JP7159809B2 - Rubber material simulation method and rubber material manufacturing method - Google Patents

Description

TECHNICAL FIELD The present invention relates to a method for simulating, using a computer, a fracture phenomenon of a rubber material containing a plurality of polymer components having different physical property values.

The following non-patent document 1 proposes a simulation method for evaluating the fracture properties at the interface of a polymer blend containing homopolymers A and B. In the method of Non-Patent Document 1 below, first, a bead spring model A, which is a model of homopolymer A using beads A, is set. Next, a bead spring model B, in which homopolymer B is modeled using beads B, is set. Interaction potentials are defined between beads A and A of bead spring model A and between beads B and B of bead spring model B, respectively.

Next, in the method of Non-Patent Document 1 below, a plurality of bead spring models A and B are arranged in a predetermined unit cell. In the unit cell, bead spring model A and bead spring model B are arranged in separate regions, and an interface is formed between these regions. Then, in the method of Non-Patent Document 1 below, the deformation of the unit cell is calculated, and the fracture energy and the like of the polymer blend are calculated.

Takeshi Aoyagi, "Coarse-Grained Molecular Dynamics Study", Nihon Reoroji Gakkaishi Vol.37, No.2, p75-79, 2009

In the method of Non-Patent Document 1, when the polymer model is subjected to a tensile test, fracture occurs mainly at the interface between the region where the bead spring model A is arranged and the region where a plurality of bead spring models B are arranged. phenomena are calculated. However, when an actual polymer blend is deformed, among the homopolymers A and B, fracture is observed in the polymer having a relatively small physical property value (for example, elastic modulus) indicating resistance to deformation. Therefore, the method of Non-Patent Document 1 has room for further improvement in order to accurately evaluate the fracture characteristics of polymer blends.

As a result of intensive research, the inventors have found that the interaction potential between beads A and A and the interaction potential between beads B and B are mutually calculated in consideration of the difference in physical property values of homopolymers A and B. We have found that defining as different is useful in assessing the fracture properties of polymer blends.

The present invention has been devised in view of the actual situation as described above, and a main object thereof is to provide a rubber material simulation method and the like capable of more accurately evaluating the fracture characteristics of the rubber material.

The present invention provides a method for simulating, using a computer, the destruction phenomenon of a rubber material containing at least a first polymer component and a second polymer component having predetermined physical property values different from each other, the method comprising: inputting into the computer a first polymer chain model representing the molecular chain structure of the first polymer component using a plurality of first coarse-grained particles; A step of inputting a second polymer chain model expressed using the second coarse-grained particles into the computer, and forming an interface between the first polymer chain model and the second polymer chain model defining a rubber material model in which the first polymer chain model and the second polymer chain model are arranged in a cell that is a virtual space corresponding to a part of the rubber material; a step of defining a first interaction potential for defining interaction between coarse-grained particles; and calculating a deformation of the rubber material model to generate the first interaction potential and the second interaction potential based on the difference between the first interaction potential and the second interaction potential. and calculating a fracture phenomenon at the interface based on the action potential.

In the rubber material simulation method according to the present invention, the first interaction potential and the second interaction potential include a strength parameter for defining the strength of interaction, and the second interaction potential is defined The step of determining may comprise defining a different strength parameter for the second interaction potential than for the first interaction potential.

ここで、
ｒ_ij：粒子間の距離
ｒ_ij,_cut：カットオフ距離
ε_ij：強度パラメータ
σ_ij：粒子の直径に相当 In the rubber material simulation method according to the present invention, the first interaction potential and the second interaction potential may be defined by the following equations.

here,
r _ij : Distance between particles r _ij , _cut : Cutoff distance ε _ij : Strength parameter σ _ij : Corresponding to particle diameter

In the rubber material simulation method according to the present invention, the step of defining the strength parameter includes the step of calculating the physical property value for each of a plurality of predetermined strength parameters ε _ij , and calculating the difference between the physical property values. and selecting the strength parameter ε _ij of the second interaction potential from the plurality of types of strength parameters ε _ij based on.

In the rubber material simulation method according to the present invention, the physical property value may include an elastic modulus.

The production method of the present invention includes the step of producing the rubber material based on the rubber material model evaluated as having good performance in the simulation method according to any one of claims 1 to 5. It is characterized by

The rubber material simulation method of the present invention comprises the steps of: inputting into a computer a first polymer chain model representing the molecular chain structure of a first polymer component using a plurality of first coarse-grained particles; inputting into the computer a second polymer chain model representing the molecular chain structure of the molecular component using a plurality of second coarse-grained particles. Furthermore, the simulation of the present invention includes the first polymer chain model and the second polymer chain model such that an interface is formed between the first polymer chain model and the second polymer chain model. It includes a step of defining a rubber material model in which the model is arranged in a cell, which is a virtual space corresponding to a portion of the rubber material.

The simulation method of the present invention comprises a step of defining a first interaction potential for defining interaction between the first coarse-grained particles, and a step of defining an interaction between the second coarse-grained particles. defining a second interaction potential of as being different from the first interaction potential based on the difference in physical property values between the first polymer component and the second polymer component . Thereby, the simulation method of the present invention can create the rubber material model that can consider the difference in the physical property values.

In the simulation method of the present invention, the computer calculates deformation of the rubber material model to calculate a fracture phenomenon at the interface based on the first interaction potential and the second interaction potential. contains. Thereby, the simulation method of the present invention can accurately evaluate the fracture characteristics of the rubber material containing the first polymer component and the second polymer component.

