Evaluation of Stiffness of Aluminum Hexagonal Honeycomb

Core Sandwich Panels by FE Methods

S. Rajkumar

Assistant Professor, Department of Mechanical Engineering, Chettinad College of Engineering

& Technology, Karur – 639114, Tamilnadu, India.

Dr. D. Ravindran

Professor & Head, Department of Mechanical Engineering,National Engineering College,

Kovilpatti-628 503, Tamilnadu, India.

Dr. V. P. Raghupathy

Professor, Department of Mechanical Engineering, P.E.S Institute of Technology,

Bangalore - 560085, Karnataka, India.

and

V. Hariprasath

Assistant Professor, Department of Mechanical Engineering, Chettinad College of Engineering

& Technology, Karur – 639114,Tamilnadu, India.

ABSTRACT

Honey Comb Sandwich Panels (HCSP) are increasingly being used for structural applications.

Obviously these structures are taller, longer, wider, more luxurious, more flamboyant, more

effective and versatile than their counter parts but are also lighter, more economical, more

durable, lower on maintenance, more resistant to fatigue, safer and far more reliable. Today

HCSP application is not only confined to peerless and indubitable structural projects but has

trickled into the world of normal populous. From flooring to wall partitions, window frames to

aesthetic arches, portable bridges to packaging, table tops to writing boards to virtually every

product which demands optimal weight to strength ratio. Today every engineered product

undergoes an analysis before realizing production and with ubiquitous application of HCSP, it’s
imperative that static properties of HCSP are precisely known in order to predict behavior of the

structure. The heterogeneous nature of honeycomb core and complex load transfer paths make it

behave like orthotropic material and prediction of stiffness becomes tedious and difficult. The

elastic properties of the core have to be evaluated first before making the stiffness analysis. In

this paper, the stiffness of Al hexagonal core sandwich panel of different span length is

determined by Finite Element and the same is compared with experimentally obtained results.

Keywords: Honeycomb core, sandwich panel, Stiffness, flexural rigidity, core shear modulus

Biographical notes:

S. Rajkumar, obtained his M.E degree in Engineering Design from Anna University, Chennai,

M.B.A from Alagappa University, M.S.W from Annamalai University, and doing Ph.D as part

time in Anna University, Tiruchirappalli. Presently he is working as Assistant Professor in the

department of mechanical engineering, Chettinad College of Engineering & Technology, karur,

India. His specific interests are Design Engineering and Composite Materials. He is the Life time

Member of Indian Society of Technology Education and International Association of Computer

Science and Information Technology, Singapore Institute of Electronics. He has Published and

Presented more than 8 national and international conferences respectively.

Dr. D.Ravindran, Professor & Head, Department of Mechanical Engineering, National

Engineering College, Kovilpatti, obtained his B.E. from Gulbarga University, M.Tech from

Annamalai University, Ph.D from Manonmanium Sundaranar University. He has 25 years of

teaching experience. He has published over 25 research papers in International and National

journals. He is the Life time Member of ISTE, IE, SME.

Dr. V.P. Raghupathy, Professor, Department of Mechanical Engineering, PES Institute of

Technology, Bangalore obtained his B.Tech, M.Tech and Ph.D from Indian Institute of

Technology, Madras in Metallurgical Engineering. He began his career as a Scientist, Materials

Division at National Aerospace Lab, Bangalore in 1975. After six years he joined Corporate

R&D. Hyderabad, Bharat Heavy Electricals Ltd. in 1980 and moved to Welding Research

Institute, BHEL, Tiruchirappalli till 2001. He took voluntary retirement in 2001. Since then, he

has been in academic institutions serving as a Professor.

He has guided seven Ph. D candidates in the field of welding technology, Fracture Mechanics

and design of light weight structures. He has published over 105 research papers in International

and National journals. He has obtained a number of awards from reputed professional bodies

including American Welding Society Best research paper award (1998), Tamil Nadu state Govt.

award (1995), Indian Inst. of Welding best paper award (1995 & 99), Two Republic day awards

from BHEL and recently Dr GV Memorial award (2011) from Indian Institute of Metals

Chapter, Tiruchirappalli.

