JP2020177375A - Method for creating composite material, method for analyzing composite material, and computer program for analyzing composite material - Google Patents

Abstract

To efficiently create a model for analyzing a composite material in a method different from conventional methods when creating a composite material model.SOLUTION: A computer creates a composite material model by a molecular dynamics method. The composite material has a configuration containing particles in a base material of the composite material. A group of particle models created by modeling the particles is initially arranged in a model creation region for modeling the composite material. Locations of a plurality of particle models in the group of initially arranged particle models are modified till the locations meet preset conditions by performing calculation for moving the plurality of particle models on the basis of force of interaction acting between the particle models by using the molecular dynamics method. Then, a model for analyzing the composite material is created on the basis of the locations of the particle models meeting the conditions.SELECTED DRAWING: Figure 1

Description

The present invention relates to a method for creating a model of a composite material by a molecular dynamics method using a computer, a method for analyzing a composite material, and a computer program for analyzing the composite material.

Conventionally, various numerical analyzes by molecular dynamics have been proposed in order to elucidate the mechanism of fracture of nanostructures of composite materials such as rubber materials.
In order to perform numerical analysis by molecular dynamics, it is necessary to create an analysis model that reproduces a composite material such as a rubber material so that numerical analysis can be performed by the molecular dynamics method. A composite material such as a rubber material has a structure in which predetermined filler particles are distributed in a base material in order to enhance the function of the composite material. Therefore, in the analysis model, a plurality of particle models that model the filler particles are arranged in the base material model in which the base material is modeled, corresponding to the structure in which the particles are distributed in the base material of the composite material. ..

On the other hand, a technique for effectively creating a model of a composite material in which particles are dispersed in a matrix material (base material) is known (Patent Document 1).
According to this technology, after setting a virtual potential created by two particle models and creating a composite material model in which a plurality of particle models are arranged in a matrix material model, the virtual potential acting between the plurality of particle models The values are totaled to calculate the value of total potential energy. After that, when one particle model is temporarily moved, the value of the total potential energy after the temporary movement is calculated, and the value of the total potential energy after the temporary movement is lower than the value of the total potential energy before the temporary movement, A modified composite material model is generated in which the temporary movement is defined as the main movement of the particle model and the arrangement of the particle model is modified. The calculation and comparison of the total potential energy values before and after the temporary movement are repeated until the modified composite material model satisfies the predetermined conditions. The modified composite material model when the predetermined conditions are satisfied is defined as the final model.
It is said that this makes it possible to create a model of a composite material having a structure in which a plurality of particle models are connected in a chain shape.

Japanese Patent No. 5169225

By the way, in the above method, every time one particle model is temporarily moved, the calculation for determining the main movement is repeated for each particle model by searching for whether or not the total potential energy is reduced, so that the number of repetitions of the calculation is very large. It takes a long time to find a composite material model that satisfies the predetermined conditions.
In addition, the above-mentioned technique may not be able to reproduce a particle arrangement under severe conditions such that the particle model aggregates to reproduce a structure close to close-packed.

Therefore, an object of the present invention is to use a composite material model creation method and a created model that can efficiently create a composite material analysis model by a method different from the conventional method when creating a composite material model. It is an object of the present invention to provide a computer program for analyzing a composite material that can execute a method for analyzing the composite material and a method for creating a model.

One aspect of the present invention is a method in which a computer creates a model of a composite material by a molecular dynamics method.
The composite material has a structure in which particles are contained in the base material of the composite material.
The method is
A step of initially arranging a group of particle models that model the particles in the model creation region that models the composite material, and
The particle model is calculated by moving a plurality of particle models in the initially arranged group of particle models based on the force of interaction acting between the particle models using molecular dynamics method. The step of modifying the position of the particle model until the position of is satisfies the preset condition, and
A step of creating an analysis model of the composite material based on the position of the particle model that satisfies the above conditions, and
To be equipped.

It is preferable that the interaction exerts an attractive force between the particle models.

It is also preferred that the interaction exerts a repulsive force between the particle models.

The exclusion volume region in which the exclusion volume effect that prohibits the proximity of other particle models to a part of the particle model group is excluded in the other part of the particle model group. It is preferable to impart a volume removal region to the part of the particle model so as to be different from the volume region.

In the step of correcting the position of the particle model, it is preferable to prohibit the movement or the correction of the position of the particle model at a predetermined position in the group of the particle models.
In the step of correcting the position of the particle model, when the position of the particle model in which the regions overlap with each other in the group of the particle models becomes a non-overlapping state, the position of the particle model is changed to the position of the non-overlapping state. It is also preferable to fix the particle model to prohibit the movement or modification of the position of the particle model.

In the method of creating a model of the composite material, at least one particle model placeable region for arranging the group of the particle models in the analysis model is modeled before the step of initially arranging the particle model. It is preferable to include a step to be set in the creation area.

It is preferable that the group of the particle models is initially arranged in the particle model displaceable region.

It is preferable to impart an interaction that generates a force between each of the particle models in the particle model placeable region and the outer edge that partitions the particle model placeable area.

It is preferable that the force generated between each of the particle models and the outer edge of the particle model displaceable region is a repulsive force.

In the step of correcting the position of the particle model, the position of the particle model is determined according to the moving distance and the moving direction by obtaining the moving distance and the moving direction of the particle model by dividing the position at a preset time interval. Repeatedly correct to the fixed position,
When the position of the particle model is repeatedly modified, the out-of-region moving particle model in which the planned moving destination determined by the moving distance and the moving direction is outside the particle model arrangable region is the particle model. It is rearranged so that it is located within the placeable area.
At this time, the straight line passing through the crossing point where the moving particle model outside the region crosses the outer edge of the particle model arrangable region and the center point of the particle model arrangable region intersects with the outer edge of the particle model arrangable region. A position moved in a direction parallel to the moving direction by the distance between the crossing point and the planned moving destination from the crossing corresponding point on the opposite side of the crossing point when viewed from the center point. It is preferable that the rearrangement position of the out-of-region moving particle model is set.

