JP2017068463A - Filler-blended rubber model creating method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To easily discretize at least one of a matrix rubber model, a filler model and an interface layer model with small elements.SOLUTION: A computerized method to create a finite element model of filler-blended rubber model containing matrix rubber, a filler arranged in the matrix rubber and at least one interface layer surrounding the filler comprises a step S5 of setting a dilated model obtained by dilating at least one of the matrix rubber model, the filler model and the interface layer model, a step S6 of re-discretizing the dilated model by using a finite number of elements and a step S7 of constricting the elements having constituted the dilated model by constricting the re-discretized dilated model to its original size.SELECTED DRAWING: Figure 3

Description

  The present invention relates to a method for creating a finite element model of a filler compounded rubber comprising a matrix rubber, a filler and an interface layer.

  In recent years, various computer simulations using the finite element method have been performed. In these simulations, a finite element model in which an object to be analyzed is discretized with a finite number of elements that can be handled by a computer is used.

  Simulation using the finite element method is used not only for mechanical structures but also for development of rubber materials and the like (for example, see Patent Document 1 below). In the following Patent Document 1, a matrix rubber model obtained by discretizing a matrix rubber using a finite number of elements, a filler model obtained by discretizing a filler using a finite number of elements, and an interface layer using a finite number of elements. By setting the discretized interface layer model, a finite element model of filler-containing rubber is created.

Japanese Patent No. 5555216

  In the simulation, a physical quantity such as displacement or stress of the finite element model is calculated by deforming the finite element model based on a predetermined condition or the like. Such physical quantities can be calculated more accurately as the size of each element constituting the matrix model, filler model, or interface layer model is smaller.

  In order to set a small element, for example, each element constituting the matrix model, the filler model, or the interface layer model needs to be subdivided using the operator's manual work or meshing software. However, there is a problem that it is difficult to discretize a region where the shape of each model is small with small elements.

  The present invention has been devised in view of the above circumstances, and is a filler-containing rubber capable of easily discretizing at least one of a matrix rubber model, a filler model, or an interface layer model with small elements. Its main purpose is to provide a model creation method.

  The present invention relates to a method for creating a finite element model of a filler-containing rubber using a computer, which includes a matrix rubber, a filler disposed in the matrix rubber, and at least one interface layer surrounding the filler. A step of setting a matrix rubber model in which the matrix rubber is discretized using a finite number of elements, a step of setting a filler model in which the filler is discretized using a finite number of elements, the interface A step of setting an interface layer model in which layers are discretized using a finite number of elements, a step of setting an expansion model obtained by expanding at least one of the matrix rubber model, the filler model, or the interface layer model Re-discretizing the expansion model using a finite number of elements, and re-discretizing the expansion model. By contracting the size, characterized in that it comprises a step of reducing the element that composed the expansion model.

  In the method for creating the filler-containing rubber model according to the present invention, a thermal expansion coefficient is applied to the element of the matrix rubber model set as the expansion model, the element of the filler model, or the element of the interface layer model. The step of setting the expansion model further includes the element of the matrix rubber model in which the coefficient of thermal expansion is defined, the element of the filler model, or the element of the interface layer model. Preferably, the step of expanding based on the thermal expansion coefficient and contracting the expansion model contracts the element of the expansion model based on the thermal expansion coefficient.

  In the method for creating the filler-containing rubber model according to the present invention, it is desirable that only the interface layer model is set as the expansion model.

  The method for creating a filler-containing rubber model of the present invention includes a step of setting an expansion model obtained by expanding at least one of a matrix rubber model, a filler model, or an interface layer model, and using a finite number of elements for the expansion model. And re-discretization. Thereby, since the area | region where the shape of each model is small can be expanded, for example, this invention can be easily discretized using the said element.

  Furthermore, the method for creating a filler-containing rubber model of the present invention includes a step of reducing the elements constituting the expansion model by contracting the re-discretized expansion model to the original size. Thereby, the present invention can easily discretize the matrix rubber model, filler model, or interface layer model set as the expansion model with small elements.

