JP2020135762A - Material analysis method, and computer program for material analysis - Google Patents

Abstract

To provide a material analysis method and the like for efficiently evaluating a crystalline structure of a polymer in an analysis object region.SOLUTION: A material analysis method includes the steps of: creating a material analysis model containing plural polymer models obtained by modeling polymers using plural polymer particles; cross-linking the polymer models according to cross-linking analysis; setting an interaction in an analysis model after the cross-linking analysis and conducting a numerical analysis; extracting particles belonging to a search start point group, and particles belonging to a search end point group differing from the search start point group; specifying one particle of the search start point group as a starting particle, and specifying plural particles contained in the search end point group as ending particles; performing processing for extracting polymer paths between the starting particle and each particle of the ending particles; and extracting polymer paths of the whole path between the particles of the search start point group and the particles of the search end point group.SELECTED DRAWING: Figure 1

Description

The present invention relates to a method for analyzing a material containing at least polymer particles and a computer program for analyzing the material, for example, a method for analyzing a material capable of efficiently and accurately analyzing a network of polymer materials formed in a composite material. Regarding computer programs for material analysis.

Conventionally, a method for simulating a polymer material using molecular dynamics has been proposed (see, for example, Patent Document 1 and Patent Document 2). In the polymer material simulation method described in Patent Document 1, a polymer material model is set by molecular dynamics calculation using a filler model that models a filler and a polymer model that models a polymer, and then the set height is set. Based on the molecular material model, deformation analysis is performed using a finite element model modeled with a finite number of elements. Further, in the method for simulating a polymer material described in Patent Document 2, molecular dynamics calculation is performed using a coarse-grained model using the polymer material and a filler model including the outer surface of the filler, and then coarse-grained. The relaxation elastic modulus is calculated by dividing the space where the model is placed into a plurality of minute regions.

Japanese Unexamined Patent Publication No. 2015-056002 Japanese Unexamined Patent Publication No. 2014-203262

Here, in a substance such as rubber containing polymer particles, a large number of polymer crystal structures are formed in the region where the polymer particles are arranged. Therefore, it is required to efficiently detect the crystal structure of the polymer.

The present invention has been made in view of such circumstances, and an object of the present invention is to provide a material analysis method and a computer program for material analysis capable of efficiently evaluating the crystal structure of a polymer.

The material analysis method of the present invention is a material analysis method using a material analysis model created by a molecular dynamics method using a computer, and is a plurality of polymer models in which a polymer is modeled by a plurality of polymer particles. A step of creating an analysis model of a material containing the particles, a step of cross-linking the polymer model by cross-linking analysis, a step of setting an interaction with the analysis model after cross-linking analysis and performing a numerical analysis, and a search start. A step of extracting particles belonging to a point group and particles belonging to a search end point group different from the search start point group, and one particle of the search start point group is specified as a start particle, and the search end point is specified. A plurality of particles included in the group are specified as end particles, a process of extracting a polymer path between the start particles and the respective particles of the end particles is performed, and the particles of the search start point group and the search end point are performed. It comprises an extraction step of extracting the polymer pathway of all pathways between the particles of the group.

The analytical model is preferably a composite material that includes a plurality of polymer models in which the polymer is modeled by the plurality of polymer particles and a plurality of filler models in which the filler is modeled.

Further, it is preferable that the polymer pathway calculated in the extraction step further includes an evaluation step of evaluating the pathway length using the number of bonds or the number of particles contained in the pathway.

Further, in the evaluation step, the distance between the ends of the polymer pathway from one end to the other end and the path length of the polymer pathway are calculated, and based on the distance between the ends and the path length, the evaluation step is performed. It is preferable to determine whether the polymer pathway is a stretched chain.

Further, in the evaluation step, it is preferable to carry out a route search in a low temperature state by temperature change analysis.

In addition, it is preferable that the evaluation step evaluates the results at at least two times.

Further, it is preferable to visualize and display the time history.

Further, it is preferable to calculate the difference between the analysis result of the first analysis time and the analysis result of the second analysis time different from the first analysis time in the time history.

Further, in the polymer pathway, the step of calculating the force generated per unit bond based on the distance between two adjacent polymer particles and the force generated per unit bond are used. It is preferable to have a step of calculating the force generated in the polymer pathway.

Further, in the extraction step, it is preferable to search the polymer pathway by breadth-first search.

Further, it is preferable that the particles in the search start point group are free-end particles, and the particles in the search end point group are free-end particles.

Further, the particles of the search start point group are particles that were free-end particles of the polymer chain at the time before the cross-linking, and the particles of the search end point group are the free-end particles of the polymer chain at the time before the cross-linking. It is preferable that the particles are present.

Further, in the extraction step, it is preferable that the search for the route merging with the searched polymer route is completed.

In addition, the extraction step preferably searches for a polymer pathway in the main chain.

In addition, the extraction step preferably searches for a polymer pathway that sandwiches a crosslinked bond.

In addition, the extraction step preferably ends the search for the polymer pathway that has passed through the cross-linking.

Further, it is preferable to compare the analysis result of the analysis model with the analysis result of a comparative analysis model different from the analysis model.

The present invention also provides a computer program for analyzing materials, which comprises causing a computer to execute the method for analyzing a material according to any one of the above.

According to the present invention, the crystal structure of a polymer can be efficiently evaluated. Further, according to the present invention, it is possible to realize a material analysis method capable of evaluating the crystal structure of a polymer and a computer program for material analysis.

FIG. 1 is a flowchart showing an outline of an analysis method of a target material according to an embodiment of the present invention. FIG. 2 is a flowchart showing an outline of a material analysis method according to an embodiment of the present invention. FIG. 3 is a flowchart showing an outline of a material analysis method according to an embodiment of the present invention. FIG. 4 is a conceptual diagram showing an example of an analysis model created by the material analysis method according to the embodiment of the present invention. FIG. 5 is an explanatory diagram showing an example of a material analysis method according to the embodiment of the present invention. FIG. 6 is an explanatory diagram showing an example of a material analysis method according to the embodiment of the present invention. FIG. 7 is an explanatory diagram showing an example of a material analysis method according to the embodiment of the present invention. FIG. 8 is an explanatory diagram showing an example of a material analysis method according to the embodiment of the present invention. FIG. 9 is an explanatory diagram of a material analysis method according to the present embodiment. FIG. 10 is an explanatory diagram showing an example of a material analysis method according to the embodiment of the present invention. FIG. 11 is an explanatory diagram showing an example of a material analysis method according to the embodiment of the present invention. FIG. 12 is an explanatory diagram showing an example of a material analysis method according to the embodiment of the present invention. FIG. 13 is a functional block diagram of an analysis device that executes the material analysis method according to the present embodiment. FIG. 14 is a graph in which the number of stretched chains and the time change of strain are associated with each other. FIG. 15 is a graph in which the stretched chain length and the strain are associated with the time change. FIG. 16 is a graph in which the elongation of the stretched chain and the time change of the strain are associated with each other.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings. The present invention is not limited to the following embodiments, and can be modified as appropriate.

FIG. 1 is a flowchart showing an outline of an analysis method of a target material according to the first embodiment of the present invention. As shown in FIG. 1, the analysis method of the target material according to the present embodiment is a material analysis method using an analysis model of the target material containing polymer particles prepared by a molecular dynamics method using a computer. This method for analyzing the target material is a method for analyzing a material containing at least polymer particles using a model for analyzing the target material created by a molecular dynamics method using a computer, and models a polymer with a plurality of polymer particles. The first step ST1 to create an analysis model of a material containing a plurality of polymer models, the second step ST2 to crosslink the polymer model by cross-linking analysis, and the numerical value by setting the interaction with the analysis model after the cross-linking analysis. The third step ST3 to carry out the analysis, the fourth step ST4 to select the polymer group to be evaluated, the fifth step ST5 to set the search start point group from the polymer group, and the search end point group from the polymer group are set. The sixth step ST6, the seventh step ST7 for extracting the polymer pathways at the start point and the end point, and the eighth step ST8 for determining whether the route search of the extracted particles is completed are included. In the eighth step ST8, when the search for all the particles in the search start point group is completed, it is determined that the search for the route is completed. That is, the path between all the particles in the search start point group and all the particles in the search end point group is searched. If it is determined that the eighth step S18 is not completed, the process returns to the seventh step ST7, and if it is determined that the eighth step S18 is completed, the ninth step ST9 for evaluating the composite material is executed based on the route search picture result. End the process. The ninth step ST9, which evaluates the composite material, evaluates each polymer pathway extracted. In the example shown in FIG. 1, the fourth step ST4 for selecting the polymer group to be evaluated was executed, but the search start point group and the search end point group may be set without selecting the polymer particle group. .. The evaluation of the polymer pathway will be described later.