In the step of correcting the position of the particle model, the position of the particle model is determined according to the moving distance and the moving direction by obtaining the moving distance and the moving direction of the particle model by dividing the position at a preset time interval. Repeatedly correct to the fixed position,
It is preferable that the size of the particle model dispositionable region is intermittently or continuously narrowed as the position of the particle model is repeatedly corrected.

When calculating the movement of the particle model using the molecular dynamics method, it is preferable to impart a resistance force that suppresses the movement of the particle model to the particle model in the particle model displaceable region.

The particle model is a filler particle model that models filler particles, and the region between the particle model and the particle model displaceable region is a first base material model that models the first base material, and the particles. The outer region surrounding the model-arrangeable region further includes a step of creating an analysis model of the composite material as a second base material model in which the second base material is modeled, in the model creation method of the composite material. Is preferable.

Another aspect of the present invention includes a step of creating the analysis model of the composite material by the method of creating the model of the composite material.
The step that the computer performs numerical analysis by the molecular dynamics method using the analysis model,
It is a method for analyzing a composite material, which is characterized by the above.

Yet another aspect of the present invention is a computer program for analyzing a composite material, which comprises causing a computer to execute the method for creating a model of the composite material.

According to the above-mentioned method for creating a model of a composite material, a method for analyzing a composite material, and a computer program for analyzing a composite material, a model for analyzing a composite material can be efficiently created.

It is a figure explaining an example of the main part of the flow of the model making method of the composite material of one Embodiment. It is a figure which shows an example of the filler model which aggregated the filler particle model created by the method of making a model of a composite material of one Embodiment. (A) is a figure explaining a particle model placeable region and a particle model, and (b) is a figure explaining an example of the initial arrangement of a filler particle model. It is a figure which shows an example of the movement of the filler particle model calculated by the model making method of the composite material of one Embodiment. (A) is a diagram showing an example in which different exclusion volume regions are given to the potential distribution used in the method for creating a model of a composite material of one embodiment, and (b) is a diagram showing an example of creating a model of a composite material of one embodiment. It is a figure explaining the example of the exclusion volume region given to the filler particle model in. (A) is a diagram showing an example in which the filler particle model performed by the method for creating a model of a composite material of one embodiment moves by a force received from an outer edge, and (b) is a diagram showing an example of moving a model of a composite material of one embodiment. It is a figure explaining the example of the relocation performed in. It is a figure explaining the example of the analysis model created by the model creation method of the composite material of one Embodiment. It is a figure explaining the example of the analysis model created by the model creation method of the composite material of one Embodiment. It is a functional block diagram of the analysis apparatus which performs the analysis method of the composite material of one Embodiment.

Hereinafter, a method for creating a model of a composite material, a method for analyzing a composite material, and a computer program for analyzing the composite material according to the embodiment of the present invention will be described with reference to the attached figures.

FIG. 1 is a diagram showing an example of a main part of the flow of the method for creating a model of a composite material of one embodiment. The composite material for which the analysis model is created in the embodiment has a configuration in which particles are contained in the base material of the composite material.
In the model creation method shown in FIG. 1, a model of a composite material is created by a molecular dynamics method using a computer. That is, the computer creates a model of the composite material. As shown in FIG. 1, the method for creating a model of this composite material includes a step of setting a particle model placeable region (ST10), a step of initially arranging a group of particle models (ST12), and an interaction between the particle models. (ST14), the step of calculating the movement of the particle model using molecular dynamics (ST16), the step of correcting the position of the particle model (ST16), and the position of the particle model are set. It mainly includes a step (ST20) for determining whether or not the above conditions are satisfied, and a step (ST20) for determining whether or not there is a problem in arranging the particle model.

The base material of the composite material is, for example, a polymer (polymer material). The particles in the base material are, for example, filler particles added to the base material which is a raw material. In the following description, a polymer will be used as a base material, and a form in which filler particles are distributed in the polymer will be described as an example. The form of the base material of the composite material may be a blend polymer composed of a plurality of types of polymers in addition to the forms described below. For example, a blend polymer having a sea-island structure and a lamella structure can be mentioned. The blended polymer may consist of a crystalline polymer and a non-crystalline polymer. Further, as the base material, a form having a hard segment phase and a soft segment phase in one molecule, such as a thermoplastic elastomer, can also be mentioned.

In a composite material containing filler particles, the filler particles are distributed in the base material, and the filler particles aggregate with each other in a state close to close-packing, for example, to form a substantially spherical mass. A plurality of such lumps are distributed in the base metal. Alternatively, they are chained together to form an elongated shape. In the following description, a method of creating a model of a composite material will be described using a form in which filler particles aggregate with each other to form a substantially spherical mass.

FIG. 2 is a diagram showing an example of a filler model in which the filler particle model created by the method for creating a model of a composite material of one embodiment is aggregated. FIG. 2 shows filler models 11A to 11D that reproduce a structure in which a group of filler particles is aggregated and agglomerated in a state close to close-packed. The filler particles include, for example, carbon black particles, silica particles, alumina particles, and the like. The filler particle model is a model of an aggregate of atoms constituting a plurality of fillers.
In the creation of the analysis model, in the example shown in FIG. 2, the analysis model 1 having the filler models 11A to 11D is created in the model creation region A for modeling the composite material. The model creation area A is a virtual space having a substantially rectangular parallelepiped shape, but may have any shape such as a spherical shape, an elliptical shape, a rectangular parallelepiped shape, or a polyhedral shape.