It is a perspective view which shows an example of the computer for performing the production method of this embodiment. It is a fragmentary sectional view of the filler compounded rubber of this embodiment. It is a flowchart which shows an example of the process sequence of the creation method of this embodiment. It is a top view which visualizes and shows the finite element model of filler compounding rubber. It is the elements on larger scale of FIG. It is a top view which shows the filler mixing | blending rubber | gum model which expanded the expansion object model of FIG. (A) is the elements on larger scale of FIG. 6, (b) is a partial top view of the filler compounded rubber model which re-discretized the expansion model of (a). It is a top view which shows the filler compounded rubber model which made the expansion | swelling model of FIG.7 (b) shrink.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
The method for creating a filler-blended rubber model of the present embodiment (hereinafter sometimes simply referred to as “creation method”) is a method for creating a finite element model of a filler-blended rubber using a computer.

  The finite element model is also called a mesh model or the like. Such a finite element model is created using a computer and used for deformation simulation and the like. The finite element model is created according to a two-dimensional or three-dimensional coordinate system. In this embodiment, a finite element model is defined as a two-dimensional model in a two-dimensional coordinate system in the X direction and the Y direction.

  FIG. 1 is a perspective view showing an example of a computer for executing the creation method of the present embodiment. The computer 1 includes a main body 1a, a keyboard 1b, a mouse 1c, and a display device 1d. The main body 1a is provided with, for example, an arithmetic processing unit (CPU), a ROM, a working memory, a storage device such as a magnetic disk, and disk drive devices 1a1 and 1a2. In addition, software (general-purpose meshing software (for example, “ICEM CFD” from ANSYS)) for executing the creation method according to the present embodiment is stored in the storage device in advance.

  FIG. 2 is a partial cross-sectional view of the filler-containing rubber 2 of the present embodiment. The filler-containing rubber 2 includes a matrix rubber 3, a filler 4 disposed in the matrix rubber 3, and at least one interface layer 5 surrounding the filler 4.

  The case where the filler 4 of this embodiment is carbon black is illustrated. In addition, as for the filler 4, a silica and another filler may be individual or may be combined.

  The interface layer 5 exhibits mechanical properties different from the bulk portion of the matrix rubber 3 around the filler 4. It is known that the characteristics of the interface layer 5 have a great influence on the characteristics of the filler-containing rubber 2. The case where the interface layer 5 of the present embodiment is one layer is illustrated, but may be two or more layers (not shown).

  FIG. 3 is a flowchart illustrating an example of a processing procedure of the creation method of the present embodiment. FIG. 4 is a plan view showing a finite element model (hereinafter, simply referred to as “filler compounded rubber model”) 2M of the filler compounded rubber visualized. FIG. 5 is a partially enlarged view of FIG.

  In the creation method of the present embodiment, first, as shown in FIG. 4, a matrix rubber model 3M obtained by modeling the matrix rubber 3 (shown in FIG. 2) is set (step S1). The matrix rubber model 3M has a finite number of elements F (i) (i = 1, 2,...) Shown in FIG. 5 representing the space occupied by the matrix rubber 3 in the filler-containing rubber 2 shown in FIG. It is defined by discretizing using. The space of the matrix rubber 3 can be specified by, for example, performing known image processing on a microscopic image of the actual filler-containing rubber 2.

  As shown in FIG. 5, the element F (i) can be handled by the finite element method. The element F (i) of this embodiment is set as a planar element. As the planar element, for example, a polygonal element such as a quadrilateral element or a triangular element is preferably used. The element F (i) has a node 11 and a side 12 connecting the nodes 11 and 11. In the element F (i), the number of the node 11 and the coordinate value of the node 11 are set. Furthermore, physical quantities such as an elastic modulus and a damping coefficient based on the physical property values of the matrix rubber 3 shown in FIG. 2 are input to each element F (i). These physical quantities are used in a deformation simulation using a filler-containing rubber model 2M described later. Such a matrix rubber model 3M is input to the computer 1.

  Next, in the creation method of this embodiment, as shown in FIG. 4, a filler model 4M that models the filler 4 (shown in FIG. 2) is set (step S2). The filler model 4M uses the finite number of elements G (i) (i = 1, 2,...) Shown in FIG. 5 to occupy the space occupied by the filler 4 in the filler-containing rubber 2 shown in FIG. It is defined by discretization. For specifying the space of the filler 4, the same method as the method of specifying the space of the matrix rubber 3 (shown in FIG. 2) is adopted.

