the Transform list, choose one of the following options:
• None (the default), for no transformation.

• Symmetric or Antisymmetric, to create a symmetric or antisymmetric layered material
when the information of layers of one side of the midplane is supplied. Choose
which side to mirror in from the Mirror in list: Upside (the default) or Downside.
Upside means that the symmetry layers are on the top of the original layers. The
symmetry line is the top-side boundary. Downside means that the symmetry layers
are on the bottom of the original layers. The symmetry line is the bottom-side
boundary. Select the Merge middle layers check box to merge the two middle layers
into one to create an odd symmetric layer.
• Repeated, to create a number of repeating stacks, which you enter in the Number of
repeats field (default: 1).
Select the Scale check box to scale the layered material’s thickness with a factor
(default: 1).The scale can be a numerical value, a parameter, or an expression. Such an

expression can, for example, be a function of the coordinates so that a surface with
variable thickness can be described.
If a single layer in a laminate has a variable thickness, you can define that
layer in either a separate Layered Material or in a Single Layer Material.
• When using a Layered Material, apply the scaling expression in a Layered

Material Link, and then use a Layered Material Stack to build the
complete laminate.
• When using a Single Layer Material with an expression for the thickness,
use a Layered Material Stack to build the complete laminate.
If you have defined a layer with a scaling factor, it appears in the preview window with
a darker color than a nonscaled layer.
The preview is not shown in the base geometry space, so it will not show
any geometrical dependency.
The labels of the newly created layers include a suffix to distinguish them from the
original layers:
• (sym) for the symmetric layers.

• (asym) for the antisymmetric layers.
• (repX) for the repeated layers (number X).
Click the Layer Cross Section Preview button ( to plot a preview of the layer cross
section including the transformation (see the following plot for an example).
Figure 2-9: A repeat laminated stacks with 2 times repeated layers.
Click the Layer Stack Preview button ( ) to get a preview of the stack with the
transformation.

Select a Coordinate system defining the principal directions of the laminate. The
orientation of each layer, given in the Layered Material node, is a rotation from the first
coordinate axis of this coordinate system. Only Boundary System coordinate systems
can be selected.
Choose a Position — Midplane on boundary, Down side on boundary, Up side on boundary,

or User defined. This controls the possible offset of the layered material from the
geometrical boundary on which the mesh exists (the reference surface). For User
defined, enter a value for the Relative midplane offset. The value 1 corresponds to Down
side on boundary, and the value −1 corresponds to Up side on boundary. Values may be
outside the range −1 to 1, in which case the reference surface is outside the laminate.
layered material, including the location of the reference surface (Figure 2-10). The
height of the laminate in the plot is controlled by the value of the Thickness-to-width
ratio specified in the Preview Plot Settings for the selected layered material.

Figure 2-10: Layer cross section preview plot with relative offset set to 0.5.
NONLAYERED MATERIAL SETTINGS

In some cases, a single standard material definition is needed on the same boundary as
a layered material. This can, for example, be the case if two different physics interfaces
are active on the same boundary, but only one of them supports a layered material
definition. You can select any nonlayered material from the Material list. The default
settings is Same as layered material, which means that the nonlayered material
properties are computed as an average value of the layer’s material properties. This
selection is completely analogous to using a Material Link.
You cannot use an ordinary Material or Material Link with the same
selection as the Layered Material Link. These nodes override each other.
selected material.

Click the Add Material from Library button ( ) to add a global material from the
material libraries or a new blank global material. The added material then becomes the
one selected in the Material list.

In this section, you can fine-tune the display in the preview plot.
The value of the Thickness-to-width ratio controls the height in the y direction. The
Deselect the Shows labels in cross-section plot check box to remove the text labels
showing layer names and materials.
MATERIAL CONTENTS
See the documentation for Material Contents for the Material node.
The Value column will usually contain the string Layer, indicating that the actual value
is layer dependent.
APPEARANCE
See the documentation for Appearance for the Material node.
Layered Material Stack

In the Layered Material Stack node ( ), you can compose a new layered material by
stacking other layered materials (including Material nodes that define single-layer
materials) on top of each other. There are three main reasons why you may want to do
this:
• The layup is repetitive, say with the same four layers repeated five times. Rather than
defining twenty layers in a Layered Material node, you define four, and then add this
definition five times in a Layered Material Stack.
• There are layer drop-offs, that is some layers are not present everywhere in the
structure. Then, it is efficient to create only subsets of the laminate in Layered
Material nodes, and use a number of Layered Material Stack nodes to combine them
into different configurations.
• Two Layered Material Stack nodes can have parts of their definitions linked to the
same Layered Material node. When a transition through a continuity feature is used,
the corresponding layers in two laminates defined as stacks can be connected
automatically.

The Layered Material Stack node is located in the Layers submenu under a Materials
node. To compose the stack, you add subnodes to the Layered Material Stack. These
subnodes can be either a Layered Material or a Layered Material Link (Subnode). You
can add any number of subnodes, and mix the two types. The order of the subnodes
determines the ordering of the layers in the final laminate.
The interface between the two Layered Material Stack nodes takes the
interface material from the first Layered Material Stack node and ignores
the interface material of the second Layered Material Stack node.
LAYERED MATERIAL SETTINGS

• None (the default), for no transformation.

Select the Scale check box to scale the layered material’s thickness with a factor (default:
1). If you have defined a layer with a scaling factor, it appears in the preview window
with a darker color than a nonscaled layer.
original layers:


section including the transformation. Click the Layer Stack Preview button ( ) to get
a preview of the stack with the transformation.
A combination of transformations can be made by defining the

transformations for both the Layered Material Stack node and a Layered
Material Link subnode.

Select a Coordinate system defining the principal directions of the laminate. The
orientation of each layer, given in the Layered Material node, is a rotation from the first
coordinate axis of this coordinate system. Only Boundary System coordinate systems
can be selected.
Choose a Position — Midplane on boundary, Down side on boundary, Up side on boundary,

or User defined. This controls the possible offset of the layered material from the
geometrical boundary on which the mesh exists (the reference surface). For User
defined, enter a value for the Relative midplane offset. The value 1 corresponds to Down
side on boundary, and the value −1 corresponds to Up side on boundary. Values may be
outside the range −1 to 1, in which case the reference surface is outside the laminate.
stacked layered material, including the location of the reference surface. In
Figure 2-11, a laminate composed of three stacked layered materials, each consisting
of three layers is shown. Note that there is a slight indentation, used for emphasizing
the transition from one part of the stack to the next.

Figure 2-11: Layer cross section preview plot with relative offset set to Down side on
boundary.
NONLAYERED MATERIAL SETTINGS

In some cases, a single standard material definition is needed on the same boundary as
a layered material. This can for example be the case if two different physics interfaces
are active on the same boundary, but only one of them supports a layered material
definition. You can select any nonlayered material from the Material list. The default
settings is Same as layered material, which means that the nonlayered material
properties are computed as an average value of the layer’s material properties. This
selection is completely analogous to using a Material Link.
You cannot use an ordinary Material or Material Link with the same
selection as the Layered Material Stack. These nodes override each other.
selected material.

Click the Add Material from Library button ( ) to add a global material from the
material libraries or a new blank global material. The added material then becomes the
one selected in the Material list.

In this section, you can fine-tune the display in the preview plot.
The value of the Thickness-to-width ratio controls the height in the y direction. The
Deselect the Shows labels in cross-section plot check box to remove the text labels
showing layer names and materials.
MATERIAL CONTENTS
See the documentation for Material Contents for the Material node.
The Value column will usually contain the string Layer, indicating that the actual value
is layer dependent.
APPEARANCE
See the documentation for Appearance for the Material node.
Layered Material Link (Subnode)

The Layered Material Link subnode ( ) is used for referencing a Layered Material
from a Layered Material Stack node. You can add any number of Layered Material Link
subnodes under a Layered Material Stack node.
LINK SETTINGS
Select a layered material from the Material list.
By clicking the Go to Material ( ) button you can jump to the settings for the selected
material.
Click the Add Layered Material button ( ) to add another Layered Material or a Switch.
The added material then becomes the one selected in the Material list.
• None (the default), for no transform.