The computer first sets the particle model placement area (ST10).
This particle model placeable region is a region in which a group of filler particles is arranged in the analysis model. The particle model displaceable region is used, for example, as a region for creating a filler model that aggregates into a mass close to close-packed state. The particle model placeable region is set in the model creation region A that models the composite material. FIG. 3A is a diagram illustrating the particle model dispositionable region 12 and the filler particle model 11a. In FIG. 3A, a model creation region A is set on a two-dimensional plane for easy understanding, and a filler particle model 11a is arranged in the model creation region A on this plane.
In the example shown in FIG. 3A, two particle model arrangable regions 12 are set in the model creation region A. The two particle model dispositionable regions 12 are regions for creating the two filler models 11A to 11D shown in FIG. In the example shown in FIG. 3A, two particle model dispositionable regions 12 are set, but the number of settings is not limited to two, and may be one or three or more. As shown in FIG. 2, when four filler models 11A to 11D are created, four particle model dispositionable regions 12 are set. The shape of the particle model displaceable region 12 shown in FIG. 3A is a perfect circle shape, but may be an elliptical shape, a rectangular shape, or a polyhedral shape, and the shape is not particularly limited.

The computer then initially places a group of particle models (ST12). That is, the group of the filler particle model 11a that models the filler particles is initially arranged in the model creation region A that models the composite material. As shown in FIG. 3A, the filler particle model 11a is arranged in each of the two particle model displaceable regions 12. In the example shown in FIG. 3A, four filler particle models 11a are arranged in one particle model placeable region 12 and five filler particles are arranged in the other particle model placeable region 12 for easy understanding. The model 11a is arranged. The number of filler particle models 11a to be arranged is not particularly limited, but the number required to create a filler model having a structure close to close-packed may be initially arranged. The initial arrangement of the filler particle model 11a may be randomly arranged or arranged at regular intervals, and the method of arrangement is not particularly limited.

The filler particle model 11a initially arranged is not limited to a model that reproduces filler particles having the same particle size, and may include a filler particle model that models filler particles having different particle sizes. In this case, the size of the filler particle model 11a and the potential distribution expressing the interaction described later are different.

Further, as shown in FIG. 3B, in the filler particle model 11a, the filler particle models 11a may overlap each other in the initial arrangement. FIG. 3B is a diagram illustrating an example of the initial arrangement of the filler particle model 11a. Even if such overlaps occur, the filler particle models 11a can be moved so as to be separated from each other by using the molecular dynamics method described later.

Next, the computer sets the interaction between the filler particle models 11a (ST14). Specifically, the filler particle model 11a is defined in the computer by numerical data including mass, volume, diameter, and position coordinates, and calculates the movement of the filler particle model 11a using the molecular dynamics method. Therefore, the interaction between the filler particle models 11a is set. The interaction is defined by the Lennard-Jones potential shown in the following equation as an example. Further, when reproducing a chain-like connected structure, for example, a dipole potential is used as the potential that defines the interaction.

In a general interaction between filler particles, a repulsive force acts when the filler particles are at a short distance, and an attractive force acts when the filler particles are at a long distance. Therefore, the Lennard-Jones potential is preferable so that such a force acts. Used for. Therefore, as shown in FIG. 3B, even if the filler particle models 11a occupy the same space in an overlapping manner, the filler particle models 11a can be moved so as to be separated from each other by the repulsive force due to the interaction. ..

Next, the computer performs a calculation to move a plurality of particle models in the initially arranged group of filler particle models 11a based on the force of interaction acting between the particle models 11a using molecular dynamics. Do (ST16).
Each of the filler particle models 11a is defined by mass and position coordinates in the computer, and each filler particle model 11a receives an interaction force from the other surrounding filler particle model 11a. Therefore, each filler particle model 11a starts moving according to the equation of motion from the received force and mass. The movement of the filler particle model 11a can be calculated by dividing the movement of the filler particle model 11a at predetermined time intervals (divided at each predetermined time interval) to obtain the movement distance and the movement direction of each filler particle model 11a. Further, the force received by each filler particle model 11a from the other filler particle model 11a also changes with the movement of the other filler particle model 11a. Therefore, the computer calculates the moving distance and the moving direction of each filler particle model 11a by dividing them at predetermined time intervals. FIG. 4 is a diagram showing an example of movement of each filler particle model 11a. In FIG. 4, the moving direction and the moving distance are represented by the direction in which the arrow points and the length of the arrow.

Next, the computer corrects the position of the filler particle model 11a by using the calculation result (movement distance and movement direction) of the movement of the filler particle model 11a (ST18).
In the modification of the position of the filler particle model 11a, when the position of the moving destination determined by the moving distance and the moving direction is within the particle model arrangable region 12, the position of the filler particle model 11a is corrected to the position of the moving destination. Further, when the position of the moving destination determined by the moving distance and the moving direction is outside the particle model arrangable region 12, the moving destination is corrected so as to be located inside the particle model arrangable region 12. The method of modification in this case is not particularly limited, but can be modified by a preferred method described later. The preferred modification method will be described later.

Next, the computer determines whether or not the modified arrangement of the filler particle model 11a satisfies a predetermined condition (ST20). The predetermined conditions are, for example, that there is no overlapping portion between the filler particle models 11a, the ratio of the volume of the overlapping portion to the volume of the filler particle model 11a is smaller than a predetermined threshold value even if there is overlap, and the filler. This includes that the closest contact distance between the surfaces of the particle models 11a is within a predetermined range, and that the number (or size) of aggregates that the filler particle models 11a are in contact with and becomes agglomerates is within a predetermined range.
Until these conditions are satisfied, the calculation of moving the filler particle model 11a using the molecular dynamics method and the correction of the position of the filler particle model 11a are repeated.

