JP7305981B2 - Material analysis method and material analysis computer program - Google Patents

Description

The present invention relates to a method for analyzing a material containing at least polymer particles and a computer program for analyzing a material. It relates to a computer program for material analysis.

Conventionally, a method for simulating polymeric materials using molecular dynamics has been proposed (see, for example, Patent Documents 1 and 2). In the polymeric material simulation method described in Patent Document 1, after setting a polymeric material model by molecular dynamics calculation using a filler model that models a filler and a polymer model that models a polymer, the set high Deformation analysis is performed using a finite element model modeled with a finite number of elements based on the molecular material model. Further, in the method for simulating a polymer material described in Patent Document 2, a coarse-grained model using a polymer material and a filler model including the outer surface of a filler are used to perform a molecular dynamics calculation, and then coarse-grained. The space in which the model is placed is divided into a plurality of minute regions to calculate the relaxation modulus.

JP 2015-056002 A JP 2014-203262 A

Here, in a substance such as rubber containing polymer particles, a large number of polymer crystal structures are formed in the regions where the polymer particles are arranged. Therefore, it is required to efficiently detect the crystal structure of a 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 material analysis computer program 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, a step of cross-linking the polymer model by a cross-linking analysis, a step of setting an interaction in the analysis model after the cross-linking analysis and performing a numerical analysis, and a search start a step of extracting a particle belonging to a point group and a particle belonging to a search end point group different from the search start point group; specifying one particle of the search start point group as a start particle; A plurality of particles included in the group are specified as end particles, a process of extracting a polymer path between each particle of the start particle and the end particle is performed, and the particles of the search start point group and the search end point and an extraction step of extracting the polymer pathways of all pathways between the particles of the group.

The analytical model is preferably a composite material including a plurality of polymer models in which a polymer is modeled using a plurality of polymer particles and a plurality of filler models in which a filler is modeled.

Moreover, it is preferable to further include an evaluation step of evaluating the length of the polymer path calculated in the extraction step using the number of bonds or the number of particles included in the path.

Further, in the evaluation step, an end-to-end distance from one end to the other end of the polymer route and a path length of the polymer route are calculated, and based on the end-to-end distance and the route length, the It is preferred to determine whether the polymer pathway is an extended chain.

In addition, it is preferable that the evaluation step performs a route search in a low temperature state by variable temperature analysis.

Also, the evaluating step preferably evaluates the results at least two times.

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

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

Further, in the polymer path, a step of calculating the force generated per unit bond based on the distance between two adjacent polymer particles; and calculating the force exerted on the polymer path.

Moreover, it is preferable that the extraction step searches the polymer path by breadth-first search.

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

In addition, the particles of the search starting point group are particles that were free terminal particles of polymer chains before crosslinking, and the particles of the search end point group are free terminal particles of polymer chains before crosslinking. It is preferable that the particles are coarse particles.

In addition, in the extraction step, it is preferable to terminate the search for a route that merges with a polymer route that has already been searched.

Moreover, it is preferable that the extraction step searches the polymer pathway of the main chain.

In addition, it is preferable that the extraction step searches for polymer pathways across cross-links.

Also, the extraction step preferably terminates the search for polymer pathways through cross-links.

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.

In addition, the present invention provides a computer program for material analysis, characterized by causing a computer to execute any of the material analysis methods described above.

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

FIG. 1 is a flow chart showing an outline of a method for analyzing a target material according to an embodiment of the present invention. FIG. 2 is a flow chart showing an outline of a material analysis method according to an embodiment of the present invention. FIG. 3 is a flow chart 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 an embodiment of the present invention. FIG. 6 is an explanatory diagram showing an example of the material analysis method according to the embodiment of the present invention. FIG. 7 is an explanatory diagram showing an example of the material analysis method according to the embodiment of the present invention. FIG. 8 is an explanatory diagram showing an example of the material analysis method according to the embodiment of the present invention. FIG. 9 is an explanatory diagram of the material analysis method according to the present embodiment. FIG. 10 is an explanatory diagram showing an example of the material analysis method according to the embodiment of the present invention. FIG. 11 is an explanatory diagram showing an example of the material analysis method according to the embodiment of the present invention. FIG. 12 is an explanatory diagram showing an example of the 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 this embodiment. FIG. 14 is a graph in which the number of stretched chains and strain are associated with each other over time. FIG. 15 is a graph showing the correspondence between the stretched chain length and strain over time. FIG. 16 is a graph in which the elongation and strain of an extended chain are associated with each other over time.