V. Hariprasath, Assistant Professor, Department of Mechanical Engineering, Chettinad College

of Engineering & Technology, Karur obtained a Bachelor in Mechanical Engineering from

Malviya National Institute of Technology, Jaipur and Master in Computer Aided Design from

Anna University, Chennai.

1. Introduction

Honeycomb Sandwich structures are widely used in the aerospace, construction, transport,

defense and safety industry due to their high stiffness-to-mass ratio. The design, manufacturing

and applications have been studied by several authors. A typical sandwich construction with

honeycomb core is depicted in Figure 1.

Figure 1: Sandwich Construction

A sandwich construction consists of a lightweight core material covered by face sheets on both

sides. All these three layers are bonded together with the aid of suitable adhesive. Although

these structures have a low weight, they have high flexural stiffness and buckling strength.

Hence, sandwich structures are an essential part of modern lightweight construction. However,

as in the aerospace industry, military interests have speeded up the development and in recent

years larger navy ships with lengths around 50 meters have been built purely in sandwich. In

recent years the idea of fast ships has become very popular with the introduction of many new

and different design concepts. The development seems to be going towards larger and faster
ships increasing the demand for lighter and stronger structures and for a better utilization of the

materials and the structure involved.

Sandwich construction is of particular interest and widely used, because the concept is very

suitable and amenable to the development of lightweight structures with high in-plane flexural

stiffness. Commonly used materials for facings are composite laminates and metals, while cores

are made of metallic and nonmetallic honeycombs, cellular foams, balsa wood and trusses. The

facings carry almost all of the bending and in-plane loads and the core helps to stabilize the

facings and define the flexural stiffness and out-of-plane shear and compressive behavior. As the

facings are intended to provide nearly all of the tension, compression, or bending resistance, they

have relatively high density and are kept at a sufficient distance from the midplane of the

sandwich panel. On the contrary, the core material with low density provides most of the

through-the-thickness shear resistance and stabilizes the skins usually through adhesive bonding.

There are two major choices for the core material, namely, isotropic foam or anisotropic

honeycomb. These types of sandwich structures have now been widely used for load-bearing

purposes in the aerospace, land transport, marine and civil construction industries due to their

lightweight, high specific bending stiffness and strength under distributed loads in addition to

their good energy-absorbing capacity.

For applications in the aerospace industry, meeting the minimum damage tolerance requirement

has a profound effect on the design of sandwich panels. Usually, the layup and thickness of

composite skins as well as the density and thickness of the core need to be tailored in a design

analysis to meet a specific performance requirement.

The overall performance of sandwich structures depends on the material properties of the

constituents (facings, adhesive and core), geometric dimensions and type of loading. Sandwich

beams under general bending, shear, and in-plane loading display various failure modes. Major

damage mechanisms in the composite sandwich panels in bending include core crush, skin–core

debond, core shear failure, skin delamination, and skin fracture. Failure modes and their

initiation can be predicted by conducting a thorough stress analysis and applying appropriate

failure criteria in the critical regions of the beam including three-dimensional effects. This

analysis is difficult because of the nonlinear and inelastic behavior of the constituent materials

and the complex interactions of failure modes. For this reason, properly designed and carefully

conducted experiments are important in elucidating the physical phenomena and helping the

analysis. Thus the understanding of initiation and propagation of these damage mechanisms

therefore imposes a tremendous challenge.

A multitude of damage mechanisms could thus occur at different stages of loading, dependent

on specific combinations of the parameters. Such tailoring could alter the characteristics of the

load transfer between the composite skins and the core and thereby the damage mechanisms.