  As shown in FIG. 5, the element G (i) can be handled by the finite element method similarly to the element F (i) of the matrix rubber model 3M, and is set as a planar element. The element G (i) has a node 13 and a side 14 connecting the nodes 13 and 13. In the element G (i), the number of the node 13 and the coordinate value of the node 13 are set. Furthermore, physical quantities such as an elastic modulus and a damping coefficient based on the physical property values of the filler 4 shown in FIG. 2 are input to each element G (i). Such a filler model 4M is input to the computer 1.

  Next, in the creation method of the present embodiment, as shown in FIG. 4, an interface layer model 5M that models the interface layer 5 (shown in FIG. 2) is set (step S3). The interface layer model 5M includes the space occupied by the interface layer 5 in the filler-containing rubber 2 shown in FIG. 2 and the finite number of elements H (i) (i = 1, 2,...) Shown in FIG. It is defined by discretizing using. For specifying the space of the interface layer 5, the same method as the method of specifying the space of the matrix rubber 3 is adopted.

  As shown in FIG. 5, the element H (i) can be handled by the finite element method, like the element F (i) of the matrix rubber model 3M and the element G (i) of the filler model 4M. Set as a planar element. The element H (i) has a node 15 and a side 16 connecting the nodes 15 and 15. In the element H (i), the number of the node 15 and the coordinate value of the node 15 are set. Furthermore, physical quantities such as an elastic modulus and a damping coefficient based on the physical property values of the interface layer 5 shown in FIG. 2 are input to each element H (i). The physical property value of the interface layer 5 is, for example, larger than that of the matrix rubber 3 and smaller than that of the filler 4.

  As shown in FIG. 5, at the boundary between the interface layer model 5M and the matrix rubber model 3M, the nodes 15 and sides 16 of the element H (i) of the interface layer model 5M are elements F (i) of the matrix rubber model 3M. It is set so that it may be shared with the node 11 and the side 12. Further, at the boundary between the interface layer model 5M and the filler model 4M, the node 15 and the side 16 of the element H (i) of the interface layer model 5M are shared with the node 13 and the side 14 of the element G (i) of the filler model 4M. Set to do. Thereby, a filler-containing rubber model 2M in which the matrix rubber model 3M, the filler model 4M, and the interface layer model 5M are integrally connected is set. The filler-containing rubber model 2M is input to the computer 1.

  By the way, in the deformation simulation using the filler-containing rubber model 2M, the computer 1 calculates physical quantities such as displacement and stress of the finite element model based on predetermined conditions. Such physical quantity can be calculated more accurately as the size of the element F (i) of the matrix rubber model 3M, the element G (i) of the filler model 4M, or the element H (i) of the interface layer model 5M is smaller.

  In this embodiment, the expansion model 7M (shown in FIG. 6) obtained by expanding the matrix rubber model 3M, the filler model 4M, or the interface layer model 5M is re-discretized using a finite number of elements, and the re-discretized expansion is performed. By contracting the model 7M to the original size, elements constituting the expansion model 7M are reduced. Thereby, the matrix rubber model 3M, the filler model 4M, or the interface layer model 5M (hereinafter, simply referred to as “expansion target model 9M”) set as the expansion model 7M is discretized with small elements. Can do.

  The expansion model 7M (shown in FIG. 6) is appropriately set from the matrix rubber model 3M, the filler model 4M, or the interface layer model 5M. Only the interface layer model 5M is set as the expansion model 7M (expansion target model 9M) of the present embodiment. As described above, the interface layer 5 shown in FIG. 2 has a great influence on the characteristics of the filler-containing rubber 2. Therefore, when the interface layer model 5M is set as the expansion model 7M, it is useful for accurately calculating a deformation simulation using the filler-containing rubber model 2M (shown in FIG. 4).

  In the creation method of this embodiment, a thermal expansion coefficient is defined for the element of the expansion target model 9M set as the expansion model 7M (shown in FIG. 6) (step S4). In step S4 of the present embodiment, the thermal expansion coefficient is defined only for the element H (i) of the interface layer model 5M shown in FIG.

