JP6283267B2 - Method for simulating polymer materials - Google Patents

Description

  The present invention relates to a polymer material simulation method capable of stably calculating a physical quantity of a polymer material.

  A filler such as carbon black or silica is blended in a polymer material such as rubber. In recent years, various simulation methods (numerical calculations) have been proposed for calculating the physical quantity of a polymer material containing a filler using a computer for the development of rubber compounding (for example, see Patent Document 1 below). ).

  In order to calculate the physical quantity (for example, free energy of the calculation system) of the polymer material containing the filler, a simulation method based on the mean field theory is considered. In this type of simulation method, first, a virtual space divided into meshes is set in a computer, and a filler model that models a filler and a polymer model that models a polymer material are arranged there. And free energy etc. are calculated based on the SCF method (Self-Consistent Field Method) which considered the entropy of arrangement | positioning of a polymer model.

JP 2006-64658 A

  In the conventional simulation method based on the mean field theory, the contour shape of the filler model is defined by the experience and intuition of the operator. For this reason, in some cases, the physical quantity of the polymer material has risen sharply, causing a problem of divergence of calculation.

  The present invention has been devised in view of the actual situation as described above, and is based on setting the minimum unit length L1 of the contour line of the filler model to be twice or more of the minimum unit length L2 of the mesh. The main object of the present invention is to provide a simulation method of a polymer material that can stably converge the calculation of the physical quantity of the polymer material based on the mean field theory.

  The present invention is a simulation method for calculating a physical quantity of a polymer material in which a filler is blended based on a mean field theory using a computer, and the computer includes a plurality of micro regions divided into meshes. Defining a virtual space including: setting a filler model that models the filler in the virtual space; setting a polymer model that models the polymer material in the virtual space; and A computer calculating a physical quantity of the polymer material using the filler model and the polymer model defined in the virtual space, the filler model surrounding a plurality of the minute regions; The polymer model is defined by an uneven contour line along the mesh, and the polymer model is defined at a plurality of intersection points of the mesh. Modeled in polymer segment, a minimum unit length L1 of the contour of the filler model is characterized by at least twice the minimum unit length L2 of the mesh.

  In the polymer material simulation method according to the present invention, it is preferable that the minimum unit length L1 of the filler model is smaller than a diameter L3 of the filler model.

In the simulation method of the polymer material according to the present invention, the minimum unit length L1 of the filler model, the minimum unit length L2 of the mesh, and the diameter L3 of the filler model satisfy the following relationship. Is desirable.
L1 ≦ L3-L2 × 4

  In the polymer material simulation method according to the present invention, the filler model is preferably defined as a three-dimensional model.

  The present invention is a simulation method for calculating a physical quantity of a polymer material in which a filler is blended based on a mean field theory using a computer. In this polymer material simulation method, in a computer, a step of defining a virtual space including a plurality of minute regions divided into meshes, a step of setting a filler model in which a filler is modeled in the virtual space, a virtual space, The method includes setting a polymer model obtained by modeling the polymer material, and calculating a physical quantity of the polymer material using a filler model and a polymer model defined in a virtual space by a computer.

  In the present invention, the filler model is defined by an uneven contour line along the mesh so as to surround the plurality of minute regions. On the other hand, the polymer model is modeled by a plurality of polymer segments defined at the intersection of meshes. The minimum unit length L1 of the contour line of the filler model is set to at least twice the minimum unit length L2 of the mesh. Therefore, according to the method of the present invention, it is possible to set the intersection of at least one mesh between both ends of the minimum unit length of the contour line, that is, between the entrance corner and the exit corner of the uneven contour line.

  The plurality of polymer segments are sequentially arranged at the intersections of the mesh. The polymer segment arranged at the intermediate intersection has a larger number of intersections where the next polymer segment can be arranged than the polymer segment arranged in the corner. In simulation based on mean field theory, the greater the number of intersections at which polymer segments can be placed, the higher the stability of the polymer model. Therefore, the polymer model including the polymer segment arranged at the intermediate intersection has higher stability in the mean field theory than the polymer model including the polymer segment arranged in the corner.