Next, the computer requests the computer operator to input whether or not the arrangement of the filler particle model 11a satisfying the predetermined conditions is an arrangement acceptable to the computer operator, and if the input is not acceptable, the computer is required to input. Further, the calculation of moving the filler particle model 11a and the correction of the position of the filler particle model 11a are repeated. If the input is acceptable, the placement of the filler particle model 11a is fixed and the placement of the filler particle model 11a used in the analysis model 1 is determined.
After that, the computer arranges a polymer particle model that models a polymer (polymer material) as a base material in a region other than the filler particle model 11a in the model creation region A.

As described above, in the method for creating the composite material model of the above-described embodiment, the plurality of filler particle models 11a are simultaneously moved by the interaction force determined by the potential by using the molecular dynamics method. It is possible to efficiently create an analysis model in which the arrangement of the filler particle model 11a is determined in a short time.

According to one embodiment, the interaction preferably exerts an attractive force between the filler particle models 11a. Thereby, a structure for agglutinating the filler particle model 11a can be easily created.
Also, according to one embodiment, the interaction preferably exerts a repulsive force between the filler particle models 11a. Thereby, a structure for dispersing the filler particle model 11a can be easily created. Of course, one of attractive force and repulsive force may act depending on the separation distance, such as Lennard-Jones potential.

According to one embodiment, the computer may include some of the filler particle models 11a in the group of filler particle models 11a in some of the particle models so that they differ from the exclusion volume region in some other particle models. It is preferable to provide a volume removal region. Here, the leaf tail volume region refers to a region in which the excluded volume effect that prohibits the proximity of other particle models to a part of the particle models in the group of particle models works.
The filler particles modeled may include filler particles of the same material but different particle sizes, or may include filler particles of different materials but different particle sizes. When the particle sizes are different in this way, the filler particle model 11a is determined as a mass point in the computer, so that another filler particle model 11a may enter within the range occupied by the filler particle model 11a. Therefore, it is preferable to provide the filler particle model 11a with a volume removal region corresponding to the size of the filer particles. That is, the computer fills the excluded volume region in which the excluded volume effect works so as to prohibit other filler particle models 11a from entering the range occupied by the filler particle model 11a in the distribution of the potential that determines the interaction. It is preferable to apply it to the particle model 11a. FIG. 5A is a diagram showing an example of potential distributions D1 and D2 in which different exclusion volume regions are given to the potential distributions that determine the interaction. The potential distribution D2 has the same distribution shape if the potential distribution D1 is slid on the horizontal axis.
Therefore, as shown in FIG. 3B, even if the filler particle model 11a has overlapping portions in the initial arrangement, the filler particle model 11a moves by the molecular dynamics method and there is no overlapping portion.
The excluded volume region is not limited to that corresponding to the size of the filler particles. For example, if it is not desired to bring the filler particle model 11a close to each other within a certain range, an exclusion volume region larger than the exclusion volume region corresponding to the size of the filler particles may be provided.

FIG. 5B is a diagram illustrating an example of an exclusion volume region provided by the method for creating a model of a composite material of one embodiment. FIG. 5B shows an example of the exclusion volume region in the filler particle model 11a and the filler particle model 11a ^* having different sizes of the filler particle model.
As shown in FIG. 5B, the filler particle model 11a is provided with the exclusion volume region V, and the filler particle model 11a ^* is provided with the exclusion volume region V ^* . In this case, as shown in FIG. 5B, the filler particle model 11a and the filler particle model 11a ^* cannot enter the inside of the exclusion volume region V ^* and the exclusion volume region V.
The exclusion volume region may be imparted in correspondence with the size of the filler particle model 11a, or may be imparted differently even in the filler particle model 11a having the same size.
The shape that defines the range of the exclusion volume region is not limited to a spherical shape (or a circular shape), and may be a polyhedral shape corresponding to the actual shape of the filler particles.
By imparting different excluded volume regions in this way, the structure of the filler particle model 11a can be adjusted in various ways.

According to one embodiment, when modifying the position of the filler particle model 11a, it is preferable to prohibit the movement or modification of the position of the filler particle model 11a at a predetermined position in the group of the filler particle model 11a. As a result, the filler particle model 11a can be arranged at a preset position.
Further, according to one embodiment, when the position of the filler particle model 11a is corrected, when the position of the filler particle model 11a in which the regions overlap with each other in the group of the filler particle model 11a is corrected, the non-overlapping state is obtained. It is also preferable to fix the position of the filler particle model 11a to the position of the non-overlapping state to prohibit the movement and modification of the position of the filler particle model 11a. The filler particle model 11a becomes non-overlapping with each other due to the position correction, but they are still close to each other. Therefore, if the movement or position correction is allowed, the filler particle model 11a may overlap again due to the movement or position correction. There is also sex. Therefore, when the filler particle models 11a having overlapping regions are in a non-overlapping state, the position of the filler particle model 11a is fixed at the position in the non-overlapping state, and the movement or correction of the position of the filler particle model 11a is prohibited. It is preferable to do so.
Prohibition of movement or modification of the position of the filler particle model 11a is, for example, a movement calculated by the molecular dynamics method in which the mass of the corresponding filler particle model 11a is made extremely large compared to the mass of another filler particle model 11a. Even if the movement distance is calculated by the molecular dynamics method, which makes the distance almost zero, the filler particle model 11a at the preset position is not moved (the movement distance is forcibly set to zero), or the movement distance is made zero. When calculating the movement distance by the method, it is performed by forcibly setting the movement speed to zero.
When calculating the movement of a plurality of filler particle models 11 by the molecular dynamics method, the filler particles are placed at preset positions by forcibly assigning the movement distance and the movement direction to one initially arranged filler particle model 11a. The model 11a can be positioned. Further, the filler particle model 11a that has come to a preset position may be captured by repeating the calculation of the movement, and the movement or the correction of the position may be prohibited.