The coefficient of thermal expansion indicates the rate at which the length and volume of an object expand with increasing temperature. The thermal expansion coefficient defines the area of the element F (i) of the matrix rubber model 3M, the element G (i) of the filler model 4M, or the element H (i) of the interface layer model 5M by the following formula (1). be able to.
V = V ₀ (1 + αt) (1)
Here, each variable and constant are as follows.
V: Area of the element at t ° C. V ₀ : Area of the element at the reference temperature (0 ° C.) α: Thermal expansion coefficient (surface expansion coefficient)
t: Temperature change from the reference temperature (0 ° C)

In the above formula (1), the coefficient of thermal expansion α is set based on the actual coefficient of thermal expansion of the matrix rubber 3, the filler 4 or the interface layer 5 shown in FIG. As shown in FIG. 5, the element F (i) of the matrix rubber model 3M, the element G (i) of the filler model 4M, and the element H (i) of the interface layer model 5M are planar elements. Is set. For this reason, the thermal expansion coefficient α is defined as a surface expansion coefficient. For example, when the interface layer model 5M is set as the expansion model 7M (shown in FIG. 6), the coefficient of thermal expansion α is set to about 1 × 10 ⁻⁶ to 200 × 10 ⁻⁶ (1 / ° C.).

  In the above formula (1), by increasing or decreasing the temperature change t, the area V of the element can be increased or decreased linearly while maintaining the ratio in the X direction and the Y direction. The element is numerical data. For this reason, the expansion model 7M (shown in FIG. 6) can be expanded to a size that is impossible in practice by substituting a very large numerical value for the temperature change t in the above equation (1). Further, the expansion calculation based on the thermal expansion coefficient has a smaller calculation load than the expansion calculation in which a load is directly applied. Therefore, the calculation time for expanding and contracting an expansion model 7M described later can be shortened. The thermal expansion coefficient is input to the computer 1.

  Next, in the creation method of the present embodiment, an expansion model 7M (shown in FIG. 6) in which at least one of the matrix rubber model 3M, the filler model 4M, or the interface layer model 5M is expanded is set (step S5). . In step S5, the element F (i) of the matrix rubber model 3M in which the thermal expansion coefficient is defined, the element G (i) of the filler model 4M, or the element H (i) of the interface layer model 5M (in this embodiment, the interface layer) The element H (i)) of the model 5M is expanded. FIG. 6 is a plan view showing a filler-containing rubber model 2M obtained by expanding the expansion target model 9M of FIG. FIG. 7A is a partially enlarged view of FIG. FIG. 7B is a partial plan view of a filler-containing rubber model 2M obtained by discretizing the expansion model 7M of FIG. 7A. In FIGS. 7A and 7B, the element F (i) of the matrix rubber model 3M and the element G (i) of the filler model 4M are omitted.

  In step S5 of the present embodiment, the element H (i) of the interface layer model 5M shown in FIG. 5 is expanded by gradually increasing the temperature change t based on the thermal expansion coefficient of the above equation (1). (The area V is increased). In this embodiment, the temperature change t is increased by increasing the temperature set in the filler-containing rubber model 2M. Thereby, an expansion model 7M is set by expanding the interface layer model 5M shown in FIGS. 6 and 7A in the radial direction.

  No thermal expansion coefficient is set for the element F (i) of the matrix rubber model 3M and the element G (i) of the filler model 4M of the present embodiment. For this reason, even if the temperature set in the filler-containing rubber model 2M is increased, the matrix rubber model 3M and the filler model 4M do not expand like the interface layer model 5M. Note that the models adjacent to the expansion model 7M (in this embodiment, the matrix rubber model 3M and the filler model 4M) are deformed according to the expansion of the expansion model 7M.

  For the deformation (expansion) calculation of the interface layer model 5M, matrix rubber model 3M and filler model 4M, commercially available finite element analysis application software (for example, LS-DYNA made by JSOL) is used in the same way as the conventional method. And is performed every unit time Tx (x = 0, 1,...) (For example, every 1 μsec).