Although the present invention can be used for analysis of materials containing polymer particles, it can be suitably used for composite materials containing polymer particles and fillers. Hereinafter, a case where it is applied to a composite material containing a plurality of polymer particles and a plurality of fillers will be described. Hereinafter, the invention will be described in detail using the case of a composite material, but the same applies to a material containing no filler, for example, a material containing only polymer particles.

FIG. 2 is a flowchart showing an outline of a material analysis method according to the first embodiment of the present invention. The flowchart shown in FIG. 2 shows a case where the analysis target is a composite material containing polymer particles and a filler. As shown in FIG. 2, the material analysis method according to the present embodiment is a material analysis method using a material analysis model created by a molecular dynamics method using a computer. This material analysis method is a material analysis method using a material analysis model created by a molecular dynamics method using a computer, and is a plurality of polymer models and fillers in which a polymer is modeled by a plurality of polymer particles. The first step ST11 to create a model for analysis of a material containing a plurality of filler models modeled on the above, the second step ST12 to crosslink the polymer model by cross-linking analysis, and the interaction are set in the analysis model after the cross-linking analysis. The third step ST13 for performing numerical analysis, the fourth step ST14 for selecting the polymer group to be evaluated, the fifth step ST15 for setting the search start point group from the polymer group, and the search end point from the polymer group. It includes a sixth step ST16 for setting the group, a seventh step ST17 for extracting the polymer pathways at the start and end points, and an eighth step ST18 for determining whether the route search of the extracted particles is completed. The eighth step ST18 determines that the search for the route is completed when the search for all the particles in the search start point group is completed. That is, the path between all the particles in the search start point group and all the particles in the search end point group is searched. If it is determined that the eighth step S18 is not completed, the process returns to the seventh step ST17, and if it is determined that the eighth step S18 is completed, the ninth step ST19 for evaluating the composite material is executed based on the route search picture result. End the process. The ninth step ST19 to evaluate the composite material evaluates each polymer pathway extracted. As an example, as shown in FIG. 3, a step ST21 for calculating the distance between ends and a pathway length, and a step ST22 for determining whether the polymer pathway is a stretched chain based on the calculation result of step ST21. It includes step ST23 for calculating the force per unit bond of the stretched chain and step ST24 for calculating the force generated in the entire stretched chain. Hereinafter, the first embodiment of the present invention will be described in detail.

FIG. 4 is a conceptual diagram showing an example of the analysis model 1 created by the material analysis method according to the present embodiment. As shown in FIG. 4, the material analysis model 1 according to the present embodiment is, for example, a model arranged in a model creation area A which is a substantially cubic virtual space having a side length of a distance L. .. Specifically, the analysis model 1 is modeled on a pair of first filler model 11 and second filler model 12 in which a plurality of filler particles 11a and 12a are modeled, and a plurality of polymer particles 21a and a binding chain 21b. It has a plurality of polymer models 21 which are made. In the present embodiment, an example in which the composite material to be analyzed contains a filler and a polymer which is a polymer material will be described, but the present invention can also be applied to a composite material containing two or more kinds of substances. .. Further, in the example shown in FIG. 4, an example in which the analysis model 1 has two first filler models 11 and a second filler model 12 and a plurality of polymer models 21 has been described, but three or more filler models are used. It may be arranged. Further, the model creation area A does not necessarily have to be a virtual space having a substantially cubic shape, and may have an arbitrary shape such as a spherical shape, an elliptical shape, a rectangular parallelepiped shape, or a polyhedral shape.

The first filler model 11 and the second filler model 12 are modeled in a state in which a plurality of filler particles 11a and 12a are assembled in a substantially spherical shape, respectively. Further, the first filler model 11 and the second filler model 12 are arranged at a predetermined distance from each other. The first filler model 11 and the second filler model 12 may be connected to each other by covalent bonds at the outer edges in a state of being mutually aggregated.

The plurality of polymer models 21 are crosslinked in the space to be analyzed. A part of the polymer models 21 among the plurality of polymer models 21 is arranged between the first filler model 11 and the second filler model 12. Some of the polymer models 21 among the plurality of polymer models 21 are arranged at least at one end in a region other than between the first filler model 11 and the second filler model 12. The plurality of polymer models 21 arranged between the first filler model 11 and the second filler model 12 are arranged in the first analysis target region A11 in which one end receives the interaction from the first filler model 11. The other end is arranged in the second analysis target region A12, which is the range where the interaction from the second filler model 12 is received. One end of the plurality of polymer models 21 may be bonded to the filler particles 11a on the surface of the first filler model 11, and the other end may be bonded to the filler particles 12a on the surface of the second filler model 12.

Examples of the filler include carbon black, silica, alumina and the like. The filler particles 11a and 12a are modeled by assembling a plurality of filler atoms. The plurality of filler particles 11a and 12a aggregate to form a filler particle group. The relative positions of the plurality of filler particles 11a and 12a are specified by the bonding chains (not shown) between the adjacent filler particles 11a and 12a. This bond chain has a function as a spring in which an equilibrium length, which is a bond distance between the filler particles 11a and 12a, and a spring constant are defined, and restrains the filler particles 11a and 12a. The bond chain is a bond in which the potential for generating a force by the relative positions, twists, and bends of the filler particles 11a and 12a is defined. The first filler model 11 and the second filler model 12 are numerical data (including the mass, volume, diameter, initial coordinates, etc. of the filler particles 11a, 12a) for handling the filler in molecular dynamics. The numerical data of the first filler model 11 and the second filler model 12 are input to the computer.

Polymers include, for example, rubbers, resins, and elastomers. The polymer particles 21a are modeled by aggregating atoms of a plurality of polymers. The plurality of polymer particles 21a aggregate to form a polymer particle group. A denaturing agent that enhances the affinity with the filler is added to the polymer, if necessary. The modifier includes, for example, a hydroxyl group, a carbonyl group, a functional group of an atomic group, and the like. The polymer model 21 is a model in which a plurality of polymer atoms and polymer particles 21a are filled in the modeling region A at a predetermined density. The relative positions of the polymer particles 21a are specified by the bonding chains 21b between adjacent ones. The bond chain 21b has a function as a spring in which an equilibrium length, which is a bond distance between the polymer particles 21a, and a spring constant are defined, and restrains each polymer particle 21a. The bond chain 21b is a bond in which the potential for generating a force by the relative position, twisting, bending, etc. of the polymer particles 21a is defined. The polymer model 21 is numerical data (including the mass, volume, diameter, initial coordinates, etc. of the polymer particles 21a) for handling the polymer in molecular dynamics. The numerical data of the polymer model 21 is input to the computer.

Next, the method of analyzing the material according to the present embodiment will be described in detail. In the following, an example of a polymer that crosslinks between two fillers will be described, but the polymer also crosslinks in a region other than between the fillers. 5 and 6 are explanatory views showing an example of a material analysis method according to the embodiment of the present invention, respectively.