Especially, once the symmetry of the sandwich panels ceases to exist due to the damage

initiation close to or within the loaded top skin, bending–stretching coupling could also

contribute to the mechanical behavior of the panels. This strongly highlights the need for a

thorough understanding of damage initiation and propagation induced in such sandwich panels,

with particular interest in the establishment of general trends of bending deformation affected by

the design parameters. This kind of experimental effort is essential to guide an effective

development of future analytical engineering or numerical models for facilitating sandwich panel

design. Besides the advantageous of mechanical feature, the outstanding thermal and acoustic
insulation capacities reveal sandwich constructions as ideal candidates of being incorporated into

various aerospace design configurations.

In order to understand the static response of the sandwich panels, it is essential to have an

accurate knowledge of the equivalent core elastic properties. The production process and the

resulting geometry of the honeycomb core create a highly orthotropic material with significantly

different characteristics from that of the isotropic base material. The nine required core material

properties are : the two in-plane Young’s modulus (E x, Ey), the out-of-plane Young’s modulus

(Ez), the in-plane shear modulus (Gxy), the out-of-plane shear modulus (G yz, Gxz) and the three

Poisson ratios (xy, yz , xz) [2]. A host of analytical and experimental approaches are suggested

in the literature to determine the equivalent material properties of honeycomb core by either

considering unit cell of the honeycomb or the entire sandwich structure. Based on the

construction of cellular solids and how the cell walls are restrained for regular hexagonal shape,

Gibson et al have analyzed the linear elastic in-plane and out-of-plane deformation behavior and

derived the nine elastic constants.

Shi et al have derived equivalent transverse shear and in-plane modulus of honeycomb

structures. The derivation is based upon a two scale method for the homogenization of periodic

media. The equivalent two dimensional constitutive equations are evaluated analytically in terms

of their geometry and material properties. The equivalent elastic properties based on the above

approaches have been used to predict stiffness properties of the sandwich panels.

The stiffness of the panels has also been determined by sandwich equation proposed in ASTM C

393 which requires estimation of flexural rigidity and core shear modulus of the panel. Finally,
the stiffness of the panels of different span lengths predicted by FE method and Sandwich

equation have been compared with experimentally determined stiffness values.

2. Details of the honeycomb sandwich Panels

Sandwich panels made of Aluminum hexagonal core with Aluminum face sheets are

commercially available in cell sizes ranging from 6.25 to 25 mm and thickness ranging from 10

to 50 mm. In this work, sandwich panel with 20 mm thickness and core cell size of 12.5 mm

was obtained for joint trials with various configurations. The different geometrical characteristics

of the sandwich panel such as Face thickness, core height, cell size and membrane thickness of

the hexagonal core sheet are indicated in Table 1.

Table 1: Geometrical characteristics of Al / Al honeycomb sandwich panel

Face Core Sandwich Membrane

Cell size
thickness (t) height (c) thickness (d) thickness
(D) mm
mm mm mm (m) mm
0.9 17.8 19.3 12.5 0.065
1.1 17.1 19.4 12.6 0.067
1.0 18.0 19.9 12.4 0.066
1.1 17.9 20.2 12.4 0.064
0.9 17.7 19.7 12.6 0.063
1.0 17.7 19.70 12.5 0.065
(avg.) (avg.) (avg.) (avg.) (avg.)

The chemical composition, density and elastic constants of Al 3003 sheet are indicated in Table

2. The density of the sandwich panel determined as per ASTM C 271 is indicated in Table 3.

The density of the core can also be theoretically computed using the expression as given below:
The density of the sandwich panel can then be computed as per the following equation:

SW = Al (2t/d) + c (c/d) = 303.7 Kg/m3

The density of the sandwich panel computed as above is indicated in Table 3. It can be seen from

Table 3 that the density of sandwich panel theoretically computed compares well with that of

experimentally determined value.