  On the other hand, the polymer segment arranged at the intermediate intersection has a smaller number of intersections at which the next polymer segment can be arranged than the polymer segment arranged at the protruding corner. Therefore, a polymer model including a polymer segment arranged at an intermediate intersection is less stable in the mean field theory than a polymer model including a polymer segment arranged at a corner.

  As described above, according to the method of the present invention, the stability of the polymer model in which the polymer segments are sequentially arranged from the exit corner to the entrance corner can be reduced stepwise via the intermediate intersection. In the simulation based on the mean field theory, the lower the stability of the polymer segment, the higher the physical quantity of the polymer material (free energy of the calculation system). Therefore, according to the present invention, it is possible to prevent the free energy of the calculation system from rapidly increasing, so that the calculation of the free energy of the calculation system can be converged stably.

It is a perspective view of the computer which performs the simulation method of this embodiment. It is a flowchart which shows an example of the process sequence of the simulation method of this embodiment. It is a conceptual diagram of the virtual space of this embodiment. It is a conceptual diagram which shows a filler model and a polymer model. It is a conceptual diagram of the virtual space which has the conventional filler model. It is the elements on larger scale of the filler model of this embodiment. It is a flowchart which shows an example of the simulation process of this embodiment. (A) is a conceptual diagram of the virtual space which a pair of filler model contact | abutted. (B) is a conceptual diagram of a virtual space in which a pair of filler models are separated. It is a graph which shows the relationship between the free energy of a calculation system, and the interparticle distance of a filler model.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
The simulation method of the polymer material of the present embodiment (hereinafter sometimes simply referred to as “simulation method”) is a method for calculating the physical quantity of the polymer material mixed with the filler using a computer.

  Examples of the filler include carbon black, silica, or alumina. In addition, examples of the polymer material include rubber, resin, and elastomer.

  FIG. 1 is a perspective view of a computer that executes the simulation 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. The storage device stores in advance processing procedures (programs) for executing the simulation method of the present embodiment.

  FIG. 2 is a flowchart illustrating an example of a processing procedure of the simulation method of the present embodiment. In the simulation method of this embodiment, first, a virtual space is defined in the computer 1 (step S1). FIG. 3 is a conceptual diagram of the virtual space of the present embodiment.

  The virtual space 3 of the present embodiment is set as a two-dimensional system formed in a horizontally long rectangular shape. Periodic boundary conditions are set for the pair of vertical sides 3a and 3a and the pair of horizontal sides 3b and 3b surrounding the virtual space 3, respectively. The length L5a of each vertical side 3a and the length L5b of each horizontal side 3b can be set as appropriate. The lengths L5a and L5b are desirably set to, for example, twice or more, more preferably 10 times or more of an inertia radius (not shown) of a filler model 4 and a polymer model 6 described later.

  The virtual space 3 is provided with a plurality of minute regions 9 divided into meshes 8. The mesh 8 of this embodiment is treated as a minimum unit of simulation based on mean field theory (such as Flory-Huggins theory). Here, the mean field theory is a statistical thermodynamic theory of a polymer solution that is used to approximate the mean field of the interaction that the focused polymer receives from the periphery.

The micro region 9 of the present embodiment is formed in a square shape in which a pair of vertical sides and a pair of horizontal sides are set to the same length. Accordingly, the lengths of the vertical sides and the horizontal sides are set as the minimum unit length L2 of the mesh 8. The minimum unit length L2 of the mesh 8 can be appropriately set according to the accuracy required for the simulation. The minimum unit length L2 of the present embodiment is set to, for example, ¼ to 1/100 of the length L5b of the horizontal side 3b of the virtual space 3. The virtual space 3 is stored in the computer 1.

  Next, in the simulation method of the present embodiment, a filler model 4 in which a filler is modeled is set in the virtual space 3 (step S2). Two filler models 4 of the present embodiment are defined in the virtual space 3. In the filler model 4, the arrangement of the polymer model 6 described later is not allowed.

  The filler model 4 is defined so as to approximate an actual filler shape. The filler model 4 of the present embodiment is defined by a contour line 10 along the mesh 8 so as to surround a plurality of minute regions 9. The contour line 10 of the present embodiment is provided with a plurality of entering corners 10i and exiting corners 10o. Thereby, as for the filler model 4, the unevenness | corrugation is formed in the outline 10. FIG.