  Next, in the creation method of the present embodiment, the expansion model 7M is re-discretized using a finite number of elements (step S6). In step S6, first, the elements constituting the expansion model 7M shown in FIG. 7A (in this embodiment, the element H (i) of the interface layer model 5M) are invalidated. In step S6, the contour of the expansion model 7M is re-discretized using a finite number of elements J (i) (i = 1, 2,...) Shown in FIG.

  The element J (i) used for the re-discretization can be handled by the finite element method similarly to the element H (i) of the interface layer model 5M shown in FIG. Is done. As shown in FIG. 7B, the element J (i) has a node 17 and a side 18 connecting the nodes 17 and 17. In the element J (i), the number of the node 17 and the coordinate value of the node 17 are set. Each element J (i) receives a physical quantity such as an elastic modulus and a damping coefficient based on the physical property values of the interface layer 5 shown in FIG.

  The element J (i) has the same thermal expansion coefficient as that of the element before re-discretization of the expansion model 7M (in this embodiment, the element H (i) of the interface layer model 5M shown in FIG. 7A). Is set. Further, the size of the element J (i) is the same as that of the element before re-discretization of the expansion model 7M under the same temperature condition (that is, the same temperature change t in the above equation (1)). The size is set smaller than the size of the element H (i)) of the interface layer model 5M shown in FIG. Accordingly, in step S6, the contour of the expansion model 7M is re-discrete using the element J (i) smaller than the element of the expansion target model 9M (in this embodiment, the element H (i) of the interface layer model 5M). Can be realized.

  In the present embodiment, it is possible to expand a region where the shape of the model (in this embodiment, the interface layer model 5M) constituting the expansion model 7M is small. For this reason, the contour of the expansion model 7M is easily discretized by using the element J (i) smaller than the element H (i) constituting the interface layer model 5M by meshing software or manual operation of the operator. it can.

  In this embodiment, the node 17 and the side 18 of the element J (i) of the expansion model 7M (interface layer model 5M) and the node 11 and the side 12 of the element F (i) of the matrix rubber model 3M adjacent to the expansion model 7M. Are shared with each other. Further, the node 17 and the side 18 of the element J (i) of the expansion model 7M (interface layer model 5M) and the node 13 and the side 14 of the element G (i) of the filler model 4M adjacent to the expansion model 7M are shared. I am letting. Thereby, the expansion model 7M (interface layer model 5M), the matrix rubber model 3M, and the filler model 4M can be connected together.

  In this embodiment, in the expansion direction of the expansion model 7M (in this embodiment, the interface layer model 5M is in the radial direction), the elements of the expansion target model 9M shown in FIG. (In this embodiment, the element is discretized with an element J (i) smaller than the element H (i) of the interface layer model 5M, but the present invention is not limited to such an aspect. For example, the expanded element H (i) may be subdivided according to the method described in Patent Document 2 (Japanese Patent No. 5227436).

  In the method described in Patent Document 2, subdivision is performed based on a preset element H (i). Therefore, the nodal point 17 and the side 18 of the element J (i) of the expansion model 7M (interface layer model 5M) and the nodal point 11 and the side 12 of the element F (i) of the matrix rubber model 3M adjacent to the expansion model 7M. It can be subdivided while maintaining sharing. Similarly, the node 17 and the side 18 of the element J (i) of the expansion model 7M and the node 13 and the side 14 of the element G (i) of the filler model 4M can be subdivided while maintaining the sharing. Therefore, in this embodiment, the contour of the expansion model 7M can be easily discretized without considering sharing of nodes and sides of each element.

  Next, in the creation method of the present embodiment, the re-discretized expansion model 7M is contracted to the original size (step S7). In step S7, the element J (i) of the expansion model 7M is reduced by contracting the re-discretized expansion model 7M to the original size. FIG. 8 is a plan view showing a filler-containing rubber model 2M in which the expansion model 7M in FIG. 7B is contracted.

  In step S7, the temperature change t is gradually returned to the original magnitude, so that the expansion model 7M shown in FIG. 7B (in this embodiment, the interface is based on the thermal expansion coefficient of the above formula (1)). The element J (i) of the layer model 5M) is contracted (the area V is reduced). In the present embodiment, the temperature change t in the above equation (1) is restored by returning the temperature set to the filler-containing rubber model 2M to the original (that is, returning to the temperature set before the expansion model 7M expands). Is restored to its original size. Thereby, an interface layer model 5M (shown in FIG. 8) in which the expansion model 7M is contracted in the radial direction is set.