It is a perspective view showing an example of a computer for executing a rubber material simulation method. 4 is a flow chart showing an example of a processing procedure of a rubber material simulation method and a manufacturing method; 4 is a flow chart showing an example of a processing procedure of a rubber material model input step; FIG. 2 is a conceptual diagram showing an example of a cell in which a first polymer chain model, a second polymer chain model, and a cross-linking agent particle model are arranged; FIG. 2 is a conceptual diagram showing an example of a first polymer chain model and a cross-linking agent particle model; 4 is a flow chart showing an example of a processing procedure of a distribution calculation step; 4 is a graph showing an example of the distribution of the first polymer component, the distribution of the second polymer component, and the distribution of the cross-linking agent. FIG. 4 is a conceptual diagram partially enlarging a cell in which a first polymer chain model and a second polymer chain model are arranged based on the distribution of polymer components; (a) and (b) are conceptual diagrams illustrating an example of a step of connecting a pair of coarse-grained particles. FIG. 11 is a flow chart showing an example of a processing procedure of a second interaction definition step; FIG. 4 is a flow chart showing an example of a processing procedure of an intensity parameter definition step; 4 is a flow chart showing an example of a processing procedure of a physical property value calculation step; FIG. 2 is a conceptual diagram showing an example of cells in which polymer chain models are arranged; 4 is a graph showing an example of stress-strain curves calculated for each strength parameter ε _ij ; 4 is a graph showing the relationship between the difference in physical property values (Young's modulus ratio E/E _1.0 ) and the strength parameter ε _ij . (A) is a diagram showing a rubber material model (strain: 0.0), (B) is a diagram showing a rubber material model (strain: 0.12), (C) is a rubber material model (strain: 0 .30), and (D) shows a rubber material model (strain: 0.60). (A) is a diagram showing a rubber material model (strain: 0.0) of a comparative example, (B) is a diagram showing a rubber material model (strain: 0.12) of a comparative example, (C) is a comparison FIG. 12D is a diagram showing a rubber material model (strain: 0.30) of an example, and (D) is a diagram showing a rubber material model (strain: 0.60) of a comparative example. 4 is a graph showing stress-strain curves of a rubber material model of an example and a rubber material model of a comparative example.

An embodiment of the present invention will be described below with reference to the drawings.
In the rubber material simulation method of the present embodiment (hereinafter sometimes simply referred to as "simulation method"), the destruction phenomenon of the rubber material is simulated (calculated) using a computer.

FIG. 1 is a perspective view showing an example of a computer for executing a rubber material simulation method. A 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. Software and the like for executing the simulation method of this embodiment are stored in advance in the storage device.

The rubber material of this embodiment contains at least a first polymer component and a second polymer component. Examples of the first polymer component and the second polymer component include, but are not limited to, natural rubber, butadiene rubber, polyisoprene rubber, styrene-butadiene rubber, and the like.

For the first polymer component and the second polymer component, for example, polymer components different from each other are selected from among the polymer components described above. In the present embodiment, the first polymer component and the second polymer component are each selected so that they have different predetermined physical property values. Physical properties are not particularly limited. The physical property values of this embodiment include an elastic modulus (Young's modulus) that indicates deformation resistance. In this embodiment, the case where the first polymer component is butadiene rubber and the second polymer component is styrene-butadiene rubber is exemplified.

The rubber material of this embodiment contains a cross-linking agent. A cross-linking agent is exemplified by sulfur.

FIG. 2 is a flow chart showing an example of the procedure of the rubber material simulation method and manufacturing method. In the simulation method of this embodiment, first, a rubber material model is input to the computer 1 (rubber material model input step S1). FIG. 3 is a flow chart showing an example of the procedure of the rubber material model input step S1. FIG. 4 is a conceptual diagram showing an example of the cell 15 in which the first polymer chain model 3, the second polymer chain model 4, and the cross-linking agent particle model 5 are arranged. FIG. 5 is a conceptual diagram showing an example of the first polymer chain model 3 and the cross-linking agent particle model 5. As shown in FIG. FIG. 4 shows one first polymer chain model 3, one second polymer chain model 4, and two cross-linking agent particle models 5 as representatives.

In the rubber material model input step S1 of the present embodiment, first, as shown in FIGS. The first polymer chain model 3 expressed using visualization particles 7 is input to the computer 1 (step S11). The first polymer chain model 3 of this embodiment is defined as a coarse-grained model (Kremer-Grest model in this embodiment). The first polymer chain model 3 of the present embodiment includes a plurality of first coarse-grained particles 7 and a first binding chain model 8 that connects adjacent first coarse-grained particles 7, 7. It is

The first coarse-grained particles 7 are obtained by substituting a monomer (not shown) of the molecular chain of the first polymer component (butadiene rubber in this embodiment) or a structural unit forming a part of the monomer. As a result, a plurality of (for example, 10 to 5000) first coarse-grained particles 7 are set in the first polymer chain model 3 . The first coarse-grained particles 7 are treated as mass points in the equation of motion in molecular dynamics calculations described later. Therefore, parameters such as mass, volume, particle diameter D1, or charge are defined for the first coarse-grained particles 7 .

The first bond chain model 8 of the present embodiment is defined by a third interaction potential P3 between the first coarse-grained particles 7, 7 with a stretched length set. The third interaction potential P3 of the present embodiment is defined by the anharmonic potential U ^ch (r) of Equation (2) below.

ここで、各定数及び変数は、次のとおりである。
ｒ：粒子モデル間の距離
ｋ：粒子モデル間のばね定数
Ｒ₀：伸びきり長
なお、距離ｒ、及び、伸びきり長Ｒ₀は、第１粗視化粒子７の中心７ｃ（図５に示す）の座標に基づいて設定される。

Here, each constant and variable are as follows.
r: distance between particle models _k : spring constant between particle models R ₀ : stretched length ) is set based on the coordinates of

For each constant and each variable of the anharmonic potential U ^ch (r), see, for example, Article 1 (Kurt Kremer & Gary S. Grest, "Dynamics of entangled linear polymer melts: A molecular-dynamics simulation", J. Chem Phys. vol.92, No.8, 15 April 1990). As a result, in step S11, the linear first polymer chain model 3 in which the first coarse-grained particles 7 are elastically constrained can be defined. The first polymer chain model 3 is stored in the computer 1 .

Next, in the rubber material model input step S1 of the present embodiment, as shown in FIG. The second polymer chain model 4 expressed using the particles 11 is input to the computer 1 (step S12). Like the first polymer chain model 3, the second polymer chain model 4 of this embodiment is defined as a coarse-grained model. The second polymer chain model 4 of the present embodiment includes a plurality of second coarse-grained particles 11 and a second binding chain model 12 that connects adjacent second coarse-grained particles 11, 11. It is

The second coarse-grained particles 11 are obtained by substituting a monomer (not shown) of the molecular chain of the second polymer component (styrene-butadiene rubber in this embodiment) or a structural unit forming a part of the monomer. As a result, a plurality of (for example, 10 to 5000) second coarse-grained particles 11 are set in the second polymer chain model 4 . The second coarse-grained particles 11 are treated as mass points in the equation of motion in molecular dynamics calculations described later. Therefore, parameters similar to those of the first coarse-grained particles 7 are defined for the second coarse-grained particles 11 .

The second bond chain model 12 is defined by a fourth interaction potential P4 between the second coarse-grained particles 11, 11 and having a stretched length. The fourth interaction potential P4 of this embodiment is defined by the anharmonic potential U ^ch (r) of Equation (2) above. Each constant and each variable of the anharmonic potential U ^ch (r) are set in the same manner as each constant and each variable of the first polymer chain model 3 . As a result, in step S12, the linear second polymer chain model 4 in which the second coarse-grained particles 11 are elastically constrained can be defined. A second polymer chain model 4 is stored in the computer 1 .