  The minimum unit length L1 of the outline 10 of the filler model 4 of the present embodiment is set to be twice or more the minimum unit length L2 of the mesh 8. As a result, at least one (8 in this embodiment) intersection 8p of the mesh 8 is formed between both ends of each minimum unit length L1, that is, in the middle of the entering corner 10i or the exiting corner 10o of the uneven contour line 10. Can be set.

  The minimum unit length L1 of the filler model 4 is preferably smaller than the diameter L3 of the filler model 4. Thereby, since the some corner 10i is reliably formed in the outline of the filler model 4, the shape of the filler model 4 can be approximated to the shape of an actual filler. Therefore, the filler model 4 can improve the simulation accuracy. When the diameter of the contour of the filler model 4 changes, the diameter L3 is the maximum value of the diameter of the filler model 4.

Desirably, the minimum unit length L1 of the filler model 4, the minimum unit length L2 of the mesh 8, and the diameter L3 of the filler model 4 satisfy the relationship of the following formula (1).
L1 ≦ L3-L2 × 4 (1)

  In the above equation (1), the minimum unit length L1 of the contour line 10 of the filler model 4 is limited to a value obtained by subtracting the minimum unit length L2 of four meshes 8 from the diameter L3 of the filler model 4. ing. Thus, the filler model 4 can reduce the minimum unit length L1 of the contour line 10 and form more corners 10i in the contour line 10. Therefore, the filler model 4 can be approximated by the actual shape of the filler. The filler model 4 is stored in the computer 1.

  Next, a polymer model 6 that models a polymer material is set in the virtual space 3 (step S3). FIG. 4 is a conceptual diagram showing a filler model and a polymer model.

  As shown in FIGS. 3 and 4, the polymer model 6 is modeled with at least one polymer segment 7 defined at the intersection 8 p of the mesh 8. The polymer model 6 of this embodiment is modeled with a plurality of polymer segments 7. Such a polymer model 6 can accurately model the polymer chain of the polymer material. Similar to the filler model 4, the polymer segment 7 is treated as a minimum unit in simulation based on mean field theory.

  Between the polymer segments 7 and 7, a bonding chain 16 is provided for restraining them. The length K1 of the connecting chain 16 is set to the same length as the minimum unit length L2 (shown in FIG. 3) of the mesh 8, for example. Accordingly, the polymer model 6 is defined as a linear two-dimensional structure in which the relative distance between the polymer segments 7 and 7 is stably maintained.

  A plurality of polymer models 6 of the present embodiment are arranged in the virtual space 3 based on a predetermined volume fraction (for example, about 50% to 99%). Between the polymer segment 7 of the polymer model 6 and the polymer segment 7 of the other polymer model 6, a χ parameter K2 that is an interaction parameter is set. The χ parameter K2 is set to about 0.0 to 10.0, for example. Thereby, the strength of repulsive interaction is defined between the polymer segments 7 and 7. The polymer model 6 is stored in the computer 1.

  Next, the χ parameter K3 that is an interaction parameter between the filler model 4 and the polymer model 6 is set in the computer 1 (step S4). As shown in FIG. 4, the χ parameter K3 is set between the filler model 4 and the polymer segment 7, respectively. The χ parameter K3 of this embodiment is set to 0.0 to 10.0, for example. Thereby, the strength of the repulsive interaction is defined between the filler model 4 and the polymer segment 7.

  When the χ parameter K3 exceeds 10.0, even in the simulation based on the mean field theory, even if the arrangement of the filler model 4 and the polymer model 6 approaches a stable state (equilibrium state), the energy difference from the immediately preceding calculation step is There is a risk that the calculation will not converge. From such a viewpoint, the χ parameter K3 is more preferably 5.0 or less. The χ parameter K3 is stored in the computer 1.

  Next, the computer 1 calculates the physical quantity of the polymer material based on the mean field theory (simulation step S5).

  In the simulation step S5 based on the mean field theory of the present embodiment, the entire system including the filler model 4 and the polymer model 6 based on the SCF method (Self-Consistent Field Method) considering the entropy of the arrangement of the polymer model 6 ( The free energy F in the equilibrium state of the virtual space 3) is calculated. Each free energy F is Helmholtz free energy. Such simulation based on the mean field theory can be processed using, for example, SUSHI included in OCTA.