  Note that no coefficient of thermal expansion is set for the element F (i) of the matrix rubber model 3M and the element G (i) of the filler model 4M. For this reason, the matrix rubber model 3M and the filler model 4M do not contract based on the thermal expansion coefficient like the expansion model 7M. Further, the models adjacent to the expansion model 7M (in this embodiment, the matrix rubber model 3M and the filler model 4M) are deformed according to the contraction of the expansion model 7M.

  As described above, the size of the element J (i) of the expansion model 7M shown in FIG. 7B is the same as that in FIG. 7 under the same temperature condition (that is, the same temperature change t in the above equation (1)). The expansion model 7M shown in (a) is smaller than the size of the element H (i) before re-discretization. Accordingly, the expansion target model 9M (in this embodiment, the interface layer model 5M) is discretized with an element J (i) smaller than the original element H (i) shown in FIG. 4 by contraction of the expansion model 7M. be able to. Thereby, the physical quantity of the expansion object model 9M (interface layer model 5M) can be accurately calculated in the deformation simulation of the filler-containing rubber model 2M of the present embodiment.

  In the present embodiment, only the interface layer model 5M that models the interface layer 5 that greatly affects the characteristics of the filler-containing rubber 2 is set as the expansion model 7M (expansion target model 9M). For this reason, the filler compounded rubber model 2M can prevent an increase in calculation time in the deformation simulation due to an increase in the number of elements while maintaining the calculation accuracy in the deformation simulation.

  In order to effectively discretize the expansion target model 9M (in this embodiment, the interface layer model 5M) with small elements J (i), the size of the expansion model 7M (shown in FIG. 6) is It is preferably 2 to 10 times the size of 9M (shown in FIG. 4). If the size of the expansion model 7M is less than twice the size of the expansion target model 9M, it may be difficult to discretize with small elements. Conversely, when the size of the expansion model 7M exceeds 10 times the size of the expansion target model 9M, the number of elements J (i) increases, and the calculation time in the deformation simulation using the filler-containing rubber model 2M increases. May increase.

  In the present embodiment, only the interface layer model 5M is set as the expansion model 7M (expansion target model 9M), but is not limited to such an aspect. For example, only the matrix rubber model 3M or only the filler model 4M may be set as the expansion model 7M (expansion target model 9M), or all of the matrix rubber model 3M, the filler model 4M, and the interface layer model 5M are It may be set as the expansion model 7M (expansion target model 9M).

  When all of the matrix rubber model 3M, the filler model 4M, and the interface layer model 5M are set as the expansion model 7M (expansion target model 9M), the element F (i) of the matrix rubber model 3M and the element G of the filler model 4M ( Different thermal expansion coefficients (that is, the thermal expansion coefficient α in the above formula (1)) are set for i) and the element H (i) of the interface layer model 5M. Each thermal expansion coefficient (that is, thermal expansion coefficient α) is set based on the matrix rubber 3, the filler 4, and the interface layer 5. Therefore, when the same temperature is set in the matrix rubber model 3M, the filler model 4M, and the interface layer model 5M, the size at the time of expansion based on the thermal expansion coefficients of the matrix rubber model 3M, the filler model 4M, and the interface layer model 5M is Each is different.

  As a result of extensive research, the inventors have a certain correlation between the size at the time of expansion based on the thermal expansion coefficient and the amount of deformation in the deformation simulation using the filler-containing rubber model 2M. It has been found that the amount of deformation in the deformation simulation increases.

  In step S6 of this embodiment, a part with a larger expansion based on the thermal expansion coefficient (that is, a part with a larger deformation amount in the deformation simulation) can be discretized with smaller elements. Therefore, the filler compounded rubber model 2M created in this embodiment can improve the calculation accuracy in the deformation simulation. On the other hand, the size of the element of the portion where the expansion based on the thermal expansion coefficient is small (that is, the portion where the deformation amount in the deformation simulation is small) can be maintained substantially the same as the original size. Therefore, it is possible to prevent an increase in calculation time in the deformation simulation due to an increase in the number of elements.