BEST MODE FOR CARRYING OUT THE INVENTION Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings. It should be noted that the present invention is not limited to the following embodiments, and can be implemented with appropriate modifications.

FIG. 1 is a flow chart showing an outline of a method for analyzing a target material according to the first embodiment of the present invention. As shown in FIG. 1, the target material analysis method according to the present embodiment is a material analysis method using an analysis model of a target material containing polymer particles created by a molecular dynamics method using a computer. This method of analyzing a target material is a method of analyzing a material containing at least polymer particles using a model for analysis of the target material created by a molecular dynamics method using a computer, wherein the polymer is modeled by a plurality of polymer particles. A first step ST1 of creating an analysis model of a material including a plurality of polymer models obtained by the analysis; A third step ST3 for performing an analysis, a fourth step ST4 for selecting a polymer group to be evaluated, a fifth step ST5 for setting a search start point group from the polymer group, and a search end point group from the polymer group. a sixth step ST6 for extracting the polymer paths at the start and end points; and an eighth step ST8 for determining whether the path search for the extracted particles has been completed. An eighth step ST8 determines that the search for the route is complete when the search for all particles in the search start point group is completed. That is, paths between all particles in the search start point group and all particles in the search end point group are searched. The eighth step S18 returns to the seventh step ST7 if it is determined not to be completed, and if it is determined to be completed, executes the ninth step ST9 of evaluating the composite material based on the route search result, End the process. A ninth step ST9 of evaluating the composite material evaluates each of the extracted polymer pathways. In the example shown in FIG. 1, the fourth step ST4 of selecting a polymer group to be evaluated is executed, but the search start point group and search end point group may be set without selecting a group of polymer particles. . Evaluation of polymer pathways is also described below.

INDUSTRIAL APPLICABILITY The present invention can be used for analysis of materials containing polymer particles, and can be suitably used for composite materials containing polymer particles and fillers. A case of application to a composite material containing a plurality of polymer particles and a plurality of fillers will be described below. Hereinafter, the invention will be described in detail using the case of a composite material, but the same applies to a material that does not contain a filler, such as a material that contains only polymer particles.

FIG. 2 is a flow chart showing an outline of a material analysis method according to the first embodiment of the present invention. The flowchart shown in FIG. 2 shows the case where the object of analysis is a composite material containing polymer particles and 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, wherein the polymer is modeled by a plurality of polymer particles and a filler. A first step ST11 for creating an analysis model of a material including a plurality of filler models modeled, a second step ST12 for cross-linking the polymer model by cross-linking analysis, and setting interaction in the analysis model after cross-linking analysis A third step ST13 for performing numerical analysis, a fourth step ST14 for selecting a polymer group to be evaluated, a fifth step ST15 for setting a search starting point group from the polymer group, and a search end point from the polymer group It includes a sixth step ST16 for setting groups, a seventh step ST17 for extracting polymer paths at the start and end points, and an eighth step ST18 for determining whether the path search for the extracted particles has been completed. An eighth step ST18 determines that the search for the route is complete when the search for all particles in the search start point group is completed. That is, paths between all particles in the search start point group and all particles in the search end point group are searched. The eighth step S18 returns to the seventh step ST17 if it is determined not to be completed, and if it is determined to be completed, executes the ninth step ST19 of evaluating the composite material based on the route search result, End the process. A ninth step ST19 of evaluating the composite material evaluates each of the extracted polymer pathways. As an example, as shown in FIG. 3, a step ST21 of calculating the end-to-end distance and the path length, a step ST22 of determining whether the polymer path is an extended chain based on the calculation results of step ST21, It includes a step ST23 of calculating the force per unit bond of the extended chain and a step ST24 of calculating the force generated in the entire extended chain. A first embodiment of the present invention will be described in detail below.