Next, in the rubber material model input step S1 of the present embodiment, as shown in FIGS. 4 and 5, a cross-linking agent particle model 5 modeling a cross-linking agent is input to the computer 1 (step S13). The cross-linking agent particle model 5 of this embodiment is set as one independent particle model. The cross-linking agent particle model 5 is treated as a mass point of the equation of motion in molecular dynamics calculations. Therefore, parameters such as mass, volume, particle diameter D2, or electric charge are defined in the cross-linking agent particle model 5 .

The particle diameter D2 of the cross-linking agent particle model 5 can be set as appropriate. The particle diameter D2 in this embodiment is set to be the same as the particle diameter D1 of the first coarse-grained particles 7 and the second coarse-grained particles 11 . A cross-linking agent particle model 5 is stored in the computer 1 .

Next, in the rubber material model input step S1 of this embodiment, as shown in FIG. 4, the cell 15 is input to the computer 1 (step S14). The cell 15 of this embodiment is a virtual space corresponding to a part of the rubber material to be analyzed. A cell 15 is defined as a cuboid with three pairs of flat surfaces 15a, 15b facing each other. A periodic boundary condition is defined on each plane 15a, 15b. Such a cell 15 is such that, for example, the first polymer chain model 3, the second polymer chain model 4, and a part of the cross-linking agent particle model 5 exiting from one plane 15a are It can be calculated to come in from 15b. Therefore, the plane 15a on one side and the plane 15b on the opposite side can be treated as continuous (connected).

Each length L1a, L1b, and L1c of one side of the cell 15 can be set appropriately. The lengths L1a, L1b, and L1c of the present embodiment are desirably twice or more the radius of inertia (not shown), which is an amount indicating the spread of the first polymer chain model 3 and the second polymer chain model 4. As a result, in the molecular dynamics calculation, the cell 15 can prevent collisions with its own image due to periodic boundary conditions. Spatial extent can be calculated appropriately. Also, the size of the cell 15 is set to a volume that is stable at, for example, 1 atmosphere. This allows the cell 15 to define at least a partial volume of the rubber material to be analyzed. Cell 15 is stored in computer 1 .

Next, in the rubber material model input step S1 of the present embodiment, the computer 1 obtains the distribution of the components (the first polymer component, the second polymer component, and the cross-linking agent) contained in the rubber material to be analyzed. (Distribution calculation step S15). FIG. 6 is a flow chart showing an example of the processing procedure of the distribution calculation step S15.

In the distribution calculation step S15 of this embodiment, first, the χ parameters of the first polymer component, the second polymer component, and the cross-linking agent are obtained (step S61). The χ parameter is based on the Flory-Huggins theory and represents the compatibility of the first polymer component, the second polymer component, and the cross-linking agent. A smaller value of the χ parameter indicates a better solvent. At the interface formed by the first polymer component and the second polymer component, the higher the compatibility (that is, the smaller the χ parameter), the more likely they are to be in a mixed state. Conversely, the lower the compatibility (the larger the χ parameter), the more difficult it is for the first polymer component and the second polymer component to mix with each other, forming a phase-separated interface.

In step S61 of the present embodiment, a first χ parameter between butadiene rubbers, a second χ parameter between styrene-butadiene rubbers, and a third χ parameter between butadiene rubbers and styrene-butadiene rubbers are determined. Further, in step S61, a fourth χ parameter between cross-linking agents, a fifth χ parameter between butadiene rubber and cross-linking agent, and a sixth χ parameter between styrene-butadiene rubber and cross-linking agent are determined. As in the past, each χ parameter is calculated using the SUSHI modeler included in JSOL Co., Ltd.'s soft material general simulator (J-OCTA), atomic group contribution method, Monte Carlo method, molecular dynamics method, or It can be calculated based on the QSPR method. Each χ parameter is stored in computer 1 .

Next, in the distribution calculation step S15 of this embodiment, the distribution of the components (the first polymer component, the second polymer component, and the cross-linking agent) contained in the rubber material to be analyzed is obtained (step S62). In the present embodiment, a static SCF method (Self-Consistent Field Method) that considers the entropy of the arrangement of the first polymer component, the second polymer component, and the cross-linking agent is used to The distribution of the first polymer component (butadiene rubber), the distribution of the second polymer component (styrene-butadiene rubber), and the distribution of the cross-linking agent are obtained. The SCF method can be calculated using, for example, SUSHI included in JSOL Co., Ltd. Soft Material General Simulator (J-OCTA).

Input values for the SCF method include the molecular weight of the first polymer component (butadiene rubber), the molecular weight of the second polymer component (styrene-butadiene rubber), the molecular weight of the cross-linking agent, and the χ parameter (in this embodiment, the first χ parameter to sixth χ parameter) are used. As a result, in step S62, the distribution (concentration distribution) of the first polymer component (butadiene rubber), the distribution (concentration distribution) of the second polymer component (styrene-butadiene rubber), and The distribution (concentration distribution) of the cross-linking agent is determined respectively. FIG. 7 is a graph showing an example of the distribution of the first polymer component, the distribution of the second polymer component, and the distribution of the cross-linking agent. This graph shows the relationship between the volume fractions of the first polymeric component, the second polymeric component and the cross-linking agent and their spatial positions in the rubber material. The distribution of components contained in the rubber material is input to computer 1 .

Next, in the rubber material model input step S1 of the present embodiment, the computer 1 generates the first polymer chain model 3, the second polymer chain model 3, and the The molecular chain model 4 and the cross-linking agent particle model 5 are arranged in the cell 15 (step S16). In step S16 of the present embodiment, a plurality of first polymer chain models 3, a plurality of second polymer chain models 4, and a plurality of cross-linking agent particle models 5 are generated using the DBMC method (Density Biased Monte Carlo). , are placed in the cell 15 . The DBMC method can be calculated using, for example, COGNAC included in the above-mentioned soft material general simulator (J-OCTA).