FIG. 5 schematically shows a crosslinked polymer model in the analysis area. In the actual polymer pathway, as shown in FIG. 4, the polymer particles are connected in various directions in a three-dimensional space, but for the sake of explanation, in FIG. 5, the polymer pathway is schematically shown by a straight line. .. As shown in FIG. 5, in the model creation region A of the target for searching the polymer pathway, the polymer particles 21a, the main chain (polymer) 34 formed by cross-linking the polymer particles 21a, and the main chains 34 are bonded to each other. Cross-linking bond 36 and The main chain 34 is a polymer chain before cross-linking, that is, a polymer bond formed before cross-linking. In this analysis method, the main chain 34 and the crosslinked bond 36 are detected.

In this analysis method, some of the polymer particles 21a of the plurality of polymer particles 21a included in the model creation region A are set as the polymer particles 21a included in the search start point group 30. In this analysis method, a plurality of polymer particles 21a included in the model creation region A and not included in the search start point group 30 are set as the polymer particles 21a included in the search end point group 32. The polymer particles 21a included in the search start point group 30 and the polymer particles 21a included in the search end point group 32 are some polymer particles 21a among a large number of polymer particles 21a included in the model creation region A. Is. Further, in the present embodiment, the polymer particles 21a included in the search start point group 30 and the polymer particles 21a included in the search end point group 32 are the end portions of the polymer pathway formed by cross-linking. As a result, the analysis can be performed efficiently, but any polymer particles 21a can be set to the polymer particles 21a included in the search start point group 30 and the polymer particles 21a included in the search end point group 32. ..

In the material analysis method, as shown in FIG. 6, one polymer particle 21a belonging to the search start point group 30 is selected as the path search start particle, and a plurality of polymer particles 21a belonging to the search end point group 32 are used as the end particles. Set. Then, the material analysis method performs a path search between the path search start particle and the path search end particle. In the material analysis method, a path search between one path search start particle and a plurality of end particles is performed by all path search.

Here, the end particles are the polymer particles 21a selected as the path search start particles (start particles) and all the polymer particles 21a belonging to the search end point group 32 for which the path has not been established. Specifically, it comprehensively searches for a path connecting one of the polymer particles 21a belonging to the search start point group 30 and the polymer particles 21a belonging to the search end point group 32. In the present embodiment, a breadth-first search is performed to search for whether there is a polymer particle 21a connected from one polymer particle 21a from one polymer particle 21a belonging to the search start point group 30, and when the polymer particle 21a is connected to two or more polymer particles 21a. Searches for a path connecting to each polymer particle 21a thereafter. In the present embodiment, the number of routes for detecting and searching for a route connected to another main chain 34 is increased at the portion connected by the cross-linking bond 36.

In the example shown in FIG. 6, by performing the first path search by the material analysis method, the polymer particles belonging to the search end point group 32 from the start point 40a, which is one polymer particle 21a belonging to the search start point group 30. The route of the region 42a including the route connected to each of the 21a is extracted. In FIG. 6, the route is established with the polymer particles 21a belonging to all the search end point groups 32, but the route may not be established with the polymer particles 21a belonging to some of the search end point groups 32.

When the first route search is completed, the polymer particles 21a belonging to the search start point group 30 are set to the polymer particles 21a different from the start point 40a at the start point 40b, and the second route search is performed. As the starting point 40b, it is preferable to select polymer particles 21a far from the starting point 40a. The material analysis method of the present embodiment ends the route search for the route when the same route as the searched route is reached during the route search. When the entire route search from the start point 40b to the search end point group 32 is performed, as shown in FIG. 6, the route of the region 42b until it overlaps with the region 42a is searched. Here, in the material analysis method of the present embodiment, as shown in the overlapping region 44, in the route search of the region 42b, the route search is not completed at the time of contact with the region 42a, and the route of a certain distance overlaps. Ends the route search with. By searching for some regions in an overlapping manner, it is possible to suppress omission of detection of the polymer pathway. Further, in the case of duplication, by ending the search, the search for the duplicated route can be suppressed, and the route can be searched efficiently. It is preferable to evaluate the overlapping region for one bond or two bonds of the polymer particles. As a result, the connection state of the polymer path can be detected with higher accuracy.

When the second route search is completed, the polymer particles 21a belonging to the search start point group 30 are set to the start point 40a and the polymer particles 21a different from the start point 40b are set to the start point 40c, and the third route search is performed. As the starting point 40c, it is preferable to select polymer particles 21a far from the starting points 40a and 40b. The material analysis method of the present embodiment ends the route search for the route when the same route as the searched route is reached during the route search. When the entire route search from the start point 40c to the search end point group 32 is performed, as shown in FIG. 6, the route of the region 42c until it overlaps with the regions 42a and 42b is searched. As shown in the overlapping region 46, the material analysis method of the present embodiment does not end the route search at the time of contact with the region 42a in the route search of the region 42c, and the route search at the time when the routes of a certain distance overlap. To finish. Further, as shown in the overlapping region 48, in the route search of the region 42c, the route search is not terminated when the route is in contact with the region 42b, but is terminated when the routes of a certain distance are overlapped.

In the examples shown in FIGS. 5 and 5, only the path in which the polymer particles 21a of the search start point group 30 and the polymer particles 21a of the search end point group 32 are connected is shown, but the material analysis method is the search start. A path that does not connect the polymer particles 21a of the point group 30 to the polymer particles 21a belonging to the search end point group 32 is also searched. In this case, the material analysis method is to end the route search if the polymer particles 21a belonging to the search end point group 32 are not reached even if they are connected by a certain distance (even if they are connected to a predetermined number of polymer particles 21a). Good.

In this way, by selecting one polymer particle 21a of the search start point group 30 and a plurality of polymer particles of the search end point group 32 and extracting the polymer pathway, the plurality of polymer pathways can be efficiently and comprehensively covered. Can be detected.

Further, as in the present embodiment, the distance from the polymer particles of the search start point group 30 is extended by one polymer particle or a predetermined distance, and a breadth-first search is performed in which branched paths are also detected in parallel, thereby efficiently performing a breadth-first search. However, a depth-first search may be performed in which each route is searched in order.

Further, as in the present embodiment, by setting each of the polymer particles of the search start point group 30 and the search end point group 32 as free end particles, the route search can be performed from the end of the polymer pathway, and the polymer pathway can be performed. Can be detected without omission.

Further, it is also preferable that the polymer particles of the search start point group 30 and the search end point group 32 are free-end particles of the polymer chain before cross-linking. This makes it possible to effectively search for a route when the free end before cross-linking is cross-linked.

Further, as in the present embodiment, the composite material can be analyzed with higher accuracy by searching for a path between all the particles in the search start point group and all the particles in the search end point group. By searching the path from all the particles in the search start point group, the path can be searched without omission, but between all the particles in the search start point group and all the particles in the search end point group. It is sufficient to search for the path of, and it is not necessary to search from some polymer particles of the search start point group. For example, in the route search from other polymer particles of the search start heavenly army, if the routes are connected, the search may not be performed.

Further, as in the present embodiment, by selecting the polymer particles in which the start point of the search start point group 30 is separated from the previous start point, the route can be searched efficiently. Further, when the area is in contact with the searched area, the duplicated search can be reduced by ending the search, and the search can be performed efficiently.

Next, the material analysis method is evaluated after the search for the polymer pathway is completed. The evaluation may be an extension analysis for detecting a stretched chain, or an unloading analysis may be performed. The method of analyzing the material analyzes the detected polymer pathway and classifies the polymer pathway between the fillers and the other polymer pathways, that is, the polymer pathways in the matrix and not between the two fillers.