As shown in FIG. 1, before initial placement of the filler particle model 11a, at least one particle model placeable region 12 for arranging the group of the filler particle model 11a may be set in the model creation area A. preferable. By setting the particle model arrangable region 12, it is possible to easily and efficiently create a configuration in which a plurality of filler particle models 11a are aggregated in the particle model arrangable region 12, that is, a structure close to close-packed. ..
At this time, the group of the filler particle model 11a is preferably initially arranged in the particle model displaceable region 12. As a result, the possibility that the filler particle model 11a goes out of the particle model dispositionable region 12 by the calculation of the movement by the molecular dynamics method is reduced, and the arrangement of the filler particle model 11a satisfying the predetermined conditions is efficiently searched. be able to.

According to one embodiment, the computer forces a force between each of the filler particle models 11a within the particle model placeable region 12 and the outer edge 12a (see FIG. 6A) that partitions the particle model placeable area 12. It is preferable to impart an interaction that causes FIG. 6A is a diagram showing an example in which one filler particle model 11a in one embodiment moves by a repulsive force received from the outer edge 12a. By receiving a repulsive force from the outer edge 12a, the filler particle model 11a is less likely to move outside the particle model arrangable region 12. Even when the filler particle model 11a in the particle model placeable region 12 receives an attractive force from the outer edge 12a, the possibility of moving to the outside of the particle model placeable area 12 is further reduced.

As described above, in the embodiment, when the position of the filler particle model 11 is modified, the moving distance and the moving direction of the filler particle model 11a are separated by a preset time interval (divided at a predetermined time interval). By obtaining, the position of the particle model is repeatedly corrected to a position determined according to the moving distance and the moving direction. When the position of the filler particle model 11a is repeatedly corrected, the planned movement destination determined by the movement distance and the movement direction of the filler particle model 11a calculated by the molecular dynamics method is outside the particle model arrangable region 12. 11b (see FIG. 6B) is preferably rearranged so as to be located within the particle model placeable region 12 by the method described below.

FIG. 6B is a diagram illustrating an example of rearrangement performed when the position of the filler particle model 11a is corrected in one embodiment.
The rearrangement position P ^* of the out-of-region moving particle model 11b shown in FIG. 6B is a cross-sectional point 12a ₁ and a particle model that can be placed across the outer edge 12a of the out-of-region moving particle model 11b. A straight line L passing through the center point O of the region 12a (the center of gravity of the particle model arrangable region 12a) intersects the outer edge 12a of the particle model arrangable region 12 and is opposite to the crossing point 12a _{1 as} viewed from the center point O. It is set to a position moved in a direction parallel to the moving direction of the out-of-region moving particle model 11b by the distance D ₁ between the crossing point 12a ₁ and the planned moving destination Q from the crossing corresponding point 12a ₂ in. To.
As a result, even if the filler particle model 11a moves significantly, it can be reliably prevented from being located outside the particle model arrangable region 12.

According to one embodiment, when the computer corrects the position of the filler particle model 11a, the filler particle model 11a is calculated by determining the moving distance and the moving direction of the filler particle model 11a by dividing the position of the filler particle model 11a at preset time intervals. The position is repeatedly corrected to a position determined according to the moving distance and the moving direction, and as the position of the filler particle model 11a is repeatedly corrected, the size of the particle model arrangable region 12 is intermittently or continuously. It is preferable to make it narrower. This makes it possible to create a structure in which the filler particle model 11a is aggregated in a narrow region, that is, a structure close to close-packed packing.

According to one embodiment, when the computer uses the molecular dynamics method to calculate the movement of the filler particle model 11a, the computer fills the resistance force that suppresses the movement of the filler particle model 11a in the particle model displaceable region 12. It is preferable to apply it to the particle model 11a. Since the movement of the filler particle model 11a is reduced by this resistance force, it is possible to efficiently search for the arrangement of the filler particle model 11a that satisfies the predetermined conditions. As the resistance force, for example, a force of proportional viscosity damping proportional to the moving speed of the filler particle model 11a is given.

In this way, the computer can create a structure with a preferred arrangement of the filler particle model 11a.
The computer further sets the region between the filler particle model 11a and the particle model displaceable region 12 as the first base material model modeled on the first base material, and sets the outer region surrounding the particle model dispositionable region 12 as the first base material model. It is preferable to create a model for analysis of composite materials as a second base material model that models the second base material. The first base material and the second base material may be the same material or may be different materials. When the first base material and the second base material are different materials from each other, the composition of the polymer model is different. Therefore, in this case, the computer sets the polymer particle model of the first base material model, the polymer particle model of the second base material model, each bond chain, and parameters that make the interaction different.
The analysis model 1 to be created will be described below.

FIGS. 7 and 8 are diagrams illustrating an example of an analysis model created by the method for creating a model of a composite material of one embodiment.
As shown in FIG. 7, the analysis model 1 is modeled in, for example, a model creation area A which is a virtual space having a substantially cubic shape. The model creation area is a three-dimensional space extending in the X-axis, Y-axis, and Z-axis directions orthogonal to each other. The analysis model 1 includes four filler models 11A, 11B, 11C, and 11D modeled by a plurality of filler particles 11a. The filler models 11A, 11B, 11C, and 11D will be described as the filler model 11 when generically described.
Further, the analysis model 1 includes four polymer models 21 in which a plurality of polymer particles 21a and a binding chain 21b are modeled as a first base material model in an outer region so as to surround the filler model 11. As shown in FIG. 8, the analytical model 1 further includes, as shown in FIG. 8, a polymer model 31 in which a plurality of polymer particles 31a and a binding chain 31b are modeled in the gaps of the filler particle model 11a as a second base material model.

The filler models 11A, 11B, 11C, and 11D are the above-mentioned filler particle models 11a that are moved and aggregated by the molecular dynamics method. In the example shown in FIG. 7, the analysis model 1 describes an example in which four filler models 11A, 11B, 11C, and 11D are modeled, but the number of filler models to be modeled is not limited. The analysis model 1 may include three or less filler models 11 and may include more than four filler models 11. Further, in FIG. 7, only four polymer models 21 are shown, but in the analysis model 1, a plurality of polymer models 21 exist over the entire area in the model creation region A. In the example shown in FIG. 7, the model creation area A is an example in which the virtual space has a substantially rectangular parallelepiped shape, but it may have any shape such as a spherical shape, an elliptical shape, a rectangular parallelepiped shape, or a polyhedral shape.