  In the simulation based on the mean field theory, for each unit step of the simulation, each polymer segment 7 is arranged so that the arrangement information (concentration distribution) of the polymer model 6 at the current step approximates the arrangement information of the polymer model 6 at the immediately preceding step. Are sequentially arranged at the intersection point 8p. In addition, each polymer segment 7 cannot be disposed at the intersection point 8 p inside the contour line 10 of the filler model 4. For this reason, when the polymer segment 7 is arranged on the contour line 10, the number of intersection points 8 p that can be arranged in the next polymer segment 7 connected to the polymer segment 7 is reduced.

  FIG. 5 is a conceptual diagram of a virtual space having a conventional filler model. In the filler model 4, the minimum unit length L1 of the contour line 10 is set to be the same as the minimum unit length L2 of the mesh 8. For this reason, the intersection point 8p arranged at the entrance corner 10i of the uneven contour line 10 and the intersection point 8p arranged at the exit corner 10o are defined adjacent to each other.

  The next polymer segment 7 coupled to the polymer segment 7 arranged at the intersection point 8p of the exit corner 10o (hereinafter simply referred to as “polymer segment 7 of the exit corner 10o”) is the intersection point 8p, It can be arranged at an intersection 8p on the upper side of the corner 10o, an intersection 8p on the right side of the outgoing corner 10o, and an intersection 8p on the lower side of the outgoing corner 10o (four in total). On the other hand, the next polymer segment 7 coupled to the polymer segment 7 disposed at the intersection 8p of the entrance corner 10i (hereinafter simply referred to as “polymer segment 7 of the entrance corner 10i”) is the intersection 8p of the exit corner 10o. , And the intersection 8p on the upper side of the corner 10i (two in total).

  In the simulation based on the mean field theory, the smaller the number of intersection points 8p at which the next polymer segment 7 is arranged, the lower the stability of the polymer model 6 becomes. Therefore, in the virtual space 3 having the conventional filler model 4, when the next polymer segment 7 joined to the polymer segment 7 at the exit corner 10o is arranged at the entrance corner 10i, the stability of the polymer model 6 is rapidly increased. To drop.

  Furthermore, in the simulation based on the mean field theory, the lower the polymer model 6 stability, the higher the physical quantity of the polymer material (free energy F of the calculation system). Therefore, in the simulation using the conventional filler model 4, the next polymer segment 7 joined to the polymer segment 7 at the exit corner 10o is disposed at the entrance corner 10i, thereby disposing the polymer model 6 with low stability. The free energy F of the calculation system increases rapidly. As described above, when the physical quantity of the polymer material rapidly increases, calculation may be diverged.

  FIG. 6 is a partially enlarged view of the filler model 4 of the present embodiment. In the filler model 4 of the present embodiment, the minimum unit length L1 of the outline 10 of the filler model 4 is set to be twice or more the minimum unit length L2 of the mesh 8. For this reason, the filler model 4 can set the intersection 8p of at least one mesh 8 in the middle of the intersection 8p arranged at the entrance corner 10i of the uneven contour line 10 or the intersection 8p arranged at the exit corner 10o. it can.

  The next polymer segment 7 coupled to the polymer segment 7 arranged at the intersection 8p of the middle 10c (hereinafter simply referred to as “the polymer segment 7 of the middle 10c”) is the intersection 8p, the exit corner of the entry corner 10i. It can be arranged at the intersection 8p of 10o and the intersection 8p on the upper side of the middle 10c (three in total). For this reason, the polymer segment 7 in the middle 10c has a larger number of intersection points 8p at which the next polymer segment 7 can be arranged than the polymer segment 7 in the corner 10i. Therefore, the polymer model 6 including the intermediate 10c polymer segment 7 has higher stability in the mean field theory than the polymer model 6 including the polymer segment 7 at the corner 10i.

  On the other hand, the polymer segment 7 in the middle 10c has a smaller number of intersection points 8p at which the next polymer segment 7 can be arranged than the polymer segment 7 in the corner 10o. Therefore, the polymer model 6 including the intermediate 10c polymer segment 7 is less stable in the mean field theory than the polymer model 6 including the polymer segment 7 at the protruding corner 10o.