7 and 8 are explanatory views showing an example of a material analysis method according to the present embodiment. The polymer pathway between the fillers will be described below. As shown in FIG. 7, in the material analysis method, among the pair of the first filler model 11 and the second filler model 12 included in the analysis model 1, the first analysis target is in the region around the first filler model 11. The region A11 is set, and the second analysis target region A12 is set in the region around the second filler model 12. The polymer particles 21a existing in the first analysis target region A11 are polymer particles belonging to the search start point group 30, and the polymer particles 21a existing in the second analysis target region A12 are polymer particles belonging to the search end point group 32. Here, the region around the first filler model 11 in which the first analysis target region A11 is set is mutual such as intermolecular force and hydrogen bond from the first filler model 11 composed of a plurality of filler particles 11a. It is a nearby region within the range affected by the action of the polymer model 21. This also applies to the second analysis target region A12. Then, it exists between the first analysis target area A11 and the second analysis target area A12, a part exists in the first analysis target area A11, and a part exists in the second analysis target area A12. The pathway R1-R3 of the specific polymer model 21 included in the plurality of polymer models 21 in which is present is defined as the polymer pathway between the fillers. It is determined that the path R2 and the path R3 are not the paths connecting the two filler particle groups.

In the polymer model (polymer pathway) 21 in which the pathway is established between the two filler particles, one end is present in the first analysis target region A11 and the other end is present in the second analysis target region A12. In the polymer model 21, a complex three-dimensional network is formed by a plurality of polymer models 21 through cross-linking. In the present embodiment, a plurality of polymer particles 21a (representative points P1 and representative points P3) on one end side arranged in the first analysis target region A11 of the polymer model 21 are extracted as the first polymer particle group, and are also extracted. A plurality of polymer particles 21a (representative points P2 and representative points P4) on the other end side arranged in the second analysis target region A12 are extracted as the second polymer particle group. The number of polymer particle groups to be extracted is not limited.

In the example shown in FIG. 7, the first analysis target region A11 is between the polymer particles 21a belonging to the first polymer particle group (representative point P1) and the polymer particles 21a belonging to the second polymer particle group (representative point P2). And the inter-filler path R1 formed by the polymer particles 21a outside the range of the second analysis target region A12 is extracted as the inter-filler polymer path.

The example shown in FIG. 8 shows a plurality of polymer pathways. The first polymer model 21-1 and the second polymer model 21-2 are arranged between the first filler model 11 and the second filler model 12. The first polymer model 21-1 is composed of polymer particles 21-1a and a binding chain 21-1b. The second polymer model 21-2 is composed of polymer particles 21-2a and a binding chain 21-2b.

In the example shown in FIG. 8, the representative points P1 and P2 and the points P3 and P4 of the first polymer model 21-1 are shown as in FIG. 7. Further, in the example shown in FIG. 8, the inter-filler path R21 between the representative point P5 and the representative point P6 is extracted as the polymer path between the fillers. In this embodiment, in addition to the above pathway, the pathway between the two filler particles is extracted as the polymer pathway between the fillers. Of the polymer pathways extracted in this way, the polymer pathway between the fillers is defined as the polymer pathway between the fillers, and if at least one of them is not within a predetermined range based on the filler, the polymer pathway in the matrix is used.

In the case of elongation analysis, it is preferable to use a filler pair in which the distance between fillers is increased (preferably 20% or more of the system) as the filler pair to be analyzed. In the case of unloading analysis (analysis of return from elongation), it is preferable to use the filler pair set in the elongation analysis as the filler pair to be analyzed. For example, the relative position and distance of the extracted polymer pathway are detected, the force generated per unit bond is calculated based on the distance between two adjacent polymer particles in the polymer pathway, and the force generated per unit bond is calculated. The force generated in the polymer pathway is calculated based on the force being applied.

First, the pathway length of each polymer pathway is calculated. In the case of the polymer pathway between the fillers shown in FIGS. 7 and 7, the bond length between the representative point P1, the representative point P2, the point P3 and the point P4 is a straight line between the representative point P1, the representative point P2, the point P3 and the point P4. The analysis may be performed using the number of particles or the number of bonds of the polymer particles 21a interposed between the representative points P1, the representative points P2, the points P3 and the points P4 without using the distance, and the polymer particles 21a may be analyzed by temperature change analysis. The analysis may be performed after reducing the fluctuation of the bond length due to the thermal vibration of. The conditions for the temperature change analysis in this case include, for example, a temperature below the glass transition point (Tg) of the prepared polymer model 21. When the bond length of the polymer model 21 is used for the analysis of the shortest path, the average value of the thermal fluctuation of the polymer particles 21a and the equilibrium length at the time of expansion and contraction of the bond chain 21b may be used. By analyzing the bond length between the representative points P1, the representative points P2, the points P3 and the points P4 in this way, the influence of the thermal fluctuation of the polymer model 21 can be eliminated, so that the representative points P1, the representative points P2, the points P3 and It is possible to analyze the path between points P4 with high accuracy.

Further, the region near the filler particles may be evaluated by specifying the distance from the center of the filler and the polymer particles in the region may be evaluated, or the distance from the surface of the filler, that is, the shortest distance from the particle group constituting the filler. You may set the distance. Further, the region near the filler is preferably set to be equal to or less than the range in which the interaction with the filler acts. The distance between the fillers may be the distance between the centers or the distance between the surfaces.

The interaction between the first filler model 11 and the polymer model 21 is set between the filler particles, between the polymer particles, and between the filler particles and the polymer particles, and is not necessarily applied to all the filler particles and the polymer particles. No need to set. The interaction between the first filler model 11 and the polymer model 21 includes, for example, chemical interactions such as intermolecular force and attractive force such as hydrogen bond and repulsive force, and physical interaction such as covalent bond. Can be mentioned. Further, when the polymer model 21 is composed of a plurality of types of polymer particles 21a, the interaction may be set for each of the plurality of types of polymer particles 21a. Further, the interaction between each of the plurality of types of polymer particles 21a and the first filler model 11 may be the same or different.

For example, as an evaluation, it is determined whether or not the path between the first filler model 11 and the second filler model 12 is a stretched chain, and the force acting between the filler models is evaluated.

Next, a method for determining whether or not the chain is fully extended will be described. FIG. 9 is an explanatory diagram showing a method of determining whether or not the path between the first filler model 11 and the second filler model 12 is a stretched chain in the present embodiment. Although FIG. 9 describes the polymer pathway between fillers as an example, the polymer pathway forming a matrix can be similarly determined. FIG. 9 shows a first polymer model 21-1, a second polymer model 21-2, and a third polymer model 21-3. Although three polymer models are shown in FIG. 9, this is an example and does not limit the present invention.

The first polymer model 21-1 to the third polymer model 21-3 are the first polymer particle 21a-1, the second polymer particle 21a-2, the third polymer particle 21a-3, and the fourth polymer particle, respectively. It is composed of 21a-4, a fifth polymer particle 21a-5, and a sixth polymer particle 21-6a. In this case, the second polymer particles 21a-2 correspond to the representative point P1, the fifth polymer particles 21a-5 correspond to the representative point P2, the first polymer particles 21a-1 correspond to the point P3, and the sixth polymer particles 21a-6 correspond to the point P4. are doing.

The first polymer particles 21a-1 and the second polymer particles 21a-2 are bound by the first bond chain 21b-1. The second polymer particles 21a-2 and the third polymer particles 21a-3 are bound by a second bond chain 21b-2. The third polymer particles 21a-3 and the fourth polymer particles 21a-4 are bound by a third bond chain 21b-3. The fourth polymer particles 21a-4 and the fifth polymer particles 21a-5 are bound by the fourth bond chain 21b-4. The fifth polymer particles 21a-5 and the sixth polymer particles 21a-6 are bound by the fifth bond chain 21b-5.