The filler model 11 is created by the above-mentioned model creation method, and a plurality of filler particle models 11a are each assembled in a substantially spherical body. Further, the filler models 11 are arranged in a state of being separated from each other at a predetermined interval, but the plurality of filler models 11 are connected to each other by a covalent bond in a state of being aggregated with each other. May be good.

The relative position of the filler particle model 11a is specified by a binding chain (not shown) between the plurality of filler particle models 11a. This bond chain has a function as a spring in which an equilibrium length and a spring constant, which are bond distances between the filler particle models 11a, are defined, and constrains the filler particle models 11a. The binding chain defines the relative position of the filler particle model 11a and the potential for force to be generated by twisting, bending, or the like. The filler model 11 is defined by numerical data including the mass, volume, diameter and initial coordinates of the filler particles 11a, the number of aggregated particles, etc. for handling in molecular dynamics. The numerical data of the filler model 11 is input to the computer.

Polymers modeled in the polymer models 21 and 31 include, for example, rubbers, resins, and elastomers. The polymer particle models 21a and 31a are models of aggregated atoms of a plurality of polymers. Further, a group of polymer particle models in which a plurality of polymer particle models 21a and 31a are connected by a binding chain is formed as the polymer models 21 and 31. That is, the polymer models 21 and 31 have a structure in which the polymer particle model 21a or the polymer particle model 31a, which models a plurality of polymer atoms and an aggregate of a plurality of polymer atoms, are connected to each other by a bonding chain, and the polymer model 21 and 31 are arranged in the model creation area A at a predetermined density. The coupling chain functions as a spring in which, for example, an equilibrium length and a spring constant are defined. The polymer particle models 21a and 31a are bound by a plurality of polymer particle models 21a or bond chains 21b and 31b between the polymer particle models 31a, and their relative positions are specified. The bonding chains 21b and 31b have a function as a spring in which the equilibrium length and the spring constant, which are the bonding distances between the polymer particle model 21a or the polymer particle model 31a, are defined, and each polymer particle model 21a or each polymer particle. The space between the models 31a is restrained. The binding chains 21b and 31b define the relative position of the polymer particle model 21a or the polymer particle model 31a and the potential for generating a force by twisting, bending, or the like. Further, the bonding chains 21b and 31b are also bonded by a crosslinked bonding chain (not shown) between the polymer model 21 or the polymer model 31 in which a plurality of polymer particle models 21a or polymer particle models 31a are connected in series. .. This crosslinked bonded chain has a function as a spring in which the equilibrium length and the spring constant, which are the bonding distances between the polymer particle model 21a and the polymer particle model 31a, are defined, and between the polymer particle model 21a and the polymer particle model 31a. Is restrained.
In addition, a modifier that enhances the affinity with the filler is added to the polymer, if necessary. Examples of the modifier include a hydroxyl group, a carbonyl group, a functional group of an atomic group, and the like. Corresponding to this modifier, a particle model in which the modifier particles are modeled and a binding chain (not shown) may be arranged between the polymer model 21 or the polymer model 31 and the filler model 11.
The polymer models 21 and 31 are defined by numerical data (including the mass, volume, diameter and initial coordinates of the polymer particle models 21a and 31a) in order to handle the polymer by the molecular dynamics method. The numerical data of the polymer models 21 and 31 is input to the computer as parameters.

In the analysis model 1, the interaction between the particles of the filler particle model 11a, between the polymer particle models 21a and 31a, and between the particles of the filler particle model 11a and the polymer particle models 21a and 31a is at least a part of the particles. give. In some cases, an interaction force may be applied to exchange forces between all the particles. As the interaction between the filler particle model 11a and the polymer particle models 21a and 31a, a chemical interaction (attractive force) may be given, or a physical interaction (bond bond) may be given. That is, as an interaction, a potential described later is given to the binding chain including the bound chain 21b shown in the drawing, and further to the particles not connected by the bound chain. As a result, a force determined by the interaction acts between the particles.
In the composite material, the polymer may be composed of a plurality of types of polymers, in which case an interaction may be imparted between the different types of polymer particle models 21a, 31a in the analytical model 1. The interaction between the filler particle model 11a and the polymer particle models 21a, 31a in this case may be different between the different types of polymer particle models 21a, 31a.
The interaction between particles is defined, for example, by the Lennard-Jones potential described above. At this time, the values of σ and ε in the following equation are adjusted as appropriate. By increasing the upper limit distance (cutoff distance) for calculating the potential, the force acting over a long distance can be adjusted. The parameters of the interaction between the filler particle models 11a and the interactions between the polymer particle models 21a and 31a are sequentially obtained until the interaction between the filler particle models 11a and the polymer particle models 21a and 31a reaches a constant value. It is preferable to reduce the size. By gradually approaching the σ and ε of the Lennard-Jones potential from a large value to the original value, the particles can approach at a gentle speed that does not lead the molecule to an unnatural state. In addition, by gradually reducing the cutoff distance, the force in the interaction can be adjusted within an appropriate range.

The analysis model 1 thus created is subjected to numerical analysis by the molecular dynamics method based on preset analysis conditions. Examples of the numerical analysis include deformation analysis such as extension analysis and shear analysis, relaxation analysis, and motion analysis such as vibration analysis. By deformation analysis or relaxation analysis, it is possible to calculate the breakage of the coupling chains 21a, 31a, etc. in the analysis model 1, and further, it is possible to determine the presence or absence of breakage in the entire analysis model 1.
Since the analysis model 1 described above is created on the computer, the computer can store the computer program for analyzing the composite material that causes the computer to execute the method for creating the model of the composite material.