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 placed in a model creation area A which is a virtual space having a substantially cubic shape with one side having a length L. . Specifically, the analysis model 1 is 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 binding chains 21b as models. It has a plurality of polymer models 21 that are transformed. In this embodiment, an example in which the composite material to be analyzed contains a filler and a polymer that is a polymeric material will be described, but the present invention is also applicable to composite materials containing two or more substances. . Further, in the example shown in FIG. 4, the analysis model 1, two first filler model 11 and second filler model 12, and described an example having a plurality of polymer models 21, three or more filler models may be placed. Also, the model creation area A does not necessarily have to be a substantially cubic virtual space, and may have any shape such as a sphere, an ellipse, a cuboid, or a polyhedron.

The 1st filler model 11 and the 2nd filler model 12 are modeled in the state which several filler particles 11a and 12a each gathered in the substantially spherical body. Moreover, the 1st filler model 11 and the 2nd filler model 12 are arrange|positioned in the state which mutually took predetermined space|interval and left|separated. In addition, the 1st filler model 11 and the 2nd filler model 12 may be mutually connected with the outer edge part by the covalent bond in the mutually aggregated state.

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

Fillers include, for example, carbon black, silica, and alumina. The filler particles 11a and 12a are modeled by aggregating a plurality of filler atoms. A plurality of filler particles 11a and 12a aggregate to form a filler particle group. The plurality of filler particles 11a, 12a have their relative positions specified by binding chains (not shown) between adjacent each other. This binding chain has a spring function defined by an equilibrium length, which is a binding distance between the filler particles 11a and 12a, and a spring constant, and constrains the filler particles 11a and 12a. A binding chain|strand is a bond with which the potential which force generate|occur|produces by the relative position of filler particles 11a and 12a, a twist, bending, etc. is defined. The first filler model 11 and the second filler model 12 are numerical data (including the mass, volume, diameter and initial coordinates of filler particles 11a and 12a) for handling fillers in molecular dynamics. The numerical data of the 1st filler model 11 and the 2nd filler model 12 are input into a computer.

Polymers include, for example, rubbers, resins, elastomers, and the like. The polymer particles 21a are modeled by assembling a plurality of polymer atoms. A plurality of polymer particles 21a aggregate to form a polymer particle group. If necessary, the polymer is blended with a modifier that enhances affinity with the filler. Modifiers include, for example, hydroxyl groups, carbonyl groups, functional groups of atomic groups, 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 model creation area A at a predetermined density. The polymer particles 21a have their relative positions specified by the linking chains 21b between adjacent each other. The binding chain 21b has a spring function defined by an equilibrium length, which is a binding distance between polymer particles 21a, and a spring constant, and binds each polymer particle 21a. The binding chain 21b is a bond having a defined potential in which force is generated by the relative position, twisting, and bending of the polymer particles 21a. This polymer model 21 is numerical data (including the mass, volume, diameter and initial coordinates of the polymer particles 21a) for handling polymers in terms of molecular dynamics. Numerical data of the polymer model 21 are input to a computer.

Next, the material analysis method according to this embodiment will be described in detail. An example of a polymer that crosslinks between two fillers will be described below, but the polymer also crosslinks in areas other than between the fillers. 5 and 6 are explanatory diagrams each showing an example of the material analysis method according to the embodiment of the present invention.

FIG. 5 schematically shows a crosslinked polymer model within the analysis area. As shown in FIG. 4, the actual polymer pathways are those in which polymer particles are linked in various directions in three-dimensional space. . As shown in FIG. 5, the model creation region A to search for the polymer pathway includes the polymer particles 21a, the main chains (polymers) 34 formed by cross-linking the polymer particles 21a, and the main chains 34 cross-links 36 that 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 cross-linking 36 are detected.