In the present embodiment, in order to determine whether or not the first polymer model 21-1 is a stretched chain, first, the distance between the first polymer particles 21a-1 and the sixth polymer particles 21a-6 is determined. L (hereinafter, also referred to as the distance between the ends) is calculated. Next, in the present embodiment, the path length of the polymer path connecting the first polymer particles 21a-1 and the sixth polymer particles 21a-6 is calculated. The pathway length is, for example, the first bond chain 21b-1, the second bond chain 21b-2, the third bond chain 21b-3, the fourth bond chain 21b-4, and the fifth bond chain 21b-5. It is calculated by adding the lengths of each. Further, the pathway length of the polymer pathway may be calculated based on the average length of each binding chain calculated and the calculated average length and the number of polymer particles constituting the polymer pathway. Further, in the present embodiment, the path length of the polymer path may be calculated based on a spline curve or a Bezier curve created based on the polymer particles constituting the polymer path. In this embodiment, it is determined whether or not the first polymer model 21-1 is a stretched chain by comparing the calculated distance between the ends with the path length of the polymer pathway. In the present embodiment, for example, when the distance between the ends and the path length of the polymer pathway have a predetermined relationship, the first polymer model 21-1 is determined to be a stretched chain. In this embodiment, for example, when the distance between the ends is 90% or more of the pathway length of the polymer pathway, it is determined that the polymer pathway is a stretched chain, but the present embodiment is not limited to this.

In the present embodiment, similarly to the first polymer model 21-1, it is determined whether or not the second polymer model 21-2 and the third polymer model 21-3 have a stretched chain. Thereby, in this embodiment, the number of stretched chains included in the analysis model 1 can be calculated. As a result, in this embodiment, it is possible to extract the stretched chain existing between the first filler model 11 and the second filler model 12 and having a large contribution to the mechanical response.

Next, a method for evaluating the state of the first polymer model 21-1 will be described.

First, in the present embodiment, in order to evaluate the state of the first polymer model 21-1, the force generated in the first polymer model 21-1 is calculated. The force generated in the first polymer model 21-1 can be evaluated by, for example, "the length of the first polymer model 21-1 x the force per unit length". Further, the force generated in the first polymer model 21-1 may be evaluated by, for example, "the number of bonds existing in the first polymer model 21-1 x the force per unit bond".

The force per unit length or the force per unit bond is, for example, the first bond chain 21b-1, the second bond chain 21b-2, the third bond chain 21b-3, and the fourth bond chain 21b-4. And the fifth bond chain 21b-5 can be calculated. Specifically, the first bond chain 21b-1, the second bond chain 21b-2, the third bond chain 21b-3, the fourth bond chain 21b-4, and the fifth bond chain 21b-5 are The equilibrium length, which is the bond length, has a distance L1, a distance L2, a distance L3, a distance L4, and a distance L5, respectively. Further, the first binding chain 21b-1, the second binding chain 21b-2, the third binding chain 21b-3, the fourth binding chain 21b-4, and the fifth binding chain 21b-5 have springs. As the constants, a spring constant k1, a spring constant k2, a spring constant k3, a spring constant k4, and a spring constant k5 are defined, respectively. Therefore, the force generated in the first coupling chain 21b-1 to the fifth coupling chain 21b-5 is calculated based on the deviation (elongation) from the distance L1 to the distance L5 and the spring constant k1 to the spring constant k5. can do. More specifically, as the first binding chain 21b-1 to the fifth binding chain 21b-5 extend and the deviation from the equilibrium length increases, the generated force increases. Thereby, in the first polymer model 21-1, the present embodiment can calculate the force per unit length and the force per unit bond. Then, as described above, in the present embodiment, for example, by multiplying the force per unit bond by the number of bonds existing in the first polymer model 21-1, the force generated in the first polymer model 21-1 is multiplied. It can be calculated and the state of the first polymer model 21-1 can be evaluated. Further, in the present embodiment, the force generated in the first polymer model 21-1 may be calculated by multiplying the force per unit length by the length of the first polymer model 21-1. The distances L1 to L5 may be the same or different. Further, the spring constants k1 to k5 may be the same or different from each other.

When there are N polymer models (N is an integer of 2 or more) between the first filler model 11 and the second filler model 12, the force generated in each of the N polymer models is calculated. You may. In this case, in this embodiment, the sum of the forces generated in each of the N polymer models may be calculated, and the force generated in the entire system may be calculated.

In this embodiment, for example, among the polymer models existing between the first filler model 11 and the second filler model 12, only the polymer model having a stretched chain may be evaluated. Specifically, in the case of the example shown in FIG. 7, the present embodiment is a stretched chain of the first polymer model 21-1, the second polymer model 21-2, and the third polymer model 21-3. You may calculate the force generated only for the target. In this case, in this embodiment, the force generated in the stretched chain extracted between the first filler model 11 and the second filler model 12 is calculated, and the force is generated in the stretched chain existing in the entire system. It is possible to calculate the sum of the forces. As a result, the present embodiment can clarify the mechanism of the increase in the rigidity (stress) of the system due to the stretched chain generated between the fillers. In addition, this embodiment can clarify the morphology of the filler, the motion of the polymer with the nanostructure factor such as the filler diameter, and the relationship between the nanostructure factor and the mechanical property of the system. Further, in the present embodiment, since the state of elongation of the stretched chain that is easily cut can be quantified, the possibility of breakage of the stretched chain can be predicted.

Further, in the present embodiment, it may be determined at predetermined time intervals whether or not the first polymer model 21-1 to the third polymer model 21-3 have a stretched chain. In this case, in this embodiment, the state of the stretched chain may be determined at predetermined time intervals. Thereby, in the present embodiment, it is possible to calculate the time history in which the analysis result of the analysis model 1 and the number of stretched chains are associated with each other. Further, in the present embodiment, it is possible to calculate the time history in which the analysis result of the analysis model 1 and the state of the stretched chain are associated with each other. The predetermined time interval is not particularly limited and may be set to an interval desired by the user. Further, in the present embodiment, the time history of one analysis result may be evaluated, or the time history of different analyzes may be evaluated. When evaluating the time history of one analysis result, for example, it is possible to evaluate the change in the stretched chain during the stretching process in the stretching test. When evaluating the time history of different analyzes, it is possible to evaluate the difference in the effect on the stretch chain according to the analysis.

Further, in the present embodiment, the time history of the number of stretched chains included in the analysis model 1 may be visualized and displayed. In this case, the present embodiment displays, for example, a graph in which the horizontal axis is time and the vertical axis is the number of stretched chains. The horizontal axis may be, for example, the number of steps such as a load test or the magnitude of strain when deformation analysis is performed. Further, in the present embodiment, the time history of the state of the stretched chain included in the analysis model 1 may be visualized and displayed. In this case, in this embodiment, for example, the horizontal axis represents time and the vertical axis represents the amount of stretched chain. The horizontal axis may be, for example, the number of steps in the load test or the magnitude of strain when deformation analysis is performed. In this embodiment, for example, a table in which the number of stretched chains and the state of stretched chains are arranged for each determined time may be displayed. In the present embodiment, the method of visualizing the time history is not limited to these.

Further, in this embodiment, based on the calculated time history of the number of stretched chains, the first analysis result analyzed in the first analysis time and the second analysis time different from the first analysis time were analyzed. The difference from the second analysis result may be calculated. Thereby, the present embodiment can calculate the material properties such as the hysteresis, the hysteresis ratio, and the stress softening of the analyzed composite material. At this time, the number of stretched chains in the first analysis time and stretched chains in the second analysis time may be calculated. As a result, in the present embodiment, by calculating the difference between the number of stretched chains in the first analysis time and the number of stretched chains in the second analysis time, the change in the number of stretched chains and the material properties Can be associated with changes in. In this embodiment, the difference in the number of stretched chains when the strains are the same in the deformation analysis performed under the first analysis condition and the second analysis condition different from the first analysis condition is calculated and calculated. It is preferable to integrate the differences over the entire time. Further, in the present embodiment, the state of the stretched chain during the first analysis time may be compared with the state of the stretched chain during the second analysis time. Thereby, in the present embodiment, the change in the state of the stretched chain can be associated with the change in the material properties.