FIG. 9 is a functional block diagram of an analysis device that performs an analysis method for a composite material of one embodiment.
As shown in FIG. 9, the analysis device 50 includes a computer including a processing unit 52 and a storage unit 54. The analyzer 50 is electrically connected to an input operation system 53 and a monitor 55 including a mouse and a keyboard. The input operation system 53 includes the size, shape, and each particle of the filler particle model 11a and the polymer particle model 21a corresponding to the size, shape, and characteristics of the polymer and the filler for which the analysis model of the composite material is created. Data such as the interaction set between the models, the type of numerical analysis to be performed, the analysis conditions in the numerical analysis, the boundary conditions, and the input conditions given to the analysis model 1 are set, and the processing unit 52 or the storage unit 54 is set. It is configured to input to.

The processing unit 52 includes, for example, a central processing unit (CPU: Central Processing Unit) and a memory. The processing unit 52 reads a computer program from the storage unit 54 and starts it when executing various processes. The computer program executes various processes. For example, the processing unit 52 expands the data related to various processes stored in advance from the storage unit 54 into an area allocated to itself on the memory as needed, and analyzes the composite material based on the expanded data. Various processes related to the creation of the model 1 and the numerical analysis of the composite material using the analysis model 1 are executed.

The processing unit 52 includes a model creation unit 52a, a condition setting unit 52b, an analysis unit 52c, and an evaluation unit 52d.
The model creation unit 52a is a filler model in which the filler particle model 11a as in the example shown in FIG. 2 has an aggregated structure close to close-packing, based on the data stored in the storage unit 54 in advance and various input conditions. A model having a plurality of 11 is created by the molecular dynamics method. That is, the model creation unit 52a executes each step shown in FIG. 1 described above. Further, the model creation unit 52a creates polymer particle models 21a and 31a around the filler model 11, and further forms cross-linked chains between the polymer particle models 21a, between the polymer particle models 31a, and the polymer particle model 21a. It is imparted to and between the polymer particle model 31a. At this time, the model creating unit 52a has the number of molecules, the molecular weight, the length of the molecular chain, the number of molecular chains, the branching, the shape, the size, and the target number of molecules included in the model 1 for analysis to be created. Filler particle models 11a and polymer particle models 21a and 31a are created so as to correspond to the above conditions.
Further, the model creation unit 52a is a mutual interaction between the filler particle model 11a, the polymer particle model 21a, the polymer particle model 31a, and between the filler particle model 11a, the polymer particle model 21a, and the polymer particle model 31a. Set the conditions of various calculation parameters such as the potential distribution that defines the action. When the above-mentioned Lennard-Jones potential distribution is used as the potential distribution, the values of σ and ε are set. As a result, the model creation unit 52a creates the filler model analysis model 1.

The condition setting unit 52b sets various conditions used for numerical analysis such as deformation analysis, relaxation analysis, and vibration analysis. The conditions include, for example, when stretching analysis is performed as deformation analysis, conditions such as the elongation rate, uniaxial stretching, biaxial stretching, and stretching speed of the analysis model 1 are included.

The analysis unit 52c executes the numerical analysis of the analysis model 1 based on the analysis conditions set by the condition setting unit 52b by using the molecular dynamics method. Here, as the numerical analysis, deformation analysis such as extension analysis and shear analysis, relaxation analysis, and vibration analysis can be mentioned. Further, the analysis unit 52c performs a predetermined calculation process using values such as displacements of the polymer particles 21a and 31a and the filler particles 11 obtained as a result of the numerical analysis to calculate physical quantities such as strain.

The evaluation unit 52d obtains a predetermined evaluation index from the physical quantity calculated by the numerical analysis of the analysis unit 52c, and evaluates the characteristics of the composite material, for example, the breaking characteristics.

The storage unit 54 can read and write to a non-volatile memory such as a hard disk device, a magneto-optical disk device, a flash memory and a CD-ROM that can only be read, and a RAM (Random Access Memory). Volatile memory, which is a possible recording medium, is appropriately combined.

In the storage unit 54, data for creating an analysis model of the composite material to be analyzed via the input operation system 53, for example, data of filler particles such as carbon black particles, silica particles, and alumina particles, and rubber. , Resins, and polymers such as elastomers are stored.
Further, the storage unit 54 stores a computer program or the like for realizing a method for analyzing the composite material. This computer program may be capable of realizing the method for analyzing a composite material according to the present embodiment in combination with a computer program already recorded in a computer or a computer system. The term "computer system" as used herein includes hardware such as an OS (Operating System) and peripheral devices.

The monitor 55 is, for example, a display device such as a liquid crystal display device. The monitor 55 displays a setting screen for setting the conditions for executing the above-mentioned numerical solution and the input given to the analysis model 1, and the analysis model in the analysis unit 52c during or at the end of the analysis. The state of 1 is displayed, and further, the evaluation result obtained by the evaluation unit 52 is displayed. The storage unit 54 may be located in another device such as a database server. For example, the analysis device 50 may access the processing unit 52 and the storage unit 54 by communication from a terminal device including the input operation system 53 and the monitor 55.

(Example, comparative example)
In order to confirm the effect of the above embodiment, the processing time of the computer in the example of creating the filler model 11 having a structure close to the close-packed packing of the filler particle model 11a by the method shown in FIG. 1 and the above-mentioned conventional technique ( The method disclosed in Patent Document 1) was used to compare the filler particle model 11a with the processing time of the computer in the comparative example of creating the filler model 11 having a structure close to close-packed.
In order to create one filler model 11 in the model creation region A, the Lennard-Jones potential distribution was used between the filler particle models 11a, and the values of σ and ε were appropriately set. The same filler particle model 11a was used in Examples and Comparative Examples.
The total number of filler particle models 11a arranged in the model creation region A was 100.