Select the Scale check box to scale the layered material’s thickness with a factor
(default: 1). The scale can be a numerical value, a parameter, or an expression. Such an
expression can, for example, be a function of the coordinates so that a surface with
variable thickness can be described.

complete laminate.
If you have defined a layer with a scaling factor, it appears in the preview window with
a darker color than a nonscaled layer.
original layers:

section including the transform. Click the Layer Stack Preview button ( ) to get a
preview of the stack with the transform.

Single-Layer Materials
To add a single-layer material, choose Single Layer Material ( ) from the global
Materials node’s context menu or the Layers submenu on the context menu of a
Materials node in a component. Then, a Material node is created with some additional
settings (see The Settings Window for Material) and a Shell property group (see
Geometric Properties (Shell)) with a default thickness of 10−4 m. You can also switch
an Material node into a single-layer material by adding a Shell property group and
define a thickness, and it can also turn into a single-layer material when you specify a
value for the requested thickness in the Material Contents table, which appears when a
layered shell feature requests the material properties from a standard material. The
thickness for a single-layer material can be defined as a numerical value, a parameter,
or an expression. Such an expression can, for example, be a function of the coordinates
so that a surface with variable thickness can be described.

complete laminate.
Single-layer materials provide a quick way to define data for a nonlayered material to
be used in physics feature designed for layered materials. Using a single-layer material
is equivalent to defining a Layered Material with only one layer and then referencing it
through a Layered Material Link. A single-layer material can be linked by a Layered
Material Link, and it can also e a stack member of a Layered Material Stackl or a switch
member of a Switch for Materials.

Material Properties
The materials included in the Material Library are defined by unique material
properties, each available as a function of temperature or another appropriate
argument. Table 2-4 lists most of the material properties in the Material Library.
It is important to check the validity of the material property function

under the conditions that you are interested in investigating. See
Checking the Validity of Properties in the Material Library.
Individual material properties contained in the Material Library are based

on the Material Property Database (MPDB) from JAHM Software, Inc.
Viewing Material Property Information

For all properties contained in the Material Library, you can view applicable literature
references, notes, and reference temperatures in the Material Browser’s Property
reference section.
1 Open the Material Browser.

2 Under Material Library, click to select a material. For example, Nitrogen. The
information about this material displays on the right-hand side of the window.
3 Under Properties in the table, click a Property to see its references in the Property
reference section. See Figure 2-12.
MATERIAL PROPERTIES | 51
Figure 2-12: An example of where you can find the property reference information for a
material. In this example, Density has this information available in the Property reference
section. You can hover over the section and drag to expand it if required.
Functions Default Values in the Material Library

The material property expressions stored in the Material Library contain calls to the
corresponding material property functions using input variables (arguments) as in
Table 2-3. The default variable name can be changed in the property expressions to
match actual variable names in a model. When a material property is used by a physics
feature set to retrieve the property From material this is not necessary. In that case, the
actual variable are retrieved from the Model Inputs section of the same feature and
automatically substituted into the material property expression.
If you, on the other hand, want to access material properties from a material explicitly,
you need to make sure that the function argument variables used in the property
expressions exist and can be evaluated in the model. For example, if the variable T2 is

used for temperature, change the argument of the property functions from T to T2 in
the expressions.
The argument does not have to be a variable defined by the model (such
as dependent variables) — it can also be a user-defined constant or
variable. In general, COMSOL Multiphysics tries to find the best match
for evaluating function arguments when material properties are accessed
explicitly.
TABLE 2-3: DEFAULT FUNCTION ARGUMENTS IN MATERIAL PROPERTY EXPRESSIONS
ARGUMENT DEFAULT VARIABLE UNIT
Temperature T K
Time t h
Effective plastic strain epe -
Number of cycles n -
Norm of H field normH_emnc A/m
Norm of B field normB_emqa T
Available Material Library Material Properties

The following table lists the material properties in the Material Library:
TABLE 2-4: MATERIAL LIBRARY: AVAILABLE MATERIAL PROPERTIES
PROPERTY SHORT NAME ARGUMENT SI UNIT
Coefficient of thermal expansion alpha Temperature 1/K

Creep strength CS Time Pa
Density rho Temperature kg/m3
Dynamic viscosity eta Temperature Pa·s
Electrical conductivity sigma Temperature S/m
Resistivity res Temperature ohm·m
Elongation elong Temperature -
Fatigue E-N curve FEN Number of cycles Pa
Fatigue S-N curve FSN Number of cycles Pa
Heat capacity C Temperature J/(kg·K)
Bulk modulus K Temperature Pa
Shear modulus G Temperature Pa
TABLE 2-4: MATERIAL LIBRARY: AVAILABLE MATERIAL PROPERTIES
PROPERTY SHORT NAME ARGUMENT SI UNIT
Instantaneous coefficient of thermal CTE Temperature 1/K

expansion
Linear expansion dL Temperature -
Molar heat capacity HC Temperature J/(mol·K)
Nonlinear magnetic flux density, norm normB Norm of H field T
Nonlinear magnetic field, norm normH Norm of B field A/m
Normal total emissivity nemiss Temperature -
Poisson’s ratio nu Temperature -
Relative permeability mur Norm of H field -
Stress rupture SR Time Pa
Surface emissivity epsilon Temperature -
Tensile strength Syt Temperature Pa
Thermal conductivity k Temperature W/(m·K)
Thermal diffusivity TD Temperature m2/s
True stress–true strain curve in tension Syfunc Strain Pa
True stress–true strain curve in Syfunccomp Strain Pa
compression
Vapor pressure VP Temperature Pa
Yield strength level Sys Temperature Pa
Young’s modulus E Temperature Pa
Checking the Validity of Properties in the Material Library

The following section lists points to consider about the definition, error estimate, and
conditions for some of the Material Library properties listed in Table 2-4.
The property functions listed below have a literature reference where you
can find more details about the conditions and validity range for that
specific property.

COEFFICIENT OF THERMAL EXPANSION
• The coefficient is defined as (ΔL/L)T/(T − Tref) and in most cases, it is calculated
from the ΔL/L values.
• The error is expected to be in the range of 10–15%, but it might be higher near
room temperature due to the small value of T − Tref.
ELASTIC AND INITIAL SHEAR MODULUS

• The data accuracy is approximately 5–10%.
• For solder alloys the literature reports a wide spread of values. Data from several
sources (when available) are evaluated, and representative values are given; the error
is estimated to be 10–25%.
• For some polymers the flexural modulus is used as the elastic modulus, and it is
typically within 10% of the elastic modulus.
• Typically, values measured with a strain gauge are approximately 10% lower than
those measured with a dynamic technique.
• Values measured by a dynamic technique are preferred over those measured by
strain gauge techniques.
• For cubic materials where the elastic and shear modulus are calculated from the
elastic constants (C11, C12, and C44), the Material Library uses the average of the
Reuss and Voigt equations (see R.F.S. Hearmon, Advances in Physics, vol. 5, 1956,
p. 232).
• For isotropic solids (glasses), it uses methods from L.D. Landau and E.M. Lifshitz,
Theory of Elasticity, Addison-Wesley, New York, 1966.
POISSON'S RATIO AND INITIAL BULK MODULUS

• Calculated from the elastic modulus and the shear modulus using standard
relationships, and in this sense they are self-consistent and accurate.
• Data accuracy is approximately 10–20%. Because these are derived quantities the
error can be significantly higher.
• The curves for these properties often show improbable shapes that are most likely
due to their derived nature and are not believed to be real. If the elastic and shear
modulus were determined in a self-consistent manner, the curves would likely be
much better behaved. However, all of the data are presented “as is” from the
original references and are self-consistent within the Material Library.
THERMAL CONDUCTIVITY
• Can be very sensitive to impurities, heat treatment, and mechanical worked state,
especially at very low temperatures.
• The sensitivity is somewhat decreased above room temperature and decreases as the
amount of alloying increases. Compare 4340-QT (quenched and tempered) and
4340-NT (annealed).
THERMAL DIFFUSIVITY
• For metals this property can be very sensitive to impurities, heat treatment, and
mechanical worked state, especially at very low temperatures.
• This sensitivity is somewhat decreased above room temperature and decreases as the
amount of alloying increases. To see an example of this, compare the data for
elemental (high purity) Fe and Armco iron (commercial purity).
ELECTRIC RESISTIVITY
This property is very sensitive to impurities, heat treatment, and mechanical worked
state, especially at very low temperatures.
ELECTRICAL CONDUCTIVITY
This property is very sensitive to impurities, heat treatment, and mechanical worked
state, especially at very low temperatures.
S U R F A C E E M I S S I V I T Y ( εT)
This property is the measured emissivity over all wavelengths and 2π radians. This is
the emissivity used in the Stefan-Boltzmann law.
N O R M A L T O T A L E M I S S I V I T Y ( εT,n)
• The measured emissivity is over all wavelengths at a direction normal to the surface.
This is the most commonly reported value.
• For polished metal, this assumption is valid: εT/εT,n = 1.15–1.20.
• Both emissivities are sensitive to the surface condition (roughness and oxide
thickness).
D E N S I T Y ( ρ)
• The density for solids is calculated from the room-temperature density and the
linear expansion coefficient and is given by ρ/(1 + ΔL/L)3.
• The data for oxides, carbides, and nitrides depend on the material’s porosity.
• For gases the ideal gas law is used.