Further, in the present embodiment, the number of stretched chains included in the comparative analysis model of the polymer model in which parameters different from those of the analysis model 1 are set is calculated, and the calculated result and the analysis model 1 are included. It may be compared with the number of stretched chains. Further, in the present embodiment, the state of the stretched chain included in the analysis model 1 may be compared with the state of the stretched chain included in the comparative analysis model. Thereby, in this embodiment, it is possible to evaluate the influence of various parameters of the polymer model on the number of stretched chains included in the analysis model 1 and the state of stretched chains. Parameters include, for example, volume fraction of filler, filler diameter, distance between fillers, amount of bound rubber, thickness of bound rubber, morphology of filler, crosslinked structure of polymer, temperature, and elongation rate in stretching test.

Further, as an evaluation method, it is also possible to analyze whether or not the polymer model 21 has a folded structure in the first analysis target region A11.

Further, in the present embodiment, the first distance between the representative points P1 and the representative points P2 of the polymer particles 21a in the first analysis time of the composite material analysis model 1 and the second analysis different from the first analysis time. The path between the representative point P1 and the second distance between the representative points P2 in time may be analyzed. By this analysis, it is possible to analyze the change in the path between the representative point P1 and the representative point P2 due to the movement of the polymer particles 21a in a certain period of time. In this case, the present embodiment may determine whether or not the path between the first distance and the second distance is a stretched chain. Thereby, in this embodiment, the change of the pathway accompanying the movement of the polymer particles 21a in a certain period can be analyzed more accurately. Specifically, in the present embodiment, it is possible to calculate the change in the number of stretched chains included in the analysis model 1 by determining the change in the path between all the fillers included in the analysis model 1. it can. Further, in the present embodiment, the state of the route between the first distance and the state of the route between the second distance may be evaluated. Thereby, the present embodiment can analyze the change in the state of the pathway accompanying the movement of the polymer particles 21a in a certain period of time.

Further, in the material analysis method according to the present embodiment, it is preferable to visualize at least one of the polymer particles 21a and the binding chain 21b included in the path between the representative points P1 and the representative points P2 of the polymer particles 21a. .. This makes it possible to easily confirm the inter-filler path R1 of the polymer particles 21a between the filler particles 11a and the filler particles 12a. The visualization of the polymer particles 21a and the binding chain 21b may be made, for example, by coloring and visualizing all the polymer particles 21a and the binding chain 21b, or by coloring and visualizing some of the polymer particles 21a and the binding chain 21b. The area of may be made transparent. Further, the visualization of the polymer particles 21a and the binding chain 21b may be visualized by designating the same polymer particles 21a and the binding chain 21b for each of a plurality of different analysis times, and for each of a plurality of different analysis times. The polymer particles 21a and the binding chain 21b may be visualized. Further, it is not always necessary to visualize only the polymer particles 21a and the binding chain 21b, and the filler particles 11a may be visualized, or a part of the region of the analysis model 1 may be visualized. Further, in the present embodiment, when the stretched chain is detected, it is preferable to color the stretched chain in order to facilitate the distinction between the stretched chain and the non-stretched chain. This makes it possible to easily confirm whether or not the polymer model 21 has a stretched chain. Further, in the present embodiment, when a plurality of stretched chains are detected, it is preferable to color different colors depending on the state of the stretched chains. As a result, in this embodiment, the state of the stretched chain included in the analysis model 1 can be easily confirmed.

Further, in the present embodiment, as the polymer model 21, a plurality of first polymer models 21-1 and a plurality of second polymer models 21-2 having parameters different from those of the first polymer model 21-1 are created, and the first polymer is prepared. The pathways of representative points of model 21-1 and second polymer model 21-2 may be analyzed and evaluated. By this analysis, the distance between the first polymer model 21-1 and the second polymer model 21-2 and the first filler model 11 and the second filler model 12 due to the change in the parameters of the polymer model 21 Changes can also be analyzed. Further, in the present embodiment, it may be determined whether the structure of a plurality of polymer models having different parameters is a stretched chain. This makes it possible to determine whether or not the chain is fully extended according to the parameters of the polymer model 21. In addition, changes in the structure of the polymer model 21 due to changes in parameters can be analyzed. Also, in this embodiment, the structural state of a plurality of polymer models with different parameters may be evaluated. This makes it possible to evaluate the state of the polymer model 21 according to the parameters of the polymer model 21. Further, in the present embodiment, the state of the stretched chain may be evaluated only when the structure of the polymer model is determined to be the stretched chain. This makes it possible to evaluate the state of the stretched chain according to the state of the polymer model 21. Also, the polymer pathways in the matrix can be evaluated in the same way.

As described above, according to the above embodiment, the state of the structure of the searched interfiller path and the state of the structure between the matrices can be evaluated, and the structure of the searched interfiller path and the structure between the matrices can be evaluated. Since it is possible to determine whether or not each of the states is a stretched chain, it becomes possible to analyze the polymer network with higher accuracy. As a result, the material properties of the composite material can be analyzed with high accuracy, and the relationship between the material properties (hysteresis) such as energy loss due to the deformation of the composite material and the mechanism of the nanostructure of the composite material is further clarified. It becomes possible to do.

Further, when detecting the stretched chain, the stretched chain may be extracted based on the orientation of the bond of the polymer pathway. That is, the bonds that are lined up within a predetermined angle range may be extracted. Here, the orientation angle is preferably 120 ° or more, and more preferably 150 ° or more. This makes it possible to appropriately detect stretched chains that generate a force in the composite material. Moreover, it is preferable to evaluate the angle of three or more bonds as the orientation angle. As a result, it is possible to suppress the extraction of a polymer pathway in which a certain number of bonds are not connected at a predetermined angle as a stretched chain.

Examples of the numerical analysis to be performed in the material analysis method according to the present embodiment include relaxation analysis, extension analysis, temperature change analysis, and transformation analysis. When performing the extension analysis, it is preferable to include at least the non-deformation state in the evaluation time. As a result, the number of particles peeled off in the stretching process can be evaluated by comparing the analysis result in the evaluation time in the non-deformed state with the analysis result after the stretching analysis. In addition, the present embodiment can evaluate the number of stretched chains broken during the stretching process. In addition, the present embodiment can evaluate the state of the stretched chain changed in the stretching process.

Further, the material analysis method according to the present embodiment can comprehensively detect the polymer pathway by searching for both the main chain and the crosslinked bond of the polymer pathway, but the method is not limited to this. FIG. 10 is an explanatory diagram showing an example of a material analysis method according to the embodiment of the present invention. As a method for analyzing the material, as shown in FIG. 10, it is not necessary to extract only the polymer pathway of the main chain 34 and not to extract the cross-linking bond (bond connecting the main chains) as the pathway. This makes it easy to search for a route.

FIG. 11 is an explanatory diagram showing an example of a material analysis method according to the embodiment of the present invention. As shown in FIG. 11, the material analysis method is such that the polymer particles of the search start particle group 30 and the polymer particles of the search end particle group 32 are located at positions sandwiching the crosslink 36, and the crosslink 36 and the crosslink 36. You may want to search for the polymer pathway in the region 50 near the cross-linked bond 36 of the main chain 34 bound to. This makes it possible to search for a polymer pathway that sandwiches a crosslinked bond. Further, as shown in FIG. 10, it is possible to search for a polymer pathway that could not be searched when only the main chain was searched.

FIG. 12 is an explanatory diagram showing an example of a material analysis method according to the embodiment of the present invention.
The method of analyzing the material may end the search for the polymer pathway through the cross-linking, as shown in FIG. As a result, the main chain 34 connecting one of the polymer particles of the search start particle group 30 and one of the polymer particles of the search end particle group 32 and the crosslinked bond 36 connected to the main chain 34 can be searched. It is possible to search the areas 60, 62, 64. As a result, by switching the polymer particles of the search start particle group 30, each main chain 34 can be searched without overlapping, and by extracting the crosslinked bond 36, the main chains 34 are connected to each other. Polymer pathways can also be explored.

Next, the material analysis method and the computer program for analyzing the composite material according to the present embodiment will be described in more detail. FIG. 13 is a functional block diagram of an analysis device that executes the material analysis method according to the present embodiment.