The input values for the DBMC method include the distribution (concentration distribution) of the first polymer component (butadiene rubber), the distribution (concentration distribution) of the second polymer component (styrene-butadiene rubber), and the cross-linking The agent distribution (concentration distribution) is used. As a result, in step S16 of the present embodiment, based on the distribution of the first polymer component, the distribution of the second polymer component, and the distribution of the cross-linking agent (shown in FIG. 7) contained in the rubber material to be analyzed, , a plurality of first polymer chain models 3 , a plurality of second polymer chain models 4 , and a plurality of crosslinker particle models 5 can be arranged in the cell 15 . FIG. 8 is a conceptual diagram showing a partially enlarged cell 15 in which the first polymer chain model 3 and the second polymer chain model 4 are arranged based on the distribution of polymer components. In FIG. 8, the cross-linking agent particle model 5, the first bond chain model 8 and the second bond chain model 12 shown in FIG. 4 are omitted, and the second polymer chain model 4 is shown in color.

As shown in FIG. 8, in step S16, a plurality of first polymer chain models 3 (butadiene rubber) and a plurality of second polymer chain models are based on the distribution of each polymer component shown in FIG. 4 (styrene-butadiene rubber) is defined.

Next, in the rubber material model input step S1 of the present embodiment, as shown in FIG. An interaction potential is defined in which an attractive force and a repulsive force act on the coarse-grained particles 11 (step S17). The interaction potentials of this embodiment are a fifth interaction potential P5 (not shown) defined between the first coarse-grained particles 7, 7 of the pair of first polymer chain models 3, 3, and a pair of second A sixth interaction potential P6 (not shown) defined between the second coarse-grained particles 11, 11 of the polymer chain models 4, 4, and the first coarse-grained particle 7 of the first polymer chain model 3 and the second coarse-grained particles 11 of the second polymer chain model 4 . The fifth interaction potential P5 to the seventh interaction potential P7 can be defined, for example, by the LJ potential U ^LJ _ij (r) of the following equation (1).

ここで、
ｒ_ij：粒子間の距離
ｒ_ij,_cut：カットオフ距離
ε_ij：強度パラメータ
σ_ij：粒子の直径に相当
なお、距離ｒ_ij、カットオフ距離ｒ_ij,_cut、及び、粒子の直径に相当するσ_ijは、第１粗視化粒子７の中心７ｃ（図５に示す）の座標に基づいて定義される。

here,
r _ij : Distance between particles r _ij , _cut : Cut-off distance ε _ij : Strength parameter σ _ij : Corresponds to diameter of particle Note that distance r _ij , cut-off distance r _ij , _cut , and diameter of particle σ _ij is defined based on the coordinates of the center 7c (shown in FIG. 5) of the first coarse-grained particle 7 .

For each constant and each variable of the fifth interaction potential P5 to the seventh interaction potential P7, see, for example, paper 2 (Ali Makke, Michel Perez, Olivier Lame and Jean-Louis Barrat, "Mechanical testing of glassy and rubbery polymers in numerical simulations: Role of boundary conditions in tensile stress experiments” J. Chem. Phys. vol.131, 014904 (2009)). Note that each intensity parameter ε _ij of the fifth interaction potential P5 to the seventh interaction potential P7 can be set as appropriate. The strength parameter ε _ij correlates with the χ parameter of butadiene rubber and styrene-butadiene rubber. Therefore, each strength parameter ε _ij of the fifth interaction potential P5 to the seventh interaction potential P7 is desirably identified based on the χ parameter of butadiene rubber and styrene-butadiene rubber. Each intensity parameter ε _ij of the fifth interaction potential P5 to the seventh interaction potential P7 in this embodiment is set to 1.0, for example. The fifth interaction potential P5 to the seventh interaction potential P7 are stored in the computer 1. FIG.

Next, in the rubber material model input step S1 of the present embodiment, interaction potentials where attractive force and repulsive force act on the cross-linking agent particle model 5 are defined (step S18). The interaction potentials of this embodiment are the eighth interaction potential P8 defined between the pair of crosslinker particle models 5, 5, and the first coarse-grained particles of the crosslinker particle model 5 and the first polymer chain model 3. 7, and a tenth interaction potential defined between the cross-linking agent particle model 5 and the second coarse-grained particles 11 of the second polymer chain model 4. Contains P10. The eighth interaction potential P8 to the tenth interaction potential P10 can be defined using, for example, the LJ potential U ^LJ _ij (r) of the above equation (1).

The intensity parameters ε _ij of the eighth interaction potential P8 to the tenth interaction potential P10 can be set appropriately. The strength parameter ε _ij correlates with the χ parameter of the crosslinker. Therefore, the strength parameter ε _ij is desirably identified based on the χ parameter of the crosslinker. The eighth interaction potential P8 to the tenth interaction potential P10 are stored in the computer 1. FIG.

Next, in the rubber material model input step S1 of the present embodiment, the computer 1 calculates structural relaxation for the first polymer chain model 3 and the second polymer chain model 4 based on molecular dynamics calculations. (Step S19). In the molecular dynamics calculation of this embodiment, for example, the first coarse-grained particles 7 of the first polymer chain model 3 and the second coarse-grained particles of the second polymer chain model 4 are used for the cell 15 for a predetermined time. Newton's equations of motion apply, assuming that the particle 11 obeys classical mechanics. Then, the movements of the first coarse-grained particles 7 and the second coarse-grained particles 11 at each time are tracked for each unit time step.

In molecular dynamics calculations, the pressure and temperature, or the volume and temperature, are kept constant in the cell 15 . As a result, in step S19, the initial arrangement of the first polymer chain model 3 and the second polymer chain model 4 can be relaxed with high accuracy by approximating the molecular motion of the actual rubber material. In this embodiment, the initial arrangement of the first polymer chain model 3 and the second polymer chain model 4 is sufficiently relaxed. Structural relaxation calculations can be processed, for example, using COGNAC included in J-OCTA mentioned above.

In step S19 of the present embodiment, a third interaction potential P3 (shown in FIG. 5) defined between the first coarse-grained particles 7 and 7 and a third interaction potential P3 defined between the second coarse-grained particles 11 and 11 A fourth interaction potential P4 (shown in FIG. 5) is defined as the anharmonic potential U ^ch (r). As a result, in step S19, it is possible to flexibly expand and contract between the first coarse-grained particles 7 and 7 and between the second coarse-grained particles 11, so that structural relaxation can be performed smoothly. . Furthermore, the same constants and variables are used for the third interaction potential P3 and the fourth interaction potential P4 in this embodiment. Therefore, in the cell 15, it is possible to prevent the arrangement of the first polymer chain model 3 and the arrangement of the second polymer chain model 4 from being biased.

Structural relaxation for the cross-linking agent particle model 5 is not calculated in step S19 of the present embodiment. This allows the cross-linking agent particle model 5 to maintain the actual cross-linking agent distribution in the cell 15 .