Table 2: Chemical composition and mechanical properties of Al 3003

E Poisson’s Density
Chemical composition in weight %
N/ mm2 ratio, Kg/ m3
Mn - 1.2
Fe - .70
Si - 0.60
69 x 103 0.33 2600
Cu – 0.1
Zr – 0.1
Al - Bal

Table 3: Density of Al Honeycomb core sandwich Panel


Mass 
Spec- Dim.  (av)
Kg Kg / m3
imen mm Kg / m3 Kg / m3
x 10-3 (Theoretical)

50.3x50.4
DEN 1 15.108 298.0
x 20.0
50.1x50.0 300.1 303.7
DEN 2 15.100 301.4
x 20.0
50.2x50.0
DEN 3 15.110 300.9
x 20.0

The mechanical properties of the epoxy resin used for joining the face sheet and the honeycomb

core are given in Table 4.

 Table 4: Mechanical properties of Epoxy resin used for joining face sheet and Al oneycomb core[11]

Property Value Unit

Density 1100 Kg/m3
Tensile strength 77.2 MPa
Tensile modulus 3.3 GPa
Elongation at break 4.2 %
Flexural modulus 3.2 GPa
Flexural strength 122 MPa

3. Elastic properties of honeycomb core

The elastic constants were determined using equations suggested by Li-Juan et al [12]. The

formulae suggested for the orthotropic elastic constants are as under: A value of 0.4 is taken for

the technology coefficient () in the formulae suggested.

3
 4  t 
E x  E y     E . Equation (1)
 3  l 
t 
E x   E . Equation (2)
l 
 3  t  3
G xy    . Equation (3)
 2  l 
E
 
 3  t 
G yz    . Equation (4)
 2  l 
G
 
   t 
G xz    G . Equation (5)
 3  l 
v xy  1; v xz  1; v yz  0.001; . Equation (6)

The nine orthotropic elastic constants determined by ANSYS and analytical equations are given

in Table 5.

Table 5: Elastic constants of Al honeycomb core

Ex Ey Ez Gxy Gyz Gzx

νx νy νz
(MPa) (MPa) (MPa) (MPa) (MPa) (MPa)
0.1 0.1 621 0.017 81 54 0.999 0.001 0.001
4. Determination of stiffness by FE method

The stiffness behavior of Al core HCSP is analyzed for simply supported beams with spans

varying from 300 to 400 mm using FEA (ANSYS) with a 5 layered 20 NODE SOLID 95 model.

Schematic diagram of the panel with 5 layers is indicated in Figure 2. The layer thickness of the

resin is taken as 0.2 mm. Elastic constants of the face-sheets, glue and Al honeycomb core are

appropriately assigned.

The meshed model with boundary conditions with a load of 100 N applied at the center is

indicated in Figure 4 and the resultant displacement of the panel is indicated in Figure 5.

Likewise, the meshed model and the resultant displacement of the panel with a span length of

400 mm are indicated in Figures 6 and 7.

Figure 2: Schematic of Al hexagonal core Figure 3: Macro-section of the hexagonal

Sandwich panel core with resin
 Figure 4: FE modeling of Sandwich beam under
Figure 5: Displacement of the panel
3 point bending with a span of 300 mm

Figure 6: FE modeling of Sandwich beam under

Figure 7: Displacement of the panel
3 Point bending with a span of 400 mm

The stiffness computed is indicated for sandwich panel with span lengths of 300 and 400 mm are

respectively indicated in Table 6. The stiffness values were also experimentally determined

using Digital flexural test system as shown in Figure 8. For each span length, three tests were

carried out and the stiffness computed from load versus central deflection plots are indicated in

Table 6 and 7.

Table 6: Stiffness of sandwich panel (span length: 300 mm) computed by FEA and experimental
method.
 Specimen P/ (N/mm) P/ (N/mm) P/ (N/mm)
Experimental experimental FEA
PMST– 1 313
PMST– 2 300 309 364
PMST - 3 313

Table 7: Stiffness of sandwich panel (span length: 400 mm) computed by FEA and experimental
method.