In the examples and the comparative examples, the filler model 11 shown in FIG. 2 could be created, but in the comparative example, the processing time was more than 30 minutes to create the filler model 11, but in the examples, the filler model 11 was created. Using the same computer, the processing time was 2 minutes.
From this, it can be seen that the model creation method of the present embodiment can efficiently create the filler model 11. Therefore, in the embodiment, it can be seen that the analysis model 1 including the polymer particle models 21a and 31a and the filler model 11 can be efficiently created.

Although the method for creating a model of a composite material, the method for analyzing a composite material, and the computer program for analyzing a composite material of the present invention have been described in detail above, the present invention is not limited to the above embodiment and deviates from the gist of the present invention. Of course, various improvements and changes may be made as long as they are not.

1 Analysis model 11, 11A, 11B, 11C, 11D Filler model 11a, 11a ^* Filler particle model 12 Particle model Placeable area 12a, 12a ₁ , 12a ₂ Outer edge 21, 21A, 21B, 21C Polymer model 21a, 31a Polymer particles Model 21b Bonded chain 21c Cross-linked coupled chain 50 Analyzer 51 Input / output device 52 Processing unit 52a Model creation unit 52b Condition setting unit 52c Analysis unit 52d Evaluation unit 53 Input operation system 54 Storage unit 55 Monitor

Claims (16)

A method in which a computer creates a model of a composite material by a molecular dynamics method, wherein the composite material has a structure in which particles are contained in a base material of the composite material.
A step of initially arranging a group of particle models that model the particles in the model creation region that models the composite material, and
The particle model is calculated by moving a plurality of particle models in the initially arranged group of particle models based on the force of interaction acting between the particle models using molecular dynamics method. The step of modifying the position of the particle model until the position of is satisfies the preset condition, and
A step of creating an analysis model of the composite material based on the position of the particle model that satisfies the above conditions, and
A method for creating a model of a composite material, which comprises. The method for creating a model of a composite material according to claim 1, wherein the interaction exerts an attractive force between the particle models. The method for creating a model of a composite material according to claim 1, wherein the interaction exerts a repulsive force between the particle models. The exclusion volume region in which the exclusion volume effect that prohibits the proximity of other particle models to a part of the particle model group is excluded in the other part of the particle model group. The method for creating a model of a composite material according to any one of claims 1 to 3, wherein a volume-removing region is imparted to the part of the particle model so as to be different from the volume region. The composite material according to any one of claims 1 to 4, which prohibits the movement or position modification of the particle model at a predetermined position in the group of particle models in the step of modifying the position of the particle model. How to create a model. In the step of correcting the position of the particle model, when the position of the particle model in the group of the particle models overlaps with each other and the position of the particle model is corrected, the position of the particle model is changed to the position of the non-overlapping state. The method for creating a model of a composite material according to any one of claims 1 to 4, which is fixed to and prohibits the movement or modification of the position of the particle model. Further, prior to the step of initially arranging the particle model, at least one particle model displaceable region for arranging the group of the particle models in the analysis model is set in the model creation region. , The method for creating a model of a composite material according to any one of claims 1 to 6. The method for creating a model of a composite material according to claim 7, wherein the group of particle models is initially arranged in the particle model displaceable region. The composite material of claim 7 or 8, which imparts a force-generating interaction between each of the particle models within the particle model disposable region and the outer edge partitioning the particle model disposable region. How to create a model. The method for creating a model of a composite material according to claim 9, wherein the force generated between each of the particle models and the outer edge of the particle model displaceable region is a repulsive force. In the step of correcting the position of the particle model, the position of the particle model is determined according to the moving distance and the moving direction by obtaining the moving distance and the moving direction of the particle model by dividing the position at a preset time interval. Repeatedly correct to the fixed position,
When the position of the particle model is repeatedly modified, the out-of-region moving particle model in which the planned moving destination determined by the moving distance and the moving direction is outside the particle model arrangable region is the particle model. Relocated to be within the placeable area,
A straight line passing through a crossing point across the outer edge of the particle model arrangable region and a central point of the particle model arrangable region by movement of the extra-regional moving particle model intersects the outer edge of the particle model arrangable region. The position is moved in a direction parallel to the moving direction by the distance between the crossing point and the planned moving destination from the crossing corresponding point on the opposite side of the crossing point when viewed from the center point. The method for creating a model of a composite material according to any one of claims 7 to 10, wherein the rearrangement position of the out-of-region moving particle model is set. In the step of correcting the position of the particle model, the position of the particle model is determined according to the moving distance and the moving direction by obtaining the moving distance and the moving direction of the particle model by dividing the position at a preset time interval. Repeatedly correct to the fixed position,
The method for creating a model of a composite material according to any one of claims 7 to 11, wherein the size of the particle model dispositionable region is intermittently or continuously narrowed as the position of the particle model is repeatedly modified. .. Claims 7 to 12 apply to the particle model a resistance force that suppresses the movement of the particle model in the particle model displaceable region when the calculation for moving the particle model is performed using the molecular dynamics method. The method for creating a model of a composite material according to any one of the above items. The particle model is a filler particle model that models filler particles, and the region between the particle model and the particle model displaceable region is a first base material model that models the first base material, and the particles. Any one of claims 7 to 13, further comprising a step of creating an analysis model of the composite material as a second base material model in which the second base material is modeled in the outer region surrounding the model-arrangeable region. The method for creating a model of the composite material described in the section. A step of creating the analysis model of the composite material by the method of creating a model of the composite material according to any one of claims 1 to 14.
The step that the computer performs numerical analysis by the molecular dynamics method using the analysis model,
A method for analyzing a composite material, which comprises. A computer program for analyzing a composite material, which comprises causing a computer to execute the method for creating a model of the composite material according to any one of claims 1 to 14.

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