Next, in the rubber material model input step S1 of the present embodiment, the computer 1 generates a pair of coarse-grained particles ( The first coarse-grained particles 7 or the second coarse-grained particles 11) are connected (step S20). In step S<b>20 of the present embodiment, a pair of coarse-grained particles (first coarse-grained particles 7 or second coarse-grained particles 11 ) are connected via a cross-linking agent particle model 5 . FIGS. 9A and 9B are conceptual diagrams illustrating an example of a process of connecting a pair of coarse-grained particles.

As shown in FIGS. 9A and 9B, in step S20, a pair of coarse grains existing within a predetermined range R (shown in FIG. 9A) from the position of the cross-linking agent particle model 5 coarse-grained particles (first coarse-grained particles 7, 7 in this example). Range R can be set as appropriate. The range R of the present embodiment is set, for example, to a region where the radius rd from the center 5c of the cross-linking agent particle model 5 is within 0.8σ.

In step S20, a pair of coarse-grained particles (first coarse-grained particles 7 and 7 in this example) are connected via a cross-linking agent particle model 5, as shown in FIG. 9(b). In the present embodiment, between one coarse-grained particle (the first coarse-grained particle 7 or the second coarse-grained particle 11) and the cross-linking agent particle model 5, and between the other coarse-grained particle (the first coarse-grained particle The visualization particles 7 or the second coarse-grained particles 11 ) and the cross-linking agent particle model 5 are connected via the third bond chain model 18 .

The third binding chain model 18 is set by the eleventh interaction potential P11. The eleventh interaction potential P11 of the present embodiment is defined by the anharmonic potential U ^ch (r) of Equation (2) above. Further, in the above equation (2), the constants and variables of the eleventh interaction potential P11 are defined, for example, in the same manner as the constants or variables of the third interaction potential P3 and the fourth interaction potential P4 shown in FIG. sell.

Thus, in step S20, a pair of coarse-grained particles (in this embodiment, the second One coarse-grained particle 7 or a second coarse-grained particle 11) is connected via a cross-linking agent particle model 5. As a result, a rubber material model 16 (shown in FIG. 4) that reproduces the crosslinked rubber material to be analyzed can be created. A rubber material model 16 is stored in the computer 1 .

As shown in FIG. 4, for the first polymer chain model 3 and the second polymer chain model 4, the third interaction potential P3 defined between the first coarse-grained particles 7 and the second A fourth interaction potential P4 defined between the coarse-grained particles 11, 11 is defined by the anharmonic potential U ^ch (r). Furthermore, the same value is set for each constant and each variable of the third interaction potential P3 and the fourth interaction potential P4. Therefore, the first polymer chain model 3 and the second polymer chain model 4 do not take into consideration the difference in physical property values between the first polymer component and the second polymer component. Therefore, the rubber material model 16 of the phase separation interface (that is, the interface where the first polymer component and the second polymer component are separated from each other) created through steps S11 to S20 can be deformed (tensile test ), similar to Non-Patent Document 1, fracture occurs at the interface between the region where the first polymer chain model 3 is arranged and the region where the second polymer chain model 4 is arranged. phenomena are calculated.

However, when the phase-separated actual rubber material containing the first polymer component and the second polymer component is deformed, the physical property value (for example, , elastic modulus) is relatively small (in this embodiment, the first polymer component).

As a result of intensive studies, the inventors have found that the interaction between the first coarse-grained particles 7, 7 and the first Defining the interaction between the two coarse-grained particles 11, 11 as different from each other is effective in evaluating the fracture properties of the actual rubber material containing the first polymer component and the second polymer component. I found out.

Based on such knowledge, in the simulation method (rubber material model input step S1) of the present embodiment, the second coarse-grained Assuming that the second interaction potential P2 for defining the interaction between the particles 11, 11 is different from the first interaction potential P1 for defining the interaction between the first coarse-grained particles 7,7 Define.

In the rubber material model input step S1 of the present embodiment, a first interaction potential P1 (shown in FIG. 4) for defining the interaction between the first coarse-grained particles 7, 7 is defined (step S21). . The first interaction potential P1 includes a strength parameter ε _ij for defining the strength of interaction and is defined by the LJ potential of equation (1) above. In step S21 of the present embodiment, the third interaction potential P3 (shown in FIG. 4) between the first coarse-grained particles 7, 7 defined by the above equation (2) is nullified, and the above equation (1) is A defined first interaction potential P1 (shown in FIG. 4) is defined.

Each constant and each variable of the first interaction potential P1 are appropriately set based on the above-mentioned article 2, for example. The strength parameter ε _ij of the first interaction potential P1 in this embodiment is set to 1.0. The first interaction potential P1 is stored in computer 1 .

Next, in the rubber material model input step S1 of the present embodiment, a second interaction potential P2 (shown in FIG. 4) for defining the interaction between the second coarse-grained particles 11, 11 is defined ( Second interaction definition step S22). The second interaction potential P2 includes a strength parameter ε _ij for defining the strength of interaction and is defined by the LJ potential of equation (1) above. In the second interaction definition step S22, the second interaction potential P1 (shown in FIG. 4) is defined as being different from the first interaction potential P1 (shown in FIG. We define the interaction potential P2. FIG. 10 is a flow chart showing an example of the processing procedure of the second interaction definition step S22.

In the second interaction definition step S22 of the present embodiment, first, the fourth interaction potential P4 (shown in FIG. 4) between the second coarse-grained particles 11 defined by the above equation (2) is disabled. and step S32 of defining the second interaction potential P2 defined by the above equation (1) (shown in FIG. 4) between the second coarse-grained particles 11, 11.

In the step S32 of the present embodiment, each constant and each variable of the second interaction potential P2 are appropriately set based on the above-mentioned article 2, for example. Note that the strength parameter ε _ij different from the first interaction potential P1 is defined in the strength parameter definition step S33, which will be _described later.

Next, in the second interaction definition step S22 of the present embodiment, a strength parameter ε _ij different from the first interaction potential P1 is defined for the second interaction potential P2 (strength parameter definition step S33). FIG. 11 is a flow chart showing an example of the processing procedure of the intensity parameter definition step S33.

In the strength parameter definition step S33 of the present embodiment, first, a physical property value is calculated for each of a plurality of types of predetermined strength parameters ε _ij (physical property value calculation step S41). FIG. 12 is a flow chart showing an example of the processing procedure of the physical property value calculation step S41. FIG. 13 is a conceptual diagram showing an example of the cell 21 in which the polymer chain model 17 is arranged.