TENSILE STRENGTH, YIELD STRENGTH LEVEL, AND ELONGATION
Most of the data for tensile strength, yield strength level, and elongation
is from supplier product brochures. When using this data, remember it is
only representative of the actual material properties.
• The variation with temperature is usually not smooth. Many of these materials are
precipitation hardening alloys, and the temperature affects the aging processes in
different ways at different temperatures.
• Unless otherwise stated, the data are for “short” times at the indicated temperatures
and not for the equilibrium structure.
• These properties are very sensitive to the details of the processing and heat
treatments. Comparison of data from different suppliers indicate that the spread in
the published values is approximately 20% for materials with similar processing. The
spread in the elongation data can be as high as 50–100%.
FATIGUE S-N CURVE

• Fatigue data is given as the maximum stress, σmax, as function of the number of
cycles. The stress amplitude, maximum stress, and minimum stress are related
through the stress ratio, R.
( σ max – σ min ) σ max
σ a = ------------------------------------ R = -------------
2 σ min
• The maximum stress, σmax, is given together with the stress ratio for all fatigue data.
Then calculate the stress amplitude as:
σ max  1 – ----
1
 R
σ a = --------------------------------
2
CREEP STRENGTH AND STRESS-RUPTURE CURVES

This property is very sensitive to the test atmosphere as well as the microstructure and
heat treatment of the material.
POLYMERS AND POLYMER-BASED COMPOSITES

Properties of polymers and polymer-based composites are sensitive to moisture and
processing conditions, and they can show time-dependence at higher temperatures.
The errors/uncertainties can be large compared to those of other materials. Keep these
aspects in mind when using the properties of these materials.
GENERAL
The magnitude of the errors reported by authors for a given property is usually smaller
by a factor of 2–3 than the error between different sources for the same data. This is
especially true for materials such as ceramics.

Other Material Properties Reference
In addition to the specific properties included with the Material Library, the other
material databases also contain predefined variables for various material properties that
can be used when creating a model.
The material properties for the predefined materials are accessible from most physics
interfaces. Using this information, either create a material property group or define a
completely new material.
In the Basic>Property Group window, you can add Output Properties under the
Quantities subsection. You can also add Model Inputs to, for example, create a
temperature-dependent material property.
About Model Inputs

Model inputs is a special type of parameter in physics features or physics properties
where you can choose from a list of announced variables (typically field quantities such
as temperature, concentration, or electric field, where vector fields have three
components). Model inputs can also be used as an input to a Property Group under a
material to represent, for example, a temperature-dependent material property. If the
property group specifies that it supports one or more model inputs, any physics feature
that uses the group’s material will display those model input lists in the Model Inputs
section of the physics node’s Settings window. Any physical quantity in COMSOL
Multiphysics can be used as a model input.
Model inputs are always available as default model inputs. See Default Model Inputs
in the COMSOL Multiphysics Reference Manual.
OTHER MATERIAL PROPERTIES REFERENCE | 59

All physical quantities that can act as model inputs declare and define common
variables that are always available (for example, minput.T for the temperature T).
To define the absolute pressure for heat transfer, see the settings for the
Fluid node in the COMSOL Multiphysics Reference Manual.
To define the absolute pressure for a Fluid Flow interface, see the settings
for the Fluid Properties node (described for the Laminar Flow interface
in the COMSOL Multiphysics Reference Manual).
If you have a license for a Nonisothermal Flow interface, see that

documentation for further information.
Model Inputs and Multiphysics Couplings in the COMSOL Multiphysics

Reference Manual
About the Output Material Properties
Some of these material groups are only used by physics interfaces in the
add-on modules and detailed information is in the applicable
documentation.
This section describes all available property groups and the material properties that
they contain. These material properties can be added to models from two Settings
windows: the Material node’s window and its subnodes’ Property Group windows.
The Basic group contains over 25 basic properties for use with all materials.
Materials in the COMSOL Multiphysics Reference Manual

BASIC MATERIAL PROPERTIES
These common material properties belong to the Basic property group.
• When this information is accessed from the Basic>Property Group window, it is listed
under Quantities>Output Properties and Variable is listed in the table.
• When this information is accessed from the Material window, it is listed under
Material Properties>Basic Properties and Name is listed in the table under
Material Contents.
TABLE 2-5: BASIC MATERIAL PROPERTIES
PROPERTY NAME/VARIABLE SI UNIT
Absorption Coefficient kappaR 1/m

Activation Energy dE J/mol
Bulk Viscosity muB Pa·s
Characteristic Acoustic Impedance Z Pa·s/m
Coefficient of Hygroscopic Swelling beta_h_iso, beta_hii m3/kg
Coefficient of Thermal Expansion alpha 1/K
Compressibility of Fluid chif 1/Pa
Density rho kg/m3
Diffusion Coefficient D m2/s
Dynamic Viscosity mu Pa·s
Electrical Conductivity sigma S/m
Electron Mobility mue m2/(Vs)
Extinction Coefficient betaR 1/m
Frequency Factor A 1/s
Heat Capacity at Constant Pressure Cp J/(kg·K)
Isotropic Structural Loss Factor eta s 1
Mass Flux Mf kg/(m2·s)
Mean Molar Mass Mn kg/mol
Permeability kappa m2
Poisson’s Ratio nu 1
Porosity epsilon 1
Ratio of Specific Heats gamma 1
Relative Permeability mur 1
Relative Permittivity epsilonr 1

TABLE 2-5: BASIC MATERIAL PROPERTIES
PROPERTY NAME/VARIABLE SI UNIT
Resistivity res Ω·m

Scattering Coefficient sigmaS 1/m
Seebeck Coefficient S V/K
Shifted Magnetic Field shiftedH A/m
Speed of Sound cp m/s
Storage S 1/Pa
Surface Emissivity epsilon rad 1
Thermal Conductivity k W/(m·K)
Thermal Conductivity Supplement b 1
Vapor Permeability delta_p s
Vapor Resistance Factor mu_vrf 1
Water Content w_c kg/m3
Young’s Modulus E Pa
The coefficient of thermal expansion (CTE) and the resistivity

temperature coefficient have the SI unit 1/K. COMSOL Multiphysics
translates this into the Fahrenheit temperature unit using an offset. This
translation means that you do not get the expected results.
Use caution when a model uses the coefficient of thermal expansion or the
resistivity temperature coefficient and the unit system’s temperature is not
kelvin.