  In the embodiments so far, the filler-containing rubber model 2M (that is, the matrix rubber model 3M, the filler model 4M, and the interface layer model 5M) is defined as a two-dimensional model created according to a two-dimensional coordinate system in the X direction and the Y direction. However, the present invention is not limited to such an embodiment. The filler-containing rubber model 2M may be defined as a three-dimensional model (not shown) created according to a three-dimensional coordinate system in the X direction, the Y direction, and the Z direction. In this case, each of the elements F (i), G (i), and H (i) is preferably defined as a solid element, and the volume expansion coefficient is desirably set as the above-described equation (1) thermal expansion coefficient α.

  As mentioned above, although especially preferable embodiment of this invention was explained in full detail, this invention is not limited to embodiment of illustration, It can deform | transform and implement in a various aspect.

  According to the procedure shown in FIG. 3, a filler-containing rubber model (shown in FIG. 8) obtained by modeling a filler-containing rubber (shown in FIG. 2) was defined (Example 1, Example 2).

  In Example 1, only the interface layer model was set as the expansion model. In Example 2, the matrix rubber model, the filler model, and the interface layer model were set as the expansion model. Each expansion model of Example 1 and Example 2 was expanded based on a thermal expansion coefficient. Each expansion model of Example 1 and Example 2 was re-discretized by a finite number of elements. And the elements which comprised each expansion model were shrunk | reduced by contracting each expansion model of Example 1 and Example 2 re-discretized to the original magnitude | size.

  For comparison, a filler-containing rubber model (shown in FIG. 4) including a matrix rubber model, a filler model, and an interface layer model was set without setting an expansion model.

  Then, using the simulation software (for example, LS-DYNA), deformation calculation (extension of 4% in the Y-axis direction) of the filler-containing rubber models of Example 1, Example 2, and Comparative Example was performed. Further, an experiment for deforming the filler-blended rubber (shown in FIG. 2) (4% extension in the Y-axis direction) was similarly performed (experiment example).

  As a result of the test, the filler compounded rubber model after deformation of Example 1 and Example 2 can be approximated to the deformed shape of the filler compounded rubber of the experimental example compared to the filler compounded rubber model after deformation of the comparative example. It was. This is presumably because Example 1 and Example 2 were able to model (discretize) the interface layer that greatly affects the properties of the filler-containing rubber 2 with small elements.

  Further, in Example 1, since only the interface layer model is discretized with small elements, the time required for deformation calculation is larger than that in Example 2 in which the matrix rubber model, the filler model, and the interface layer model are discretized with small elements. Was reduced by 25%.

S5 Step of setting an expansion model S6 Step of re-discretizing the expansion model S7 Step of reducing elements constituting the expansion model

Claims (3)

A method for creating, using a computer, a finite element model of a filler-containing rubber including a matrix rubber, a filler disposed in the matrix rubber, and at least one interface layer surrounding the filler,
Setting a matrix rubber model obtained by discretizing the matrix rubber using a finite number of elements;
Setting a filler model obtained by discretizing the filler using a finite number of elements;
Setting an interface layer model in which the interface layer is discretized using a finite number of elements;
Setting an expansion model obtained by expanding at least one of the matrix rubber model, the filler model, or the interface layer model;
The step of re-discretizing the expansion model using a finite number of elements, and shrinking the re-discretized expansion model to the original size, thereby reducing the elements constituting the expansion model A method for creating a filler-containing rubber model, comprising a step of: Further comprising defining a thermal expansion coefficient for the element of the matrix rubber model set as the expansion model, the element of the filler model, or the element of the interface layer model,
The step of setting the expansion model is based on the coefficient of thermal expansion of the element of the matrix rubber model in which the coefficient of thermal expansion is defined, the element of the filler model, or the element of the interface layer model. Inflated,
The method of creating a filler-blended rubber model according to claim 1, wherein the step of contracting the expansion model contracts the element of the expansion model based on the thermal expansion coefficient.   The method for creating a filler-containing rubber model according to claim 1, wherein only the interface layer model is set as the expansion model.