  As described above, according to the simulation method of the present embodiment, for example, the stability of the polymer model 6 in which the polymer segments 7 are sequentially arranged from the protruding corner 10o to the entering corner 10i is obtained through the intersection 8p of the intermediate 10c. Can be reduced. Therefore, in the simulation method using the filler model 4 of the present embodiment, it is possible to prevent the physical quantity of the polymer material from abruptly rising, so that the calculation of the physical quantity can be converged stably.

  In order to effectively exhibit such an action, the minimum unit length L1 of the contour line 10 of the filler model 4 is preferably at least twice the minimum unit length L2 of the mesh 8, more preferably at least three times. It is. Thereby, since the filler model 4 can set the some intersection 8p in the intermediate | middle 10c of the corner 10i of the uneven | corrugated outline 10, or the corner 10o, until the polymer segment 7 is arrange | positioned in the corner 10i. The distance can be increased. Therefore, the stability of the polymer model 6 can be prevented from rapidly decreasing, and the physical quantity of the polymer material can be reliably prevented from rapidly increasing.

  FIG. 7 is a flowchart illustrating an example of the simulation step S5 of the present embodiment. In the simulation step S5 of the present embodiment, a pair of filler models 4 and 4 are arranged in the virtual space 3. For this reason, in simulation process S5 of this embodiment, the change of the free energy F of the calculation system according to the interparticle distance between the filler models 4 and 4 can be calculated.

  In the simulation step S5 of the present embodiment, first, the pair of filler models 4 and 4 are brought into contact with each other to calculate the minimum free energy Fs of the calculation system (step S51). FIG. 8A is a conceptual diagram of a virtual space in which a pair of filler models 4 and 4 are in contact with each other. FIG. 8B is a conceptual diagram of a virtual space in which the pair of filler models 4 and 4 are separated. In FIGS. 8A and 8B, the polymer model 6 (shown in FIG. 3) is omitted.

  In step S51, as shown in FIG. 8A, the pair of filler models 4 and 4 are brought into contact with each other. Thereby, the free energy F of the calculation system in a state where the pair of filler models 4 and 4 are in contact with each other is calculated. In the state where the pair of filler models 4 and 4 are in contact with each other, the polymer model 6 (shown in FIG. 3) arranged in the vicinity of the filler model 4 is minimized, so that the entropy reduction of the arrangement of the polymer model 6 can be suppressed. The free energy F is minimized.

  In step S51, the interparticle distance R (minimum interparticle distance Rs) in a state where the pair of filler models 4 and 4 are in contact with each other is calculated. The interparticle distance R is defined as the distance between the centroids 5c and 5c of the regions 5 and 5 where the filler model 4 is disposed. In step S51, the minimum value Fs of free energy and the minimum interparticle distance Rs are stored in the computer 1.

  Next, the pair of filler models 4 and 4 are separated from each other, and the maximum free energy Fm of the calculation system is calculated (step S52). As shown in FIG. 8B, in step S52, the free energy F of the calculation system at each inter-particle distance R is separated from the state where the pair of filler models 4 and 4 are in contact with each other at a constant interval. Calculated. The interparticle distance R and the free energy F of the calculation system at each interparticle distance R are stored in the computer 1. FIG. 9 is a graph showing the relationship between the free energy F of the calculation system and the interparticle distance R of the filler model 4.

  When the inter-particle distance R between the pair of filler models 4 and 4 is increased, the contact portion between the filler model 4 and the polymer model 6 is increased. For this reason, the free energy F of the calculation system increases. In step S52 of the present embodiment, the inter-particle distance R of the pair of filler models 4 and 4 is increased until the increment of the free energy F of the calculation system becomes zero, and the free energy F of the calculation system is calculated. Thereby, in process S52, the maximum value Fm of the free energy F of a calculation system can be calculated | required. In step S52, the maximum value Fm of free energy is stored in the computer 1.

  Thus, in the simulation step S5 of the present embodiment, since the pair of filler models 4 and 4 are provided in the virtual space 3, the free energy F of the calculation system corresponding to the interparticle distance between the filler models 4 and 4 is provided. Can be determined. Such a change in the free energy F of the calculation system can be used, for example, to estimate a parameter of an interaction potential between fillers.