In the physical property value calculation step S41 of the present embodiment, first, as shown in FIG. 13, a polymer chain model 17 for calculating physical property values is input to the computer 1 (step S51). Like the first polymer chain model 3 and the second polymer chain model 4 shown in FIG. and a connecting chain model 20 that connects the As the polymer chain model 17, the first polymer chain model 3 or the second polymer chain model 4 shown in FIG. 4 may be used as it is, or the first polymer chain model 3 and the second polymer chain It may be defined independently of Model 4.

The coarse-grained particles 19 are treated as mass points in the equation of motion in molecular dynamics calculations described later. Therefore, parameters similar to those of the first coarse-grained particles 7 and the second coarse-grained particles 11 shown in FIG. 4 are defined for the coarse-grained particles 19 .

Bonded chain model 20 is defined by a fifteenth interaction potential P15 set between coarse-grained particles 19,19. The fifteenth interaction potential P15 is defined by the LJ potential of the above equation (1), like the first interaction potential P1 and the second interaction potential P2 shown in FIG. Each constant and each variable of the fifteenth interaction potential P15 can be set, for example, to be the same as those of the first interaction potential P1 and the second interaction potential P2, except for the strength parameter ε _ij . . A polymer chain model 17 is stored in the computer 1 .

Next, in the physical property value calculation step S41 of this embodiment, the cell 21 is input to the computer 1 (step S52). The cells 21 of this embodiment are defined independently of the cells 15 of the rubber material model 16 shown in FIG. The cells 21 may be set to have the same size as the cells 15 of the rubber material model 16, or may be set to have different sizes. Cell 21 is stored in computer 1 .

Next, in the physical property value calculation step S41 of the present embodiment, a plurality of polymer chain models 17 are arranged in the cell 21 (step S53), and the coarse-grained particles 19 of the polymer chain models 17 are subjected to attractive forces and repulsive forces. A working sixteenth interaction potential P16 is defined (step S54). The sixteenth interaction potential P16 of this embodiment is defined between the coarse-grained particles 19, 19 of the pair of polymer chain models 17, 17, respectively. The sixteenth interaction potential P16 can be defined by the LJ potential U ^LJ _ij (r) of the above equation (1), like the fifth interaction potential P5 to the seventh interaction potential P7 (shown in FIG. 4). can.

Each constant and each variable of the sixteenth interaction potential P16 are appropriately set based on, for example, Paper 2 above. The strength parameter ε _ij of the sixteenth interaction potential P16 in this embodiment is set to 1.0. The sixteenth interaction potential P16 is stored in computer 1 .

Next, in the physical property value calculation step S41 of the present embodiment, the computer 1 calculates structural relaxation for the polymer chain model 17 based on molecular dynamics calculations (step S55). The molecular dynamics calculation is as described above. In this embodiment, the initial arrangement of the polymer chain model 17 is performed until it is sufficiently relaxed. As a result, a rubber material model (hereinafter sometimes simply referred to as "single rubber material model") 22 that models a rubber material containing a single polymer component is defined.

Next, in the physical property value calculation step S41 of the present embodiment, the computer 1 calculates physical property values for each of a plurality of predetermined strength parameters ε _ij (step S56). In step S56, elongation calculation of the single rubber material model 22 is performed for each of a plurality of types of strength parameters ε _ij set to the fifteenth interaction potential P15 of the polymer chain model 17, and physical property values are calculated.

A plurality of types of intensity parameters ε _ij can be appropriately set, for example, based on the difference in physical property values between the first polymer component and the second polymer component. As an example of the strength parameter ε _ij , the strength parameter ε _ij (for example, 1.0) when there is no difference in physical property values between the first polymer component and the second polymer component is Multiple settings (e.g., ε _ij =1.0, 1.2, 1.4, 1.6) among strength parameters ε _ij (e.g., 2.4) that increase the difference in physical property values from the two polymer components , 1.8, 2.0, 2.2 and 2.4). Note that the strength parameter ε _ij is not limited to such a mode.

In step S56, first, one strength parameter ε _ij selected from a plurality of types of strength parameters ε _ij is defined as the fifteenth interaction potential P15 of the polymer chain model 17 . Next, in step S56, a deformation simulation is performed by stretching the single rubber material model 22 in one direction (for example, 0% to 50% in the Y-axis direction) based on a uniaxial tensile test, and its physical property value ( In this embodiment, the elastic modulus) is calculated. The deformation simulation can be performed in the same procedure as the rubber material simulation method using the rubber material model 16, which will be described later.

In step S56, physical property values are calculated for each of the plurality of set strength parameters ε _ij . FIG. 14 is a graph showing an example of a stress-strain curve calculated for each strength parameter ε _ij . FIG. 14 representatively shows only intensity parameters ε _ij of 1.0, 1.6, and 2.4. FIG. 15 is a graph showing the relationship between the physical property value difference (Young's modulus ratio E/E _1.0 ) and the strength parameter ε _ij . The Young's modulus ratio E/E _1.0 indicates the ratio of the Young's modulus E _1.0 for the strength parameter ε _ij =1.0 to the Young's modulus E for the other strength parameter ε _ij . Physical property values calculated for each of the plurality of types of intensity parameters ε _ij are stored in the computer 1 .

Next, as shown in FIG. 11, in the strength parameter definition step S33 of the present embodiment, a plurality of types of strength parameters ε _ij (eg, ε _ij =1.0, 1.2) are calculated based on differences in physical property values. , 1.4, 1.6, 1.8, 2.0, 2.2, and 2.4), select the strength parameter ε _ij of the second interaction potential P2 (step S42). In step S42, first, the actual difference in physical property values between the first polymer component and the second polymer component is obtained. As the difference in the physical property value ₍ elastic modulus), the ratio E2 _/ E1 between the Young's modulus E1 of the _first polymer component and the Young's modulus E2 of the _second polymer component is obtained. The Young's modulus E ₁ of the first polymer component and the Young's modulus E ₂ of the second polymer component are, for example, in accordance with the test method described in JISK6251 "Vulcanized rubber and thermoplastic rubber - Determination of tensile properties". Tensile properties are determined and can be determined from the ratio of the tensile stress within the range in which the stress varies linearly with strain (ie, the range in which a linear response is obtained) to the corresponding strain.

Next, in step S42 of the present embodiment, in the graph of _FIG . ₁₅ , there is An intensity parameter ε _ij is chosen. In the graph of FIG. 15, for example, when the difference in physical property values (Young's modulus ratio E ₂ /E ₁ ) is 2.5, the strength parameter ε _ij =2.0 is selected.