In this analysis method, some polymer particles 21 a of the plurality of polymer particles 21 a included in the model creation region A are set as the polymer particles 21 a included in the search starting point group 30 . In this analysis method, a plurality of polymer particles 21 a that are included in the model creation region A but not included in the search start point group 30 are set as the polymer particles 21 a included in the search end point group 32 . Note that 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 of the many polymer particles 21a included in the model creation area A. is. In this 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 ends of polymer paths formed by crosslinking. As a result, the analysis can be efficiently performed, and arbitrary 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 selected as the end particles. set. Then, in the material analysis method, a path search is performed between the path search start particle and the 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 a full path search.

Here, the end particles are all the polymer particles 21a belonging to the search end point group 32 that have not established a path with the polymer particles 21a selected as the path search start particles (start particles). Specifically, a comprehensive search is made to see if there is a path that connects to either one of the polymer particles 21a belonging to the search start point group 30 or to the polymer particles 21a belonging to the search end point group 32 . In this embodiment, a breadth-first search is performed to search for polymer particles 21a connected from one polymer particle 21a from one polymer particle 21a belonging to the search starting point group 30, and two or more polymer particles 21a are connected. searches for a route connecting to each polymer particle 21a thereafter. In this embodiment, a route connecting with another main chain 34 is detected at a portion connected by a cross-linking bond 36, and the number of routes to be searched is increased.

In the example shown in FIG. 6, by performing the first route search by the material analysis method, from the starting point 40a, which is one polymer particle 21a belonging to the search starting point group 30, to the polymer particles belonging to the search ending point group 32 21a is extracted. In FIG. 6 , paths are established with polymer particles 21 a belonging to all search end point groups 32 , but paths may not be established with some of the polymer particles 21 a belonging to search end point groups 32 .

When the first route search is completed, the polymer particles 21a belonging to the search start point group 30 and different from the starting point 40a are set as the starting point 40b, and the second route search is performed. For the starting point 40b, it is preferable to select polymer particles 21a far from the starting point 40a. In the material analysis method of the present embodiment, when the same route as a searched route is reached during the route search, the route search for the route is terminated. When an all-routes search is performed from the start point 40b toward the search end point group 32, 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 by the overlap region 44, in the route search of the region 42b, the route search is not terminated at the time of contact with the region 42a. to end the route search. Overlapping detection of polymer pathways can be suppressed by overlapping search of some regions. In addition, when the routes overlap, by ending the search, duplicate route searches can be suppressed, and routes can be searched efficiently. In addition, it is preferable to evaluate the overlapping region for one or two bonds of the polymer particles. This makes it possible to detect the connection state of polymer pathways with higher accuracy.

When the second route search is completed, the starting point 40a is set from the polymer particles 21a belonging to the search starting point group 30, and the polymer particle 21a different from the starting point 40b is set as the starting point 40c, and the third route search is performed. For the starting point 40c, it is preferable to select polymer particles 21a far from the starting points 40a and 40b. In the material analysis method of the present embodiment, when the same route as a searched route is reached during the route search, the route search for the route is terminated. When a full route search is performed from the start point 40c toward the search end point group 32, as shown in FIG. 6, the route of the region 42c until it overlaps with the regions 42a and 42b is searched. In the material analysis method of the present embodiment, as shown by the overlap region 46, in the route search of the region 42c, the route search does not end when the region 42a is contacted, and the route search is performed when the routes of a certain distance overlap. exit. Further, as indicated by the overlapping area 48, in the route search of the area 42c, the route search is not terminated when the area 42b is touched, but is terminated when the paths of a certain distance are overlapped.

In the examples shown in FIGS. 5 and 5, only the paths connecting the polymer particles 21a of the search start point group 30 and the polymer particles 21a of the search end point group 32 are shown. A route that does not connect from the polymer particle 21a of the point group 30 to the polymer particle 21a belonging to the search end point group 32 is also searched. In this case, the material analysis method is that if the polymer particles 21a belonging to the search end point group 32 are not reached even after a certain distance connection (connection with a predetermined number of polymer particles 21a), the route search is terminated. good.

In this way, by selecting one polymer particle 21a in the search start point group 30 and a plurality of polymer particles in the search end point group 32 and extracting the polymer paths, the polymer paths can be efficiently and exhaustively extracted. can be detected.