The rest of the material properties are grouped by application area:
• Acoustics Material Properties • Piezoresistive Models

• Electrochemistry Material • Semiconductors Material Properties
Properties • Solid Mechanics Material Properties
• Electromagnetic Models • Solid Mechanics Material Properties:
• Equilibrium Discharge Nonlinear Structural Materials
• Gas Models Module
• Geometric Properties (Shell) • Solid Mechanics Material Properties:

Fatigue Module
• Magnetostrictive Models
• Solid Mechanics Material Properties:
• Piezoelectric Models
Geomechanics Material Model
Acoustics Material Properties

Under Acoustics, you find the following acoustic material models with their associated
material properties: a Poroacoustics Model, a Thermoviscous Acoustics Model, and a
Viscous Model.
These material property groups (including their associated physical properties) can be
added to models from the Material window. These property groups are used by the
Acoustics Module.
TABLE 2-6: ACOUSTICS MATERIALS
PROPERTY GROUP AND PROPERTY NAME/VARIABLE SI UNIT
NONLINEAR MODEL
Parameter of nonlinearity BA 1
POROACOUSTICS MODEL
Flow resistivity Rf Pa·s/m2

Thermal characteristic length Lth m
Viscous characteristic length Lv m
Tortuosity factor tau 1
THERMOVISCOUS ACOUSTICS MODEL
Bulk viscosity muB Pa·s

Density rho kg/m3
Dynamic viscosity mu Pa·s

TABLE 2-6: ACOUSTICS MATERIALS
Heat capacity at constant pressure Cp J/(kg·K)

Thermal conductivity k W/(m·K)
VISCOUS MODEL
Bulk viscosity muB Pa·s
Electrochemistry Material Properties

These material property groups for electrochemistry (including their associated
physical properties) can be added to models from the Material window. These property
groups are used by the Batteries & Fuel Cells Module, Corrosion Module,
Electrochemistry Module, and Electrodeposition Module.
TABLE 2-7: ELECTROCHEMISTRY MATERIALS
EQUILIBRIUM POTENTIAL
Equilibrium potential Eeq V

Reference concentration cEeqref mol/m3
Temperature derivative of dEeqdT V/K
equilibrium potential
ELECTROLYTE CONDUCTIVITY
Electrolyte conductivity sigmal S/m

ELECTROLYTE SALT CONCENTRATION
Electrolyte salt concentration cElsalt mol/m3

LINEARIZED RESISTIVITY This material node defines the electric resistivity
(and conductivity) as a linear function of
temperature.
Reference resistivity rho0 Ω·m
Reference temperature Tref K
Resistivity temperature coefficient alpha 1/K
OPERATIONAL ELECTRODE
STATE-OF-CHARGE
Maximum electrode socmax 1

state-of-charge
Minimum electrode socmin 1
state-of-charge

TABLE 2-7: ELECTROCHEMISTRY MATERIALS
SPECIES PROPERTIES
Transport number transNum 1
Electromagnetic Models
These material property groups for various electromagnetic material models (including
their associated physical properties) can be added to models from the Material window.
These property groups are used by the AC/DC Module, RF Module, and Wave Optics
Module.
TABLE 2-8: ELECTROMAGNETIC MODELS MATERIALS
B-H CURVE This material node is only available with the

AC/DC Module.
Local Properties normH -
Magnetic flux density norm normB T
DIELECTRIC LOSSES
Dielectric loss factor eta_epsilon -

Relative permittivity (imaginary part) epsilonBis 1
Relative permittivity (real part) epsilonPrim 1
E-J CHARACTERISTIC This material node is only available with the
AC/DC Module.
Electric field norm normE V/M
Local Properties normJ -
EFFECTIVE B-H CURVE This material node is only available with the
AC/DC Module.
Local Properties normHeff -
Magnetic flux density norm normBeff T
EFFECTIVE H-B CURVE This material node is only available with the
AC/DC Module.
Local Properties normBeff -
Magnetic field norm normHeff A/m
H-B CURVE This material node is only available with the
AC/DC Module.
Local Properties normB -

Magnetic field norm normH A/m

JILES-ATHERTON MODEL PARAMETERS This material node is only available with the
AC/DC Module.
Maximum magnetization parameter MsJA (3x3 matrix) A/m
Langevin slope parameter aJA (3x3 matrix) A/m
Pinning parameter kJA (3x3 matrix) A/m
Reversibility parameter cJA (3x3 matrix) 1
Interdomain coupling parameter alphaJA (3x3 matrix) 1
LINEARIZED RESISTIVITY This material node defines the electric
resistivity (and conductivity) as a linear
function of temperature.
Reference resistivity rho0 Ω·m
Reference temperature Tref K
Resistivity temperature coefficient alpha 1/K
LOSS TANGENT, LOSS ANGLE This material node assumes zero
conductivity.
Loss tangent, loss angle delta rad
LOSS TANGENT, DISSIPATION FACTOR This material node assumes zero
conductivity.
Loss tangent, dissipation factor tanDelta 1
MAGNETIC LOSSES
Relative permeability (imaginary part) murBis -

Relative permeability (real part) murPrim -
REFRACTIVE INDEX This material node assumes a relative
permeability of unity and zero conductivity.
This material node is only available with the
RF Module or the Wave Optics Module.
Refractive index, imaginary part ki -
Refractive index n 1
REMANENT FLUX DENSITY This material node is only available with the
AC/DC Module.

Recoil permeability murec 1

Remanent flux density norm normBr T
Equilibrium Discharge
These material property groups for all the material models in the Equilibrium
Discharge (including their associated physical properties) can be added to models from
the Material window. These property groups are used by the Plasma Module.
TABLE 2-9: EQUILIBRIUM DISCHARGE MATERIALS
RADIATION HEAT TRANSFER
Total volumetric emission Qrad W/m3

coefficient
Gas Models
This material property group for an ideal gas (including its associated physical
properties) can be added to models from the Material page.
TABLE 2-10: GAS MODELS MATERIALS
IDEAL GAS
Heat capacity at constant pressure Cp J/(kg·K)

Mean molar mass Mn kg/mol
Ratio of specific heats gamma 1
Specific gas constant Rs J/(kg·K)
Geometric Properties (Shell)

The Shell material property group is used in connection with layered materials (it is, for
example, added when you add a Material node by choosing Single Layer Material
from the Layers submenu on the Materials node’s context menu. This property group

contains geometric properties for the definition of a layer in the Layer Definition
section.
TABLE 2-11: SHELL PROPERTIES
SHELL
Thickness lth m
Rotation lrot rad/mol
Mesh elements lne 1
Magnetostrictive Models
These material property groups for various magnetostrictive material models
(including their associated physical properties) can be added to models from the
Material window. These property groups are used by the AC/DC Module.
TABLE 2-12: MAGNETOSTRICTIVE MODELS MATERIALS
MAGNETOSTRICTIVE
Saturation magnetization Ms A/m

Initial magnetic susceptibility chi 1
Saturation magnetostriction lambdas 1
Magnetostriction constants lambda100 1
Magnetostriction constants lambda111 1
STRAIN-MAGNETIZATION FORM This material node is only available with the
AC/DC Module.
Compliance matrix sH (6x6 matrix) 1/Pa
Loss factor for compliance matrix sH eta_sH (6x6 matrix) 1
Piezomagnetic coupling matrix dHT (3x6 matrix) m/A
Relative permeability murT (3x3 matrix) 1
STRESS-MAGNETIZATION FORM This material node is only available with the
AC/DC Module.
Elasticity matrix cH (6x6 matrix) Pa
Loss factor for elasticity matrix cH eta_cH (6x6 matrix) 1
Piezomagnetic coupling matrix eHS (3x6 matrix) T
Relative permeability murS (3x3 matrix) 1

Piezoelectric Models
These material property groups for piezoelectric materials (including their associated
groups are used by the Acoustics Module, MEMS Module, or Structural Mechanics
Module.
TABLE 2-13: PIEZOELECTRIC MATERIALS
STRAIN-CHARGE FORM
Compliance matrix sE 1/Pa

Coupling matrix dET C/N
Loss factor for compliance sE 1
matrix
Loss factor for coupling matrix d 1
Loss factor for electrical εT 1
permittivity
Relative permittivity epsilonrT 1
STRESS-CHARGE FORM
Coupling matrix eES C/m2

Elasticity matrix cE Pa
Loss factor for elasticity matrix cE 1
Loss factor for coupling matrix e 1
Loss factor for electrical εS 1
permittivity
Relative permittivity epsilonrS 1
Piezoresistive Models
These material property groups for piezoresistive materials (including their associated
groups are used by the MEMS Module.
ELASTORESISTANCE FORM
Elastoresistive coupling matrix ml Ω·m

PIEZORESISTANCE FORM
Piezoresistive coupling matrix Pil A/m2
Semiconductors Material Properties