Next, in the strength parameter definition step S33 of the present embodiment, the selected strength parameter (ε _ij =2.0 in this example) is defined for the second interaction potential P2 (shown in FIG. 4) ( step S43). The strength parameter ε _ij =2.0 is different from the strength parameter ε _ij =1.0 of the first interaction potential P1 (shown in FIG. 4). Thus, in the second interaction definition step S22, the second interaction potential P2 is defined as the difference in physical property values between the first polymer component and the second polymer component (in this embodiment, the ratio of Young's modulus E ₂ / E ₁ ) can be defined as different from the first interaction potential P1. Therefore, the simulation method (rubber material model input step S1) of the present embodiment uses the rubber material model 16 (Fig. 4 shown) can be created. A rubber material model 16 is stored in the computer 1 .

In the rubber material model input step S1 of the present embodiment, after the second interaction definition step S22, the computer 1 generates the first polymer chain model 3 and the second polymer chain model 3 shown in FIG. 4 based on molecular dynamics calculations. It is desirable to calculate the structural relaxation for the molecular chain model 4. As a result, the degree of aggregation between molecules, the size of the cell 21, the density in the cell 21 (that is, the number of particles in the cell 21/ Even if the size of the cells 21 changes, a balanced structure can be created based on the new second interaction potential P2, so the cells 21 can be made to have an appropriate density. In this embodiment, NPT (N: number of particles, P: pressure, T: temperature) desirably undergoes structural relaxation under constant conditions, and the pressure in the cell 15 is zero (or any value close to zero). It is desirable that the structural relaxation is calculated so that This makes it possible to avoid different initial stresses between structures with different potentials, and enables stress comparison between structures with different interface states.

In the rubber material model input step S1 of the present embodiment, the cross-linking agent particle model 5 that models the cross-linking agent is placed in the cell 15, but it is not limited to such a mode. In the rubber material model input step S1 of this embodiment, the cross-linking agent particle model 5 (shown in FIGS. 4 and 5) may be omitted. In this case, in step S20, it is desirable to connect the pair of coarse-grained particles (the first coarse-grained particles 7 or the second coarse-grained particles 11) without using the cross-linking agent particle model 5. A filler model (not shown) that models a filler compounded in the rubber material may be arranged in the cell 15 . Thereby, the rubber material model 16 that reproduces the rubber material containing the filler can be created.

Next, in the simulation method of this embodiment, the computer 1 calculates the deformation of the rubber material model 16 shown in FIG. 4 (hereinafter sometimes simply referred to as "deformation calculation") (step S2). As deformation calculation of the rubber material model 16, for example, tensile deformation, compression deformation, or the like can be appropriately selected. In the deformation calculation of this embodiment, tensile deformation is performed.

In step S2, the tensile deformation of the rubber material model 16 is calculated with the one end 16a and the other end 16b of the rubber material model 16 separated in the Y-axis direction. In the present embodiment, for example, similar to the method described in JP-A- ^2016-81297 , the rubber material model 16 is subjected to tensile deformation based on affine deformation. In step S2, the thermal motion (molecular motion) of the first polymer chain model 3, the second polymer chain model 4, and the cross-linking agent particle model 5 are calculated.

Next, in the simulation method of this embodiment, the stress of the rubber material model 16 is calculated (step S3). In step S3, the stress of the rubber material model 16 is calculated per unit time based on the strain given in step S2. Furthermore, in step S3, the movements of the first coarse-grained particles 7, the second coarse-grained particles 11, and the cross-linking agent particle model 5 calculated by the tensile deformation of the rubber material model 16 are tracked for each unit time. be. FIG. 16A is a diagram showing a rubber material model (strain: 0.0). FIG. 16B is a diagram showing a rubber material model (strain: 0.12). FIG. 16C is a diagram showing a rubber material model (strain: 0.30). FIG. 16(D) is a diagram showing a rubber material model (strain: 0.60).

In step S3, the heat of the first polymer chain model 3, the second polymer chain model 4, and the cross-linking agent particle model 5 is generated based on the strain given to the rubber material model 16, each interaction potential, and the equation of motion. Movement is calculated. By calculating these thermal motions, a small region in which the first polymer chain model 3, the second polymer chain model 4, and the cross-linking agent particle model 5 (not shown) do not exist is formed in the cell 15. be done. Such small regions are defined as voids 24 formed in the rubber material model 16 .

As shown in FIGS. 16A to 16D, in the deformation calculation of this embodiment, in the first polymer chain model 3 defined with a smaller strength parameter ε _ij than the second polymer chain model 4, The phenomenon of fracture (cavity 24) was calculated. This matches the destruction phenomenon of actual rubber materials. Therefore, in the simulation method of the present embodiment, the rubber material model 16 created in the rubber material model input step S1 is used in the simulation for performing the deformation calculation, so that the first polymer component and the second polymer component are Fracture properties of the rubber material containing can be evaluated with high accuracy. Each coordinate value of the stress of the rubber material model 16 , the first polymer chain model 3 , the second polymer chain model 4 , and the cross-linking agent particle model 5 is stored in the computer 1 .

Next, in the simulation method of this embodiment, the performance of the rubber material is evaluated based on the deformation calculation result of the rubber material model 16 (step S4). In step S4 of the present embodiment, for example, the strength of the rubber material is evaluated based on the stress-strain curve calculated based on the deformation result of the rubber material model 16, the growth curve of the voids 24, and the like. be.

In the present embodiment, when the performance of the rubber material (deformation calculation result) is evaluated as good ("Y" in step S4), the rubber material is manufactured based on the rubber material model 16 (step S5). On the other hand, if it is determined that the performance of the rubber material is not good (“N” in step S4), various conditions of the rubber material are changed (step S6), and based on the procedure shown in FIG. The material model 16 is recreated (step S7), and steps S1 to S4 are performed again. As described above, in the simulation method and the manufacturing method of the present embodiment, various conditions of the rubber material are changed until the performance of the rubber material becomes good, so that a rubber material having good strength (fracture characteristics) can be obtained. , can be efficiently manufactured.

Although the particularly preferred embodiments of the present invention have been described in detail above, the present invention is not limited to the illustrated embodiments and can be modified in various ways.

A rubber material model for numerical analysis of a rubber material containing at least a first polymer component and a second polymer component having predetermined physical property values different from each other was created (Example, Comparative Example).

In Examples and Comparative Examples, a first polymer chain model expressing the molecular chain structure of the first polymer component using a plurality of first coarse-grained particles, and a plurality of molecular chain structures of the second polymer component were used. was input into the computer. A first interaction potential for defining the interaction between the first coarse-grained particles was defined in the first polymer chain model. A second interaction potential was defined in the second polymer chain model to define the interaction between the second coarse-grained particles. Furthermore, in Examples and Comparative Examples, a cross-linking agent particle model modeling a cross-linking agent was input into the computer.