As shown in FIG. 13, the material analysis method according to the present embodiment is realized by the analysis device 50, which is a computer including the processing unit 52 and the storage unit 54. The analysis device 50 is electrically connected to an input / output device 51 including an input means 53. The input means 53 processes various physical property values of the polymer and the filler for which the analysis model of the composite material is to be created, the actual measurement result of the elongation test result using the composite material containing the polymer and the filler, and the boundary conditions in the analysis. Input to unit 52 or storage unit 54. As the input means 53, for example, an input device such as a keyboard or a mouse is used.

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 expands it in the memory when executing various processes. The computer program expanded in the memory 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. Model creation and composite material analysis Various processes related to composite material analysis using the model are executed.

The processing unit 52 includes a model creation unit 52a, a condition setting unit 52b, and an analysis unit 52c. The model creation unit 52a has the number of particles, the number of molecules, and the molecular weight of the composite material such as filler and polymer when creating the model 1 for analysis of the composite material by the molecular dynamics method based on the data stored in the storage unit 54 in advance. , Molecular chain length, number of molecular chains, branching, shape, size, reaction time, reaction conditions, number of molecules included in the model for analysis to be created, target number of molecules, etc. The initial conditions of various calculation parameters such as the coarsening model of and the interaction between molecular chains are set.

As the calculation parameters for adjusting the interaction between the filler particles 11a and the interaction between the polymer particles 21a, σ and ε of the Lennard-Jones potential represented by the following formula (1) are used, and these are adjusted. By increasing the upper limit distance (cutoff distance) for calculating the potential, it is possible to adjust the attractive force and repulsive force that worked over a long distance. It is preferable to sequentially reduce the parameters of the interaction between the filler particles 11a and the interaction between the polymer particles 21a until the interaction between the filler particles 11a and the interaction between the polymer particles 21a reaches a constant value. 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 attractive force and repulsive force can be adjusted within an appropriate range.

The condition setting unit 52b sets various analysis conditions such as cross-linking analysis and various numerical analyzes such as relaxation analysis, extension analysis, temperature change analysis and transformation analysis. The analysis unit 52c executes the cross-linking analysis of the polymer model 21 and various numerical analyzes of the analysis model 1 based on the analysis conditions set by the condition setting unit 52b. Further, the analysis unit 52c sets the first analysis target region A11 around the first filler model 11 and sets the second analysis target region A12 around the second filler model 12. In addition, the analysis unit 52c extracts a specific polymer model 21 in which a part thereof exists in the first analysis target region A11 and the second analysis target region A12, respectively. Further, the analysis unit 52c sets a representative point P1 or the like for the polymer particles 21a of the first polymer particle group in the first analysis target region A11 of the specific polymer model 21, and also sets a second analysis target region A12 in the second analysis target region A12. A representative point P2 or the like is set for the polymer particles 21a of the polymer particle group. Then, the analysis unit 52c searches for an inter-filler path between the polymer particles 21a of the first polymer particle group and the polymer particles 21a of the second polymer particle group in the second analysis target region A12.

Further, the analysis unit 52c determines whether or not the structure of the inter-filler path between the polymer particles in the first analysis target region A11 and the polymer particles in the second analysis target region A12 is a stretched chain. To do. The analysis unit 52c determines, for example, whether or not the structure of the inter-filler path between the polymer particles 21a of the first polymer particle group and the polymer particles 21a of the second polymer particle group is a stretched chain. In this case, the analysis unit 52c calculates the distance between the ends of the polymer particles 21a of the first polymer particle group and the polymer particles 21a of the second polymer particle group. In addition, the analysis unit 52c calculates the path length of the path connecting the polymer particles 21a of the first polymer particle group and the polymer particles 21a of the second polymer particle group. The analysis unit 52c compares the distance between the ends and the path length, and determines that the structure of the path between the fillers is a stretched chain when the distance between the ends and the path length have a predetermined relationship. The analysis unit 52c determines, for example, that the structure of the interfiller path is a stretched chain when the distance between the ends is 90% or more of the path length.

In addition, the analysis unit 52c evaluates the state of the structure of the inter-filler path between the polymer particles in the first analysis target region A11 and the polymer particles in the second analysis target region A12. Specifically, the analysis unit 52c calculates the force generated in the inter-filler path. The analysis unit 52c calculates, for example, the force generated per unit bond based on the distance between adjacent polymer particles existing in the interfiller path. In this case, the analysis unit 52c calculates the force generated in the inter-filler path by multiplying the number of bonds between the polymer particles by the force generated per unit bond in the inter-filler path. The analysis unit 52c may calculate the force generated in the inter-filler path only when the inter-filler path is a stretched chain.

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, which is a recording medium capable of reading only, and a RAM (Random Access Memory). Volatile memory, which is a possible recording medium, is appropriately combined.

The storage unit 54 contains data on fillers such as rubber carbon black, silica, and alumina, which are data for creating an analysis model of the composite material to be analyzed via the input means 53, rubber, resin, and elastomer. Data of polymers such as, stress-strain curve which is a preset physical quantity history, a method of creating a model for analysis of a composite material according to the present embodiment, a computer program for realizing a method of analyzing a material, and the like are stored. This computer program may be capable of realizing the material analysis method according to the present embodiment in combination with a computer program already recorded in the computer or the computer system. The term "computer system" as used herein includes hardware such as an OS (Operating System) and peripheral devices.

The display means 55 is, for example, a display device such as a liquid crystal display device. The storage unit 54 may be provided 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 provided with the input / output device 51.

Next, the method of analyzing the material according to the present embodiment will be described in more detail with reference to FIG. 2 again. The same applies to FIG. 1 except that the filler particles are not included and the comparison between the fillers and the matrix is not performed.

As shown in FIG. 2, the model creation unit 52a creates an uncrosslinked polymer model 21 in a predetermined model creation region A and also creates a first filler model 11 (step ST11). As shown in FIG. 3, the uncrosslinked polymer model 21 is formed by connecting a plurality of polymer particles 21a by a binding chain 21b. Here, the model creation unit 52a creates a plurality of first filler models 11 and a plurality of polymer models 21 as needed. Next, the model creation unit 52a arranges the uncrosslinked polymer model 21 in the created first filler model 11 to create the composite material analysis model 1. Here, the model creation unit 52a performs the equilibrium calculation after setting the initial conditions. In the equilibrium calculation, molecular dynamics calculation is performed at a predetermined temperature, density, and pressure for a predetermined time for various components after initial setting to reach an equilibrium state. Then, the model creation unit 52a includes the polymer particles 21a and the binding chain 21b in the model creation region A for creating the analysis model of the composite material set in the calculation region after the initial condition setting and the equilibrium calculation processing. A first filler model 11 including the polymer model 21 and the filler particles 11a is created. Further, the model creation unit 52a may add a modifying agent such as a hydroxyl group, a carbonyl group, and a functional group of an atomic group, which enhances the affinity with the filler, to the polymer, if necessary.

Next, the condition setting unit 52b sets various conditions for executing the cross-linking analysis, the numerical analysis, and the motion analysis (simulation) by the molecular dynamics method using the composite material analysis model 1 created by the model creation unit 52a. Set. The condition setting unit 52b sets various conditions based on the input from the input means 53 and the information stored in the storage unit 54. Various conditions include the position and number of the first filler model 11 for performing the analysis, the filler atom, the filler atom group, the position and number of the filler particles 11a and the filler particle group, the filler particle 11a number, the position and the position of the molecular chain of the polymer, and so on. Number, position and number of polymer atom, polymer atomic group, polymer particle 21a and polymer particle group, polymer particle number, position and number of bond chain 21b and bond chain 21b, number of bond chain 21b, preset physical quantity history. Includes stress-strain curves and fixed values that do not change conditions.