These material property groups for all the material models in semiconductors
(including their associated physical properties) can be added to models from the
Material window. These property groups are used by the Semiconductor Module.
The Property Group, Variable Names, and SI Unit columns are applicable
to all materials in the Semiconductor Module. However, the Values and
References columns listed in Table 2-15 are specifically for silicon in the
COMSOL Multiphysics Reference Manual.
TABLE 2-15: SEMICONDUCTOR MATERIAL PROPERTIES (ALL MATERIALS) AND VALUES AND REFERENCES FOR
SILICON
PROPERTY GROUP AND NAME/VARIABLE (ALL SI UNIT VALUE FOR REFERENCE

PROPERTY (ALL MATERIALS) SILICON FOR
MATERIALS) SILICON
BASIC
Relative permittivity epsilonr 1 11.7 Ref. 1

Thermal k W/(m·K) 131 W/(m·K) Ref. 1
conductivity
Density rho kg/m3 2329 kg/m3 Ref. 1
Heat capacity at Cp J/(kg·K) 700 J/(kg·K) Ref. 1
constant pressure
BAND-GAP NARROWING MODELS>JAIN-ROULSTON MODEL
Jain-Roulston An_jr V 3.5·10-8 V Ref. 12

coefficient (n-type),
A
Jain-Roulston Bn_jr V 0V Ref. 12
B
Jain-Roulston Cn_jr V 0V Ref. 12
C

SILICON

MATERIALS) SILICON
Jain-Roulston Ap_jr V 3.5·10-8 V Ref. 12

coefficient (p-type),
A
Jain-Roulston Bp_jr V 0V Ref. 12
B
Jain-Roulston Cp_jr V 0V Ref. 12
C
Band-gap narrowing Nref_jr 1/m3 1 1/cm3 Ref. 12
reference
concentration
Conduction band alpha_jr 1 0.5 Ref. 12
fraction
BAND-GAP NARROWING MODELS>SLOTBOOM MODEL
Band-gap narrowing Eref_sb V 0.00692 V Ref. 11

reference energy
Band-gap narrowing Nref_sb 1/m3 1.3·1017 1/ Ref. 11
reference cm3
concentration
Conduction band alpha_sb 1 0.5 Ref. 11
fraction
GENERATION-RECOMBINATION>AUGER RECOMBINATION
Auger Cn m6/s 2.8·10-31 cm6 Ref. 2

recombination /s
factor, electrons (valid at
300 K)
Auger Cp m6/s 9.9·10-32 cm6 Ref. 2
recombination /s
factor, holes (valid
at 300 K)
GENERATION-RECOMBINATION>DIRECT RECOMBINATION
Direct C m3/s 0 m3/s N/A

recombination factor

SILICON

MATERIALS) SILICON
GENERATION-RECOMBINATION>IMPACT IONIZATION
a factor, electrons, an 1/V 0.426 1/V Ref. 3

impact ionization
a factor, holes, ap 1/V 0.243 1/V Ref. 3
impact ionization
b factor, electrons, bn V/m 4.81·105 V/ Ref. 3
impact ionization cm
b factor, holes, bp V/m 6.53·105 V/ Ref. 3
impact ionization cm
c factor, electrons, cn 1/KValues 3.05·10-4 1/K Ref. 3
impact ionization
c factor, holes, cp 1/K 5.35·10-4 1/K Ref. 3
impact ionization
d factor, electrons, dn 1/K 6.86·10-4 1/K Ref. 3
impact ionization
d factor, holes, dp 1/K 5.67·10-4 1/K Ref. 3
impact ionization
GENERATION-RECOMBINATION>SHOCKLEY-READ-HALL RECOMBINATION
Electron lifetime, taun s 10 μs Ref. 4

SRH
Hole lifetime, SRH taup s 10 μs Ref. 4
MOBILITY MODELS>ARORA MOBILITY MODEL
Electron mobility mun0_ref_arora m2/(V·s) 1252 cm2/ Ref. 5

reference (V·s)
Hole mobility mup0_ref_arora m2/(V·s) 407 cm2/(V·s) Ref. 5
reference
Electron mobility mun_min_ref_arora m2/(V·s) 88 cm2/(V·s) Ref. 5
reference minimum
Hole mobility mup_min_ref_arora m2/(V·s) 53.4 cm2/ Ref. 5
reference minimum (V·s)
Electron reference Nn0_ref_arora 1/m3 1.26·10171/ Ref. 5
impurity cm3
concentration

SILICON

MATERIALS) SILICON
Hole reference Np0_ref_arora 1/m3 2.35·10171/ Ref. 5

impurity cm3
concentration
Alpha coefficient alpha0_arora 1 0.88 Ref. 5
Mobility reference beta1_arora 1 -0.57 Ref. 5
minimum exponent
Mobility reference beta2_arora 1 -2.33 Ref. 5
exponent
Impurity beta3_arora 1 2.4 Ref. 5
concentration
reference exponent
Alpha coefficient beta4_arora m2/(V·s) -0.146 Ref. 5
exponent
Reference Tref_arora K 300 K Ref. 5
temperature
MOBILITY MODELS>CAUGHEY-THOMAS MOBILITY MODEL
Electron alpha alphan0_ct 1 1.11 Ref. 6

coefficient
Electron alpha betan1_ct 1 0.66 Ref. 6
exponent
Electron saturation vn0_ct m/s 1·107 cm/s Ref. 6
velocity
Electron velocity betan2_ct 1 -0.87 Ref. 6
saturation exponent
Hole alpha alphap0_ct 1 1.21 Ref. 6
coefficient
Hole alpha exponent betap1_ct 0.17 Ref. 6
Hole saturation vp0_ct m/s 8.37·106 cm/s Ref. 6
velocity
Hole velocity betap2_ct 1 -0.52 Ref. 6
saturation exponent
Reference Tref_ct K 300 K Ref. 6
temperature

SILICON

MATERIALS) SILICON
MOBILITY MODELS>FLETCHER MOBILITY MODEL
Fletcher mobility F1_fl 1/(cm·V·s) 1.04×1021 1/ Ref. 7

coefficient 1 (cm·V·s)
Fletcher mobility F2_fl 1/m2 7.45×1013 1/ Ref. 7
coefficient 2 cm2
Reference Tref_fl K 300 K Ref. 7
temperature
MOBILITY MODELS>LOMBARDI SURFACE MOBILITY MODEL
Electron delta deltan_ls V/s 5.82 x 1014 Ref. 8

coefficient V/s
Electron mobility mun1_ls m2/(V·s) 4.75 x Ref. 8
reference 107cm2/(V·s)
Electron mobility mun2_ls m2/(V·s) 1.74 x 105 Ref. 8
reference cm2/(V·s)
Electron alpha alphan_ls 1 0.125 Ref. 8
coefficient
Hole delta deltap_ls V/s 2.05 x 1014 V/ Ref. 8
coefficient s
Hole mobility mup1_ls m2/(V·s) 9.93 x 107 Ref. 8
Hole mobility mup2_ls m2/(V·s) 8.84 x 105 Ref. 8
Hole alpha alphap_ls 1 0.0317 Ref. 8
coefficient
Reference Tref_ls K 1K Ref. 8
temperature
Electric field Eref_ls V/m 1 V/cm Ref. 8
reference
Doping Nref_ls 1/m3 1 1/cm3 Ref. 8
concentration
reference
MOBILITY MODELS>POWER LAW MOBILITY MODEL
Electron mobility mun0_pl m2/(V·s) 1448 cm2/ Ref. 5

reference (V·s)

SILICON

MATERIALS) SILICON
Hole mobility mup0_pl m2/(V·s) 473 cm2/(V·s) Ref. 5

reference
Electron exponent alphan_pl 1 2.33 Ref. 5
Hole exponent alphap_pl 1 2.23 Ref. 5
Reference Tref_pl K 300 K Ref. 5
temperature
SEMICONDUCTOR MATERIAL
Band gap Eg0 V 1.12 V Ref. 1

(valid at
300 K)
Effective density of Nc 1/m3 2.8×1019 1/ Ref. 1
states, conduction cm3
band ×(T/300 K)3/2
Effective density of Nv 1/m3 1.04×1019 1/ Ref. 1
states, valence band cm3
×(T/300 K)3/2
Electron affinity chi0 V 4.05 V Ref. 1
2 2
Electron mobility mun m /(V·s) 1450 cm / Ref. 1
(V·s)
Hole mobility mup m2/(V·s) 500 cm2/(V·s) Ref. 1
Solid Mechanics Material Properties