  Next, the computer 1 determines whether the physical quantity of the polymer material is within an allowable range (step S6). In step S6, when it is determined that the physical quantity of the polymer material is within the allowable range, a deformation simulation of the entire system is performed based on the conditions of the filler model 4 and the polymer model 6 (step S7). The deformation simulation can be processed using KAPSEL included in OCTA as in the conventional case. And if the result of a deformation | transformation simulation is favorable, the polymeric material containing a filler will be manufactured (process S8).

  On the other hand, when it is determined that the physical quantity of the polymer material is outside the allowable range, various conditions of the filler model 4 and the polymer model 6 are changed (step 9), and the steps S1 to S6 are performed again. As described above, in this embodiment, since the various conditions of the filler model 4 and the polymer model 6 are changed until the physical quantity of the polymer material is within the allowable range, the polymer material having the desired performance can be efficiently obtained. Can be designed.

  In the present embodiment, the virtual space 3 and the filler model 4 are defined as two-dimensional models, but may be defined as three-dimensional models. In this case, the virtual space 3 is preferably defined as a three-dimensional rectangular parallelepiped. The filler model 4 is preferably modeled based on, for example, an electron beam transmission image of the filler obtained using a scanning transmission electron microscope. In the simulation method using such a filler model 4, the shape of the filler can be modeled with high accuracy, so that the calculation accuracy of the free energy F of the calculation system can be further increased.

  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 FIGS. 2 and 6, a virtual space having the filler model shown in FIG. 3 was defined, and the physical quantity of the polymer material based on the mean field theory was calculated (Example). In the filler model of the embodiment, the minimum unit length L1 of the contour line is set to be twice the minimum unit length L2 of the mesh 8.

  For comparison, a virtual space having the filler model shown in FIG. 5 was defined, and the physical quantity of the polymer material based on the mean field theory was calculated (comparative example). In the filler model of the comparative example, the minimum unit length L1 of the contour line and the minimum unit length L2 of the mesh 8 are set to be the same.

In each of the examples and comparative examples, each simulation method was performed 10 times, and it was confirmed whether or not the calculation of the physical quantity of the polymer material converged. Each parameter is as described in the specification, and the common specifications are as follows.
Simulation of mean field theory:
Virtual space:
Length L5a: 30σ
Length L5b: 60σ
Fine unit length L2 of mesh: 1σ
Filler model:
Number of virtual space: 2
Diameter: 6σ
Polymer model:
Volume fraction placed in virtual space: 80%
Polymer segment chain length: 50 (linear molecule)
Polymer segment diameter (distance between adjacent segments): 1σ
Χ parameter K2 between polymer segments: 0.0
Χ parameter K3 between polymer segment and filler segment: 3.0

  As a result of the test, in the example, convergence was possible in all calculations. On the other hand, in the comparative example, the calculation divergence occurred five times. Therefore, it was confirmed that the simulation method of the example can stably converge the calculation of the physical quantity of the polymer material based on the mean field theory.

3 Virtual space 4 Filler model 6 Polymer model 7 Polymer segment 8 Mesh 9 Micro area 10 Outline

Claims (4)

A simulation method for calculating a physical quantity of a polymer material containing a filler based on mean field theory using a computer,
Defining, in the computer, a virtual space including a plurality of minute regions divided into meshes;
Setting a filler model that models the filler in the virtual space;
A step of setting a polymer model obtained by modeling the polymer material in the virtual space; and the computer using the filler model and the polymer model defined in the virtual space. Including a step of calculating a physical quantity,
The filler model is defined by an uneven contour line along the mesh so as to surround a plurality of the minute regions,
The polymer model is modeled with a plurality of polymer segments defined at the intersection of the mesh,
The method for simulating a polymer material, wherein the minimum unit length L1 of the contour line of the filler model is at least twice the minimum unit length L2 of the mesh.   The method for simulating a polymer material according to claim 1, wherein the minimum unit length L1 of the filler model is smaller than a diameter L3 of the filler model. The method for simulating a polymer material according to claim 1 or 2, wherein the minimum unit length L1 of the filler model, the minimum unit length L2 of the mesh, and the diameter L3 of the filler model satisfy the following relationship.
L1 ≦ L3-L2 × 4   4. The polymer material simulation method according to claim 1, wherein the filler model is defined as a three-dimensional model.

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