In addition, as in the present embodiment, the distance from the polymer particle of the search starting 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. can be searched, but a depth-first search that sequentially searches paths one by one may be performed.

Further, as in the present embodiment, by making the polymer particles of the search start point group 30 and the search end point group 32 free terminal particles, the path search can be performed from the end of the polymer path. can be detected without omission.

It is also preferable that the polymer particles of the search start point group 30 and the search end point group 32 are free terminal particles of polymer chains before cross-linking. As a result, the route can be effectively searched when the free ends before cross-linking are cross-linked.

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

Moreover, by selecting a polymer particle whose starting point of the search starting point group 30 is distant from the previous starting point as in the present embodiment, it is possible to efficiently search for a route. In addition, when the search area is touched, by ending the search, duplicate searches can be reduced, and the search can be performed efficiently.

The material analysis method is then evaluated once the search for polymer pathways is complete. The evaluation may be carried out by elongation analysis for detecting stretched chains or by unloading analysis. The material analysis method analyzes the detected polymer pathways and classifies them into polymer pathways between fillers and other polymer pathways, that is, polymer pathways in the matrix but not between two fillers.

7 and 8 are explanatory diagrams showing an example of the material analysis method according to the present embodiment. The polymer pathways between fillers are described below. As shown in FIG. 7, in the material analysis method, in the area around the first filler model 11 of the pair of the first filler model 11 and the second filler model 12 included in the analysis model 1, the first analysis object A region A11 is set, and a second analysis target region A12 is set in a region around the second filler model 12 . The polymer particles 21a existing in the first analysis target area A11 are the polymer particles belonging to the search start point group 30, and the polymer particles 21a existing in the second analysis target area A12 are the polymer particles belonging to the search end point group 32. Here, the area around the first filler model 11 where the first analysis target area A11 is set is mutual interaction such as intermolecular forces and hydrogen bonds from the first filler model 11 composed of a plurality of filler particles 11a This is the neighboring area within the range where the polymer model 21 is affected by the action. This also applies to the second analysis target area A12. Then, the Paths R1-R3 of a specific polymer model 21 included in a plurality of polymer models 21 in which are present are defined as polymer paths between fillers. It is determined that route R2 and route R3 are not routes connecting two filler particle groups.

A polymer model (polymer path) 21 that establishes a path between two filler particles has one end in the first analysis target area A11 and the other end in the second analysis target area A12. The polymer model 21 forms a complicated three-dimensional network through cross-linking by a plurality of polymer models 21 . In the present embodiment, a plurality of polymer particles 21a (representative point P1 and representative point P3) on one end side arranged in the first analysis target area A11 are extracted from the polymer model 21 as the first polymer particle group, A plurality of polymer particles 21a (representative point P2 and representative point P4) on the other end side arranged in the second analysis target area A12 are extracted as a second polymer particle group. The number of polymer particle groups to be extracted is not limited.

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

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

In the example shown in FIG. 8, representative points P1, P2 and points P3, P4 of the first polymer model 21-1 are shown as in FIG. Furthermore, in the example shown in FIG. 8, the path|route R21 between fillers between the representative point P5 and the representative point P6 is extracted as a polymer path|route between fillers. In the present embodiment, in addition to the paths described above, paths between two filler particles are extracted as polymer paths between fillers. Among the polymer paths extracted in this manner, the polymer paths between the fillers are defined as the polymer paths between the fillers, and when at least one of the polymer paths is not within the predetermined range based on the filler, the polymer paths are defined as those in the matrix.

In the case of elongation analysis, it is preferable to use filler pairs with an increased inter-filler distance (preferably 20% or more of the system) as filler pairs 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 path are detected, the force generated per unit bond is calculated based on the distance between two adjacent polymer particles in the polymer path, and the force generated per unit bond is calculated. Based on the force exerted, the force exerted on the polymer path is calculated.

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

In addition, the vicinity region of the filler particles may be evaluated by specifying the distance from the center of the filler, and the polymer particles in that region may be evaluated, or the distance from the surface of the filler, that is, the shortest You can set the distance. In addition, it is preferable that the region near the filler be less than or equal to the range where the interaction with the filler acts. The distance between fillers may be the center-to-center distance or the surface-to-surface distance.