These material property groups for material models in solid mechanics (including their
associated physical properties) can be added to models from the Material window. Most
of these properties are used by the Structural Mechanics Module. The property groups
of the external material are of a special type that depends on the selected interface type
and are not individually documented.
TABLE 2-16: SOLID MECHANICS MATERIALS
LINEAR ELASTIC MATERIAL
ANISOTROPIC
Elasticity matrix D Pa
Loss factor for elasticity matrix D eta_D 1

ANISOTROPIC, VOIGT NOTATION
Elasticity matrix, Voigt notation DV0 Pa

Loss factor for elasticity matrix D, Voigt notation eta_DVo 1
BULK MODULUS AND SHEAR MODULUS
Bulk modulus K N/m2

Shear modulus G N/m2
LAMÉ PARAMETERS
Lamé parameter λ lambLame N/m2

Lamé parameter μ muLame N/m2
ORTHOTROPIC
Young’s modulus Evector Pa

Poisson’s ratio nuvector 1
Shear modulus Gvector N/m2
Loss factor for orthotropic Young’s modulus eta_Evector 1
Loss factor for orthotropic shear modulus eta_Gvector 1
ORTHOTROPIC, VOIGT NOTATION
Shear modulus, Voigt notation GvectorVo N/m2

Loss factor for orthotropic shear modulus, Voigt notation eta_GvectorVo 1
PRESSURE-WAVE AND SHEAR-WAVE SPEEDS
Pressure-wave speed cp m/s

Shear-wave speed cs m/s
YOUNG’S MODULUS AND POISSON'S RATIO
Young’s modulus E Pa
Poisson’s ratio nu 1
YOUNG’S MODULUS AND SHEAR MODULUS
Young’s modulus E Pa
Shear modulus G N/m2
LINEAR VISCOELASTIC MATERIAL
Long-term shear modulus Gv N/m2

Bulk modulus K N/m2
POROELASTIC MATERIAL
Biot-Willis coefficient alphaB 1

Porosity epsilon 1

Permeability kappa m2
SAFETY
ISOTROPIC STRENGTH PARAMETERS
Tensile strength sigmat Pa

Compressive strength sigmac Pa
Biaxial compressive strength sigmabc Pa
ISOTROPIC ULTIMATE STRAINS
Ultimate tensile strain epsilont 1

Ultimate compressive strain epsilonc 1
ORTHOTROPIC STRENGTH PARAMETERS, VOIGT NOTATION
Tensile strengths sigmats Pa

Compressive strengths sigmacs Pa
Shear strengths sigmass Pa
ORTHOTROPIC ULTIMATE STRAINS, VOIGT NOTATION
Ultimate tensile strains epsilonts 1

Ultimate compressive strains epsiloncs 1
Ultimate shear strains gammass 1
ANISOTROPIC STRENGTH PARAMETERS, VOIGT NOTATION
Second rank tensor, Voigt notation F_s 1/Pa

Fourth rank tensor, Voigt notation F_f m2·s4/kg2
• The Structural Mechanics Module User’s Guide and Table 2-19

• The Structural Mechanics Module User’s Guide and Table 2-17
• The Fatigue Module User’s Guide and Table 2-18

Solid Mechanics Material Properties: Nonlinear Structural Materials
Module
These material property groups for material models in solid mechanics using the
Nonlinear Structural Materials Module (including their associated physical properties)
can be added to models from the Material window.
TABLE 2-17: HYPERELASTIC AND ELASTOPLASTIC MATERIAL PROPERTIES
ELASTOPLASTIC MATERIAL
Hardening function sigmagh Pa

Hill’s coefficients Hillcoefficients (m2·s4)/kg2
Initial tensile and shear yield stresses ys N/m2
Initial yield stress sigmags Pa
Isotropic tangent modulus Et Pa
Kinematic tangent modulus Ek Pa
ARMSTRONG-FREDERICK
Kinematic hardening modulus Ck Pa

Kinematic hardening parameter gammak 1
CHABOCHE
Kinematic hardening modulus Ck0_cha Pa

LUDWIK
Strength coefficient k_lud Pa

Hardening exponent n_lud 1
SWIFT
Reference strain e0_swi 1

Hardening exponent n_swi 1
VOCE
Saturation flow stress sigma_voc Pa

Saturation exponent beta_voc 1
HOCKETT-SHERBY
Steady-state flow stress sigma_hoc Pa

Saturation coefficient m_hoc 1
Saturation exponent n_hoc 1
CREEP
NORTON

Creep rate coefficient A_nor 1/s

Reference stress sigRef_nor Pa
Stress exponent n_nor 1
GAROFALO (HYPERBOLIC SINE)
Creep rate coefficient A_gar 1/s

Reference stress sigRef_gar Pa
Stress exponent n_gar 1
NABARRO-HERRING
Volume diffusivity D_nav m2/s

Burgers vector b_nav m
Grain diameter dg_nav m
COBLE
Ionic diffusivity D_cob m2/s

Burgers vector b_cob m
Grain diameter dg_cob m
WEERTMAN
Diffusivity D_wee m2/s

Burgers vector b_wee m
Stress exponent n_wee 1
Reference stress sigRef_wee Pa
VISCOPLASTIC MATERIAL
ANAND
Viscoplastic rate coefficient A_ana 1/s

Activation energy Q_ana J/mol
Multiplier of stress xi_ana 1
Stress sensitivity m_ana 1
Deformation resistance saturation coefficient s0_ana Pa
Deformation resistance initial value sa_init Pa
Hardening constant h0_ana Pa
Hardening sensitivity a_ana 1
Deformation resistance sensitivity n_ana 1
CHABOCHE
Viscoplastic rate coefficient A_cha 1/s

Reference stress sigRef_cha Pa

Stress exponent n_cha 1
PREZYNA
Viscoplastic rate coefficient A_per 1/s

Reference stress sigRef_per Pa
POROPLASTIC MATERIAL
Initial yield stress sigmags Pa

Shima-Oyane alpha parameter alphaShima 1
Shima-Oyane gamma parameter gammaShima 1
Shima-Oyane m parameter mShima 1
Initial void volume fraction f0 1
Critical void volume fraction fc 1
Failure void volume fraction ff 1
Tvergaard correction coefficient q1 q1GTN 1
Maximum void volume fraction fmax 1
NONLINEAR ELASTIC MATERIAL
Reference stress sigRef Pa

Reference strain eRef 1
Stress exponent n_stress 1
Reference shear strain gammaRef 1
Strain exponent n_strain 1
Bulk modulus in tension Kt Pa
Bulk modulus in compression Kc Pa
Ultimate deviatoric stress q_ult Pa
Ultimate strain e_ult 1
ELASTOPLASTIC SOIL MATERIAL
CAM-CLAY
Swelling index kappaSwelling 1

Compression index lambdaComp 1
Void ratio at reference pressure evoidref 1

Slope of critical state line M 1

STRUCTURED CAM-CLAY
Swelling index for structured clay kappaSwellingS 1

Compression index for destructured clay lambdaCompS 1
Void ratio at reference pressure for destructured evoidrefS 1
clay
Destructuring index for volumetric deformation dvS 1
Destructuring index for shear deformation dsS 1
Slope of critical state line M 1
Additional void ratio at initial yielding Deltaei 1
Initial structure strength pbi Pa
Plastic potential shape parameter zetaS 1
Critical effective deviatoric plastic strain epdevc 1
BARCELONA BASIC
Swelling index kappaSwelling 1

Swelling index for changes in suction kappaSwellings 1
Compression index at saturation lambdaComp0 1
Weight parameter wB 1
Soil stiffness parameter mB Pa
Plastic potential smoothing parameter bB 1
Tension to suction ratio kB 1
Void ratio at reference pressure and saturation evoidref0 1
Initial yield value for suction sy0 Pa
HARDENING SOIL
Reference stiffness for primary loading E50Ref Pa

Reference stiffness for unloading and reloading EurRef Pa
Stress exponent mH 1
Bulk modulus in compression Kc Pa
Void ratio at reference pressure evoidref 1
HYPERELASTIC MATERIALS
ARRUDA-BOYCE
Macroscopic shear modulus mu0 N/m2