Specimen P/ (N/mm) P/ (N/mm) P/ (N/mm)

Experimental experimental FEA
PMST – 4 188
PMST – 5 185 188 213
PMST - 6 190

It can be seen from Tables 6 and 7 that the error between stiffness values predicted by ANSYS

and experimental results are within 13 to 17%. This is acceptable considering the complex

nature of the sandwich panel and subtle variations in the geometry modeled and actual

dimensions used in the experiments.

Figure 8: Three point bend test to determine the flexural stiffness

From this investigation, it can be garnered that stiffness of Aluminum sandwich panels of any

shape and size can be predicted with reasonable accuracy which is very vital for structural
applications.

5. Conclusions

Flexural stiffness behavior of Aluminum honeycomb core sandwich panels of 20 mm thickness

and with a core cell size of 12.5 mm has been analyzed using FE tool using ANSYS for two

different span lengths, viz, 300 and 400 mm. Each layer of the sandwich panel was assigned

appropriate elastic constants and a 20 noded solid 95 element was chosen for the analysis. The

result of stiffness obtained from ANSYS is in excellent agreement with experimental flexural

test results. This investigation indicates that flexural behavior of straight hexagonal core

sandwich beams and panels can be predicted with reasonable accuracy. Similar work can be

taken up for curved beams and panels so that design guide lines can be drawn for selection of

sandwich panels for a wide variety of structural applications.

Acknowledgement

The authors thank the Management of Chettinad College of Engineering and Technology, Karur,

National Engineering College, Kovilpatti, and P.E.S. Institute of Technology, Bangalore for the

encouragement.

References

C.W. Schwingsshacki, G.S. Aglietti and P.R. Cunnigham, (2006), “Determination of

Honeycomb Material properties: Existing theories and an alternative dynamic approach”,

Journal of Aerospace Engineering © ASCE, Page 177 – 183

Johnson, A. F. and Sims, G. D. (1986). Mechanical Properties and Design of Sandwich

Materials, Composites, 17(4): 321–328.

Gibson, L. J. (1984). Optimization of Stiffness in Sandwich Beams with Rigid Foam Cores,

Materials Science and Engineering, 67 (2): 125–135.

Olsson, K.A. (2000). Sandwich Structures for Naval Ships: Design and Experience. In:

Rajapakse, Y.D.S. et al. (Ed.), Mechanics of Sandwich Structures, Proceedings of ASME Ad Vol.

62, AMD Vol. 245, Page 1–9.

Stephen R. Swanson and Jongman Kim, (2003) Failure Modes and Optimization of Sandwich

Structures for Load Resistance”, Journal of Composite Materials, Vol. 37, No.7, Page 649 -667

Robson, B.L (1989), Robson B.L, The Royal Australian Inshore Minehunter – Lessons learned,

in Sandwich construction 1, Proceedings of the first International conference on sandwich

Construction, Stockholm, Sweeden, June 1989, EMAS, U.K Page 395 – 423.

Ramesh S. Sharma and V. P. Raghupathy (2009), “Influence of Rigid Inserts on Shear Modulus

and Strength of Sandwich Beams with Polyurethane Foam as Core” , Journal of Reinforced

Plastics and Composites, Vol. 28, No. 24/page 3037 – 3047

Ramesh S Sharma and V.P. Raghupathy (2008), “A holistic approach to the static design of

sandwich beams with foam cores”, Journal of Sandwich Structures and Materials, Vol. 10, Page

429 – 441

G. Shi and P. Tong, (1995)“The derivation of equivalent constitutive equations of honeycomb

structures by a two scale method”, Computational Mechanics, Vol. 15, No. 5, Page 395 – 407

Handbook of Composites by George Lubin (1981)

www.mscsoftware.com, XLA Li-Juan, JIN Xian-fing, Wang Yang-bao, (2001) “The equivalent

analysis of Honeycomb sandwich plates for satellite structure”,