Then, in the examples and comparative examples, the first polymer chain model, the second polymer chain model, the second polymer chain model, and the second polymer chain model based on the distribution of the first polymer component, the distribution of the second polymer component, and the distribution of the cross-linking agent shown in FIG. A molecular chain model and a cross-linking agent particle model were placed in a cell to create a rubber material model.

The second interaction potential of the example is calculated based on the difference in physical property values between the first polymer component and the second polymer component according to the processing procedure of the strength parameter definition step shown in FIG. defined as different from potential. On the other hand, the second interaction potential of the comparative example was the same as the first interaction potential without considering the difference in physical property values. Then, the tensile deformation of the rubber material models of Examples and Comparative Examples was calculated. Common specifications are as follows.

First and second polymer chain models:
Number of first and second coarse-grained particles (chain length): 200
Each number: 40
Third and fourth interaction potentials:
Spring constant k between particle models: 30 [ε/σ ² ]
Stretched length R ₀ : 1 [σ]
Crosslinker particle model: 229 cells:
Volume: 16229 [σ ³ ]
Example density: 0.94 [/σ ³ ]
Density of Comparative Example: 0.87 [/σ ³ ]
Crosslink density: 0.01 [σ ³ ]
5th to 10th interaction potentials:
Cutoff distance r _ij , _cut : 2.5 [σ]
Strength parameter ε _ij : 1.0 [ε]
Eleventh interaction potential:
Spring constant k between particle models: 30 [ε/σ ² ]
Stretched length R ₀ : 1 [σ]
Strength parameter definition step:
Polymer chain model:
Number of coarse-grained particles (chain length): 200
Number of molecules: 40
Fifteenth interaction potential:
Spring constant k between particle models: 30 [ε/σ ² ]
Stretched length R ₀ : 1 [σ]
strength parameter ε: 1.0, 1.2, 1.4, 1.6,
1.8, 2.0, 2.2, 2.4 [ε]
Sixteenth interaction potential:
Cutoff distance r _ij , _cut : 2.5 [σ]
Strength parameter ε _ij : 1.0 [ε]
Corresponding to particle diameter σ _ij : 1 [σ]
First interaction potential:
Intensity parameter ε _ij : 1 [ε]
Cutoff distance r _ij , _cut : 2.5 [σ]
Corresponding to particle diameter σ _ij : 1 [σ]
Second interaction potential:
Strength parameter ε _ij (Example): 2 [ε]
Strength parameter ε _ij (comparative example): 1 [ε]
Cutoff distance r _ij , _cut : 2.5 [σ]
Corresponding to particle diameter σ _ij : 1 [σ]
Calculation condition:
Time step (unit time): 0.006 [τ]
Total time: 6000 [τ]
Strain rate: 0.0001 [1/τ]
Maximum strain: 0.6
Poisson's ratio: 0

FIG. 17A is a diagram showing a rubber material model (strain: 0.0) of a comparative example. FIG. 17B is a diagram showing a rubber material model (strain: 0.12) of a comparative example. FIG. 17C is a diagram showing a rubber material model (strain: 0.30) of a comparative example. FIG. 17D is a diagram showing a rubber material model (strain: 0.60) of a comparative example. In the comparative example, a phenomenon in which fracture occurs mainly at the interface between the region in which the first polymer chain model 3 is arranged and the region in which the second polymer chain model 4 is arranged was calculated, and the actual fracture of the rubber material was calculated. did not match the phenomenon.

On the other hand, in the example, as shown in FIGS. 16(A) to 16(D), the first polymer chain model 3 defined with a smaller strength parameter ε _ij than the second polymer chain model 4 was arranged. In the region, the phenomenon of destruction (cavities 24 are generated) was calculated, which matched the actual destruction phenomenon of the rubber material.

FIG. 18 is a graph showing stress-strain curves of the rubber material model of Example and the rubber material model of Comparative Example. The calculated Young's modulus of the example is larger than that of the comparative example. This approximates the trend of Young's modulus of actual rubber materials.

Thus, it was confirmed that the rubber material model of the example can accurately evaluate the fracture characteristics of the rubber material containing the first polymer component and the second polymer component by using the simulation for performing deformation calculation. did it.

S11 Step of inputting the first polymer chain model S12 Step of inputting the second polymer chain model S21 Step of defining the first interaction potential S22 Step of defining the second interaction potential

Claims (6)

A method for simulating, using a computer, the destruction phenomenon of a rubber material containing at least a first polymer component and a second polymer component having predetermined differences in physical property values, comprising:
inputting into the computer a first polymer chain model representing the molecular chain structure of the first polymer component using a plurality of first coarse-grained particles;
inputting into the computer a second polymer chain model representing the molecular chain structure of the second polymer component using a plurality of second coarse-grained particles;
The first polymer chain model and the second polymer chain model are part of the rubber material so that an interface is formed between the first polymer chain model and the second polymer chain model. A step of defining a rubber material model placed in a cell, which is a virtual space corresponding to
defining a first interaction potential for defining interactions between the first coarse-grained grains;
defining a second interaction potential for defining an interaction between the second coarse-grained particles as being different from the first interaction potential based on the difference in the physical property value;
the computer calculating deformation of the rubber material model to calculate a fracture phenomenon at the interface based on the first interaction potential and the second interaction potential;
How to simulate rubber materials. said first interaction potential and said second interaction potential comprising a strength parameter for defining the strength of the interaction;
2. The method of simulating a rubber material according to claim 1, wherein the step of defining said second interaction potential comprises defining said strength parameter for said second interaction potential that is different from said first interaction potential. 3. The rubber material simulation method according to claim 2, wherein said first interaction potential and said second interaction potential are defined by the following equations.

here,
r _ij : Distance between particles r _ij , _cut : Cutoff distance ε _ij : Strength parameter σ _ij : Corresponding to particle diameter The step of defining the strength parameter is a step of calculating the physical property value for each of a plurality of predetermined types of the strength parameter _εij ;
4. The rubber material simulation method according to claim 3, further comprising the step of selecting said strength parameter ε _ij of said second interaction potential from said plurality of types of said strength parameter ε _ij based on the difference in said physical property value. . 5. The method of simulating a rubber material according to claim 1, wherein said physical property value includes an elastic modulus. 6. The rubber material simulation method according to any one of claims 1 to 5, comprising the step of manufacturing the rubber material based on the rubber material model evaluated as having good performance,
A method of manufacturing a rubber material.

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