Number of segments Nseg 1

BLATZ-KO
Model parameters phiBK 1

Model parameters betaBK 1
Shear modulus muBK Pa
GAO
Model parameters aG Pa
Model parameters nG 1
GENT
Macroscopic shear modulus muG Pa

Model parameters jmG 1
MOONEY-RIVLIN
Model parameters C01, C02, C03, Pa

C10, C11, C12,
C20, C21, C30
MURNAGHAN The Murnaghan node adds five
model parameters. The model is
based on strain invariants and is
typically used in acoustoelasticity.
Murnaghan third-order elastic moduli l Pa
Murnaghan third-order elastic moduli m Pa
Murnaghan third-order elastic moduli n Pa
Lamé parameter λ lambLame Pa
Lamé parameter μ muLame Pa
VARGA
Model parameters c1VA Pa

Model parameters c2VA Pa
YEOH
Model parameters c1YE Pa


Solid Mechanics Material Properties: Fatigue Module
These material property groups for material models in solid mechanics using the
Fatigue Module (including their associated physical properties) can be added to
models from the Material window.
TABLE 2-18: ELASTOPLASTIC AND FATIGUE BEHAVIOR MATERIAL PROPERTIES
ELASTOPLASTIC MATERIAL>RAMBERG-OSGOOD
Cyclic hardening coefficient K_ROcyclic Pa

Cyclic hardening coefficient n_ROcyclic 1
FATIGUE BEHAVIOR>ENERGY-BASED
DARVEAUX
Crack initiation energy coefficient K1_Darveaux 1

Crack initiation energy exponent k2_Darveaux 1
Crack propagation energy K3_Darveaux m
coefficient
Crack propagation energy k4_Darveaux 1
exponent
Reference energy density Wref_Darveaux J/m3
MORROW
Fatigue energy coefficient Wf_Morrow J/m3

Fatigue energy exponent m_Morrow 1
FATIGUE BEHAVIOR>FATIGUE BEHAVIOR>APPROXIMATE S-N CURVE
Transition stress sigmat Pa

Transition life Nt 1
Endurance life Ne 1
FATIGUE BEHAVIOR>GENERAL
Endurance limit sigmae Pa

FATIGUE BEHAVIOR>STRAIN-BASED
COFFIN-MANSON
Fatigue ductility coefficient epsilonf_CM 1

Fatigue ductility exponent c_CM 1
Shear fatigue ductility coefficient gammaf_CM 1
Shear fatigue ductility exponent cgamma_CM 1
FATEMI-SOCIE

TABLE 2-18: ELASTOPLASTIC AND FATIGUE BEHAVIOR MATERIAL PROPERTIES
Normal stress sensitivity k_FS 1

coefficient
WANG-BROWN
Normal stress sensitivity S_WB 1

coefficient
FATIGUE BEHAVIOR>STRESS-BASED
BASQUIN
Fatigue strength coefficient sigmaf_Basquin Pa

Fatigue strength exponent b_Basquin 1
Shear fatigue strength coefficient tauf_Basquin Pa
Shear fatigue strength exponent bgamma_Basquin 1
FINDLEY
Normal stress sensitivity k_Findley 1

coefficient
Limit factor f_Findley Pa
MATAKE
Normal stress sensitivity k_Matake 1

coefficient
Limit factor f_Matake Pa
NORMAL STRESS
Limit factor f_NormalStress Pa

DANG VAN
Hydrostatic stress sensitivity a_DangVan 1

coefficient
Limit factor b_DangVan Pa
Solid Mechanics Material Properties: Geomechanics Material Model

These material property groups for material models in solid mechanics (including their
associated physical properties) can be added to models from the Material window.
These property groups are used by the Geomechanics Module.
TABLE 2-19: GEOMECHANICS MODELS MATERIALS
DRUCKER-PRAGER
Drucker-Prager alpha coefficient alphaDrucker 1

TABLE 2-19: GEOMECHANICS MODELS MATERIALS
Drucker-Prager k coefficient kDrucker Pa

HOEK BROWN
Hoek-Brown m parameter mHB 1

Hoek-Brown s parameter sHB 1
Geological strength index GSI 1
Disturbance factor Dfactor 1
Intact rock parameter miHB 1
LADE-DUNCAN
Lade-Duncan k coefficient kLade 1

MATSUOKA-NAKAI
Matsuoka-Nakai mu coefficient muMatsuoka 1

MOHR-COULOMB
Cohesion cohesion Pa
Angle of internal friction internalphi rad
OTTOSEN
Ottosen a parameter aOttosen 1

Ottosen b parameter bOttosen 1
Size factor k1Ottosen 1
Shape factor k2Ottosen 1
YIELD STRESS PARAMETERS
Uniaxial tensile strength sigmaut Pa

Uniaxial compressive strength sigmauc Pa
Biaxial compressive strength sigmabc Pa
Thermal Expansion Material Properties

This material property group for thermal expansion properties can be added to models
from the Material page.
TABLE 2-20: THERMAL EXPANSION MATERIAL PROPERTIES
IDEAL GAS
Isotropic tangent coefficient of thermal alphatanIso 1/K

expansion
Isotropic thermal strain dLIso 1

TABLE 2-20: THERMAL EXPANSION MATERIAL PROPERTIES
Tangent coefficient of thermal expansion alphatan_iso; alphatanij 1/K

Thermal strain dLi_iso, dLij 1
External Material Properties

The property groups of the external materials are of a special type that depends on the
selected interface type and are not individually documented. You can incorporate as
many parameters in the call to the external DLL when you add an external material,
these parameters will appear in the Material node as material inputs, see Working with
External Materials for more information.

Using Functions
The Material Library describes material properties with functions, usually functions of
temperature, and for this purpose it uses piecewise analytic functions (polynomials).
For user-defined property functions, three types of functions can be defined: analytic
functions, piecewise analytic functions, and interpolation functions.
Functions are useful for describing material properties as, for example, functions of
temperature or pressure.
Adding a Function to the Material

Material functions are either automatically added to the Model Builder sequence
(usually with materials from the material library) or functions can be added based on
individual requirements.
1 Add a material to the Component node (see The Material Browser Window and The
Add Material Window).
2 Add an Analytic ( ), Interpolation ( ), or Piecewise ( ) function.
To add an Analytic ( ), Interpolation ( ), or Piecewise ( ) function:
• On the Materials toolbar, click Analytic, Interpolation, or Piecewise.

• Right-click a property group node (for example, Basic) and select a
function from the Functions list.
To add an Analytic ( ), Interpolation ( ), or Piecewise ( ) function:
• Right-click a property group node, for example, Basic and select a

function from the Functions list.
• On the Materials contextual toolbar, click Analytic, Interpolation, or
Piecewise.
USING FUNCTIONS | 87
- Select Analytic to add an analytic function of one or more input arguments.
- Select Interpolation to add an interpolation function that can interpolate from
structured data (defined on a grid) or unstructured data (defined on a generic
point cloud).
- Select Piecewise to add a piecewise function that is useful if a material property has
different definitions on different intervals. The intervals must not overlap, and
there cannot be any holes between intervals.
• Defining an Analytic Function

• Analytic, Interpolation, and Piecewise in the COMSOL Multiphysics
Reference Manual
Once a function is created, you can use it for any property in the same
property group.
Defining an Analytic Function

Assume that you want to define the density ρ1 for a material as a function of pressure
and temperature: ρ1= ρ1(p,T). You can name the function rho1(p,T) and use the
expression p*0.02897/8.314/T to define the function.
1 On the Materials toolbar, click the Browse Materials , Add Material , or Blank
Material button to add a new material to the Component (or use an existing
material where density is not defined, or redefine the current expression for the
density).
2 Add a Density property to the material.
a In the Model Builder, click the Material node.
b In the Settings window for Material, click to expand the Material Properties
section. Under Basic Properties, right-click Density and Add to Material.
A Density property is added to the Basic property group.
3 In the Model Builder, under the material node, right-click Basic and select
Functions>Analytic. This adds an Analytic subnode ( ) under Basic.
4 On the Settings window for Analytic, enter rho1 in Function name. Replace the
default name.