Next, the analysis unit 52c executes a cross-linking analysis in the uncross-linked polymer model in the composite material analysis model 1 to create a cross-linking point (step ST12). Here, the model creation unit 52a identifies predetermined polymer particles 21a in the uncrosslinked polymer model 21 and creates a crosslink point. As a result, in the composite material analysis model 1, a large polymer model 21 after cross-linking is created by the plurality of polymer models 21. In addition, the cross-linking here means forming a polymer model 21 including polymer particles 21a formed by connecting three or more bonding chains 21b.

Next, the analysis unit 52c sets an interaction with the analysis model 1 after the cross-linking analysis and performs various numerical analyzes (step ST13). The interaction here includes, for example, the interaction between the filler particles 11a, the polymer particles 21a, the interaction between the filler particles 11a and the polymer particles 21a, and the state in which the filler particles 11a and the polymer particles 21a are bonded by a binding chain. Interactions can be mentioned, but not all of these need to be set. Numerical analysis includes relaxation analysis, extension analysis, temperature change analysis, and transformation by molecular dynamics using the first filler model 11 created by the model creation unit 52a and model 1 for analysis of composite materials including the polymer model 21. Numerical analysis by motion analysis such as analysis and deformation analysis such as shear analysis can be mentioned. Further, the analysis unit 51c acquires various physical quantities such as the motion displacement obtained as a result of the motion analysis by the numerical analysis and the nominal stress or the nominal strain obtained by calculating the motion displacement.

Next, the analysis unit 52c selects a polymer group to be evaluated (step ST14). Here, the analysis unit 52c selects at least a part of the polymer particles from the polymer group in the analysis region. The analysis unit 52c sets a search start point group from the polymer group (step ST15). Some polymer particles of the selected polymer group are set as polymer particles of the search start point group. For example, free-end particles are extracted and used as polymer particles in the search start point group. Further, the polymer particles of the search start point group may be determined based on the data input to the operator. The analysis unit 52c sets a search end point group from the polymer group (step ST16). A part of the polymer particles of the selected polymer group is set as the polymer particles of the search end point group. For example, free-end particles are extracted and used as polymer particles in the search end point group. Further, the polymer particles of the search end point group may be determined based on the data input to the operator. The analysis unit 52c extracts the path of the polymer at the start point and the end point (step ST17), and determines whether the path search of the extracted particles is completed (step ST18). The analysis unit sequentially selects polymer particles in the search start point group and repeats the search for the polymer path until the path search for the particles in the particle group satisfies the end condition.

If it is determined that the analysis unit 52c is not completed, the analysis unit 52c returns to step ST17, and if it is determined that the analysis unit is completed, the analysis unit 52c evaluates the composite material based on the route search picture result (step ST19). For example, the analysis unit 52c identifies whether the polymer pathway between the polymer particles in the search start point group and the polymer particles in the search end point group is between the fillers or in the matrix. Further, the analysis unit 52c calculates the distance between the ends and the path length between the polymer particles of the search start point group and the polymer particles of the search end point group, and calculates the distance between the ends and the path. Based on the length, it is determined whether or not the structure of the path between the polymer particles of the search start point group and the polymer particles of the search end point group is a stretched chain. Further, the analysis unit 52c calculates the force generated per unit bond in the stretched chain extracted between the fillers or in each region in the matrix, and in the extracted stretched chain, the unit bond is generated. Based on the force generated in the hit, the force generated in the entire stretch is calculated. The analysis unit 52c calculates the force generated per unit bond in the extracted path. The analysis unit 52c calculates the force generated in the entire extracted path based on the force generated per unit bond in the extracted path. Thereby, in the present embodiment, the mechanism of increasing the rigidity (stress) of the system due to the state of the path between the fillers, the mechanism of increasing the rigidity (stress) of the system due to the state of the path in the matrix, and the mechanism between the fillers. It is possible to clarify the relationship between the path of the above and the path in the matrix.

FIG. 14 is a graph in which the number of stretched chains and the time change of strain are associated with each other. FIG. 15 is a graph in which the stretched chain length and the strain are associated with the time change. FIG. 16 is a graph in which the elongation of the stretched chain and the time change of the strain are associated with each other. By performing analysis by the analysis unit 52c and analyzing the time changes such as the stretched chain and the strain between the fillers and in the matrix, the strain and the stretched chain are as shown in FIGS. 14 to 16. Changes in relationships can be analyzed.

1 Analysis model 11 1st filler model 12 2nd filler model 11a, 12a Filler particles 21 Polymer model 21a Polymer particles 21b Bonded chain 50 Analysis device 51 Input / output device 52 Processing unit 52a Model creation unit 52b Condition setting unit 52c Analysis unit 53 Input means 54 Storage unit 55 Display means A Model creation area A11 First analysis target area A12 Second analysis target area

Claims (18)

It is a material analysis method using a material analysis model created by the molecular dynamics method using a computer.
Steps to create a model for analysis of a material containing multiple polymer models that model a polymer with multiple polymer particles,
The step of cross-linking the polymer model by cross-linking analysis,
The step of setting the interaction in the analysis model after the cross-linking analysis and performing the numerical analysis,
A step of extracting particles belonging to a search start point group and particles belonging to a search end point group different from the search start point group.
One particle of the search start point group is specified as a start particle, a plurality of particles included in the search end point group are specified as end particles, and a polymer between the start particle and each particle of the end particle is specified. A method for analyzing a material, which comprises an extraction step of performing a process of extracting a path and extracting a polymer path of all paths between the particles of the search start point group and the particles of the search end point group. .. The method for analyzing a material according to claim 1, wherein the analysis model is a composite material including a plurality of polymer models in which a polymer is modeled by a plurality of polymer particles and a plurality of filler models in which fillers are modeled. The material analysis method according to claim 1 or 2, further comprising an evaluation step of evaluating the path length of the polymer pathway calculated in the extraction step using the number of bonds or the number of particles contained in the pathway. In the evaluation step, the distance between the ends of the polymer pathway from one end to the other end and the path length of the polymer pathway are calculated, and the polymer pathway is based on the distance between the ends and the pathway length. The method for analyzing a material according to claim 3, wherein it is determined whether or not is a stretched chain. The material analysis method according to claim 3 or 4, wherein the evaluation step is to carry out a route search in a low temperature state by temperature change analysis. The method for analyzing a material according to any one of claims 3 to 5, wherein the evaluation step evaluates the results at at least two times. The material analysis method according to claim 6, wherein the time history is visualized and displayed. The material analysis method according to claim 6 or 7, wherein the difference between the analysis result of the first analysis time and the analysis result of the second analysis time different from the first analysis time in the time history is calculated. .. A step of calculating the force generated per unit bond in the polymer pathway based on the distance between two adjacent polymer particles.
Analysis of the material according to any one of claims 6 to 8, comprising a step of calculating the force generated in the polymer pathway based on the force generated per unit bond. Method. The method for analyzing a material according to any one of claims 1 to 9, wherein the extraction step searches for a polymer pathway by breadth-first search. The particles of the search start point group are free-end particles, and are
The method for analyzing a material according to any one of claims 1 to 10, wherein the particles in the search end point group are free-ended particles. The particles in the search start point group are particles that were free-end particles of the polymer chain at the time before cross-linking.
The material analysis method according to any one of claims 1 to 11, wherein the particles in the search end point group are particles that were free-end particles of the polymer chain at the time before crosslinking. The method for analyzing a material according to any one of claims 1 to 11, wherein the extraction step ends the search for a route that merges with the searched polymer route. The method for analyzing a material according to any one of claims 1 to 12, wherein the extraction step searches for a polymer pathway in the main chain. The method for analyzing a material according to any one of claims 1 to 12, wherein the extraction step searches for a polymer pathway that sandwiches a crosslinked bond. The method for analyzing a material according to any one of claims 1 to 12, wherein the extraction step ends the search for a polymer pathway that has passed through a crosslinked bond. The method for analyzing a material according to any one of claims 1 to 16, wherein the analysis result of the analysis model is compared with the analysis result of a comparative analysis model different from the analysis model. A computer program for analyzing materials, which comprises causing a computer to execute the method for analyzing a material according to any one of claims 1 to 16.

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