5 Under the Definition section:
a In the Expression field, enter p*0.02897/8.314/T.
b In the Arguments column, enter p,T.
6 Under Units:
a In the Arguments field, enter Pa, K as the units for the pressure and the
temperature, respectively.
b In the Function field, enter kg/m^3 as the unit for the function’s output (density).
The function rho1 can now be used to define the density in your material.
7 Click the Material node. In the Settings window for Material, under Material Contents,
enter rho1(p,T) in the Value column (in the Density row).
Click the Basic node to notice that the Density analytic function is defined in the
Settings window for Property Group under Output Properties. The expression will be
orange if there are no variables p and T for pressure and temperature, respectively,
defined in the component. See Figure 2-13.
USING FUNCTIONS | 89
Figure 2-13: A density property is defined using an analytic function.

I n d e x
A add material (window) 17 creep strength 57
adding
D Dang Van (material node) 84
material properties 30
Darveaux (material node) 83
model inputs 31
density 56
analytic functions, materials and 88
dielectric losses (material node) 65
Anand viscoplasticity (material node) 79
DIN number 13
anisotropic (material node) 75
documentation 7
anisotropic materials
Drucker-Prager (material node) 84
properties 30
anisotropic strength parameters, Voigt E editing
notation (node) 77 material properties 30
anisotropic, Voigt notation (material Effective BH curve (material node) 65
node) 76 E-J characteristic (material node) 65
Application Libraries window 9 elastoplastic material model (material
Armstrong-Frederick (material node) 78 node) 78
Arruda-Boyce (material node) 81 elastoresistance form (material node) 69
Arruda-Boyce (node) 81 electric resistivity 56

electrical conductivity 56
B Barcelona basic (material node) 81
electrode potential (material node) 64
Basquin (material node) 84
electrolyte conductivity (material node)
BH curve (material node) 65
64
Blatz-Ko (material node) 82
electrolyte salt concentration (material
Blinn-Phong lighting model 28
node) 64
bulk modulus 55
elongation 57
bulk modulus (material node) 76
emailing COMSOL 9
C Chaboche (node) 78 emissivity
Chaboche viscoplasticity (material node) normal total 56
79 surface 56
check mark definition, materials 25
F Fatemi-Socie (material node) 84
Coble (material node) 79
fatigue S-N curve 57
coefficient of thermal expansion 55
Findley (material node) 84
for non-SI units 62
functions
Coffin-Manson (material node) 83
adding to materials 87
colors of materials 26
composition 13 G Gao (material node) 82
Cook-Torrance lighting model 28 Garofalo (hyperbolic sine) (material

node) 79
INDEX| 91
Gent (material node) 82 M magnetic losses (material node) 66
geometric scope magnetostrictive (material node) 68
materials, and 22 magnitude of errors 58
Matake (material node) 84
H hardening soil (material node) 81
material (node) 21
HB curve (material node) 65–66
Material Browser (window) 12
Hockett-Sherby (material node) 78
material data, properties 6
Hoek-Brown (material node) 85
material libraries
I ideal gas (material node) 67, 85 reloading 12
input properties 59 material properties
internet resources 7 adding 30
interpolation editing 30
functions, materials and 88 magnitude of errors 58
isotropic strength parameters (node) 77 references for 6, 51
isotropic ultimate strains (node) 77 Material Property Database (MPDB) 6
J JAHM Software, Inc 6 material type 24
materials
K knowledge base, COMSOL 10
geometric scope, and 22
L Lade-Duncan (material node) 85 local properties 31
Lamé parameters (material node) 76 output properties 30, 60
layered material searching 13
node 34 status 25
layered material link materials (node) 20
node 40 Matsuoka-Nakai (material node) 85
layered material stack model inputs
node 44 adding 31
lighting models 27 Mohr-Coulomb (material node) 85
linear viscoelastic material (node) 76 Mooney-Rivlin (material node) 82
linearized resistivity (material node) 64 Morrow (material node) 83
literature references, material proper- MPH-files 9
ties 51 Murnaghan (material node) 82
local
N Nabarro-Herring (material node) 79
properties, materials 31
nonlinear elastic material (material node)
loss tangent, dissipation factor (material
80
node) 66
normal stress (material node) 84
loss tangent, loss angle (material node)
normal total emissivity 56
66
Norton (material node) 78
Ludwik (material node) 78
O operational electrode state-of-charge
92 | I N D E X
(material node) 64 S search materials 6
orthotropic (material node) 76 searching
orthotropic strength parameters, Voigt materials 13
notation (node) 77 shear modulus 55
orthotropic ultimate strains, Voigt nota- shear modulus (material node) 76
tion (node) 77 shear-wave speed (material node) 76
orthotropic, Voigt notation (material single layer materials 50
node) 76 smoothing 6
Ottosen (material node) 85 species properties (material node) 65
output properties, materials 30, 60 specular exponent 28
specular highlight 27
P Perzyna viscoplasticity (material node)
stop sign definition, materials 25
80
strain-charge form (material node) 69
piecewise functions, materials and 88
strain-magnetization form (material
piezoresistance form (material node) 70
node) 68
Poisson’s ratio 55
stress-charge form (material node) 69
Poisson’s ratio (material node) 76
stress-magnetization form (material
polymer-based composites 57
node) 68
polymers 57
stress-rupture curves 57
poroacoustics model (material node) 63
structured Cam-clay (material node) 81
poroelastic material (node) 76
surface emissivity 56
poroplastic material model (material
Swift (material node) 78
node) 80
switch functions 33
pressure-wave speed (material node) 76
switch materials 33
properties, material library 51
property groups 28 T technical support, COMSOL 9
property information 51 tensile strength 57
thermal conductivity 56
R radiation heat transfer (material node)
thermal diffusivity 56
67
thermoacoustics model (material node)
reference temperatures, material prop-
63
erties 51
references U UNS number 13
for material properties 51 user-defined property group 32
references, for material properties 6 V Varga (material node) 82
refractive index (material node) 66 viscous model (material node) 64
reloading material libraries 12 Voce (material node) 78
resistivity temperature coefficient
W Wang-Brown (material node) 84
for non-SI units 62
warning sign definition, materials 25
INDEX| 93
websites, COMSOL 10
Weertman (material node) 79
Y Yeoh (material node) 82

yield strength level 57
yield stress parameters (material node)
85
Young’s modulus (material node) 76
94 | I N D E X

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Material Library

• Support Center: www.comsol.com/support

Part number: CM021201

The Material Library Environment 6

Chapter 2: Using the Material Library

Working with Materials 12

Other Material Properties Reference 59

Welcome to the Material Library, an add-on product that provides predefined

The Material Library is ideal for multiphysics couplings such as electrical-thermal

See Materials in the COMSOL Multiphysics Reference Manual for an

About the Material Library

• The Material Library incorporates mechanical, thermal, and electrical properties

• Working with Materials

Where Do I Access the Documentation and Application Libraries?

If you are reading the documentation as a PDF file on your computer,

THE DOCUMENTATION AND ONLINE HELP

Opening Topic-Based Help

THE MATERIAL LIBRARY ENVIRONMENT | 7

To open the Help window:

• In the Model Builder, Application Builder, or Physics Builder click a node or

To open the Help window:

Opening the Documentation Window

To open the Documentation window:

To open the Documentation window:

The Application Libraries Window in the COMSOL Multiphysics

Opening the Application Libraries Window

• From the Home toolbar, Windows menu, click ( ) Applications

To include the latest versions of model examples, from the File>Help

Select Application Libraries from the main File> or Windows> menus.

CONTACTING COMSOL BY EMAIL

COMSOL ACCESS AND TECHNICAL SUPPORT

THE MATERIAL LIBRARY ENVIRONMENT | 9

COMSOL ONLINE RESOURCES

COMSOL website www.comsol.com

Using the Material Library

• Working with Materials

To open the Material Browser :

• On the Materials toolbar, click Browse Materials.

To open the Material Browser :

• On the Model Toolbar, click Browse Materials.

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Material availability is based on the type of COMSOL Multiphysics

CREATE A NEW MATERIAL LIBRARY OR IMPORT A MATERIAL LIBRARY

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TABLE 2-1: MATERIAL LIBRARY FOLDERS

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Minerals, Rocks, and Soils

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The Add Material Window

To open the Add Material window :

• From the Materials toolbar, click Add Material.

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ADDING MATERIALS TO A COMPONENT

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Using the Add Material Window

Using the Material Browser Window

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ERRORS RELATING TO THE MATERIAL NODES