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 not necessarily for all filler particles and 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 forces and hydrogen bonds, attractive forces and repulsive forces, and physical interactions such as covalent bonds. mentioned. Moreover, when the polymer model 21 is composed of a plurality of types of polymer particles 21a, interactions may be set for each of the plurality of types of polymer particles 21a. Moreover, the interaction between each polymer particle 21a of several kinds and the 1st filler model 11 may be the same, and may differ.

For example, as evaluation, it determines whether the path|route between the 1st filler model 11 and the 2nd filler model 12 is an extended chain, and evaluates the force which acts between filler models.

Next, a method for determining whether or not a chain is an extended chain will be described. FIG. 9 : is explanatory drawing which shows the method of determining whether the path|route between the 1st filler model 11 and the 2nd filler model 12 is an extended chain in this embodiment. Although FIG. 9 illustrates polymer paths between fillers as an example, polymer paths forming a matrix can also be determined in the same manner. 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 respectively a first polymer particle 21a-1, a second polymer particle 21a-2, a third polymer particle 21a-3, and a fourth polymer particle. 21a-4, fifth polymer particles 21a-5, and sixth polymer particles 21-6a. In this case, the second polymer particle 21a-2 corresponds to the representative point P1, the fifth polymer particle 21a-5 corresponds to the representative point P2, the first polymer particle 21a-1 corresponds to the point P3, and the sixth polymer particle 21a-6 corresponds to the point P4. are doing.

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

In the present embodiment, in order to determine whether the first polymer model 21-1 is an extended chain, first, the distance between the first polymer particle 21a-1 and the sixth polymer particle 21a-6 L (hereinafter also referred to as the end-to-end distance) is calculated. Next, in this embodiment, the path length of the polymer path connecting the first polymer particle 21a-1 and the sixth polymer particle 21a-6 is calculated. The path length is, for example, 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. It is calculated by adding each length. Alternatively, the path length of the polymer path may be calculated by calculating the average length of each binding chain and based on the calculated average length and the number of polymer particles constituting the polymer path. Further, in this embodiment, the path length of the polymer path may be calculated based on a spline curve or Bezier curve created based on the polymer particles forming the polymer path. This embodiment determines whether or not the first polymer model 21-1 is an extended chain by comparing the calculated end-to-end distance with the path length of the polymer path. This embodiment determines that the first polymer model 21-1 is an extended chain, for example, when the distance between the ends and the path length of the polymer path have a predetermined relationship. For example, but not by way of limitation, this embodiment determines that a polymer pathway is an extended chain when the end-to-end distance is 90% or more of the path length of the polymer pathway.

In this embodiment, it is determined whether or not the second polymer model 21-2 and the third polymer model 21-3 are extended chains in the same manner as the first polymer model 21-1. Thereby, the present embodiment can calculate the number of extended chains included in the analysis model 1 . As a result, this embodiment can extract the extended chain|strand with large contribution to the dynamic response which exists between the 1st filler model 11 and the 2nd filler model 12. FIG.

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

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

The force per unit length or the force per unit bond is, for example, the first linking chain 21b-1, the second linking chain 21b-2, the third linking chain 21b-3, and the fourth linking chain 21b-4. and the fifth binding strand 21b-5. Specifically, 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 are , have a distance L1, a distance L2, a distance L3, a distance L4, and a distance L5 as equilibrium lengths, which are bond distances. In addition, spring As constants, a spring constant k1, a spring constant k2, a spring constant k3, a spring constant k4, and a spring constant k5 are defined. Therefore, based on the deviation (elongation) from the distances L1 to L5 and the spring constants k1 to k5, the forces generated in the first connecting chain 21b-1 to the fifth connecting chain 21b-5 are calculated. can do. More specifically, as the length of the first to fifth coupled chains 21b-1 to 21b-5 increases and the deviation from the equilibrium length increases, the generated force increases. As a result, the present embodiment can calculate the force per unit length and the force per unit bond in the first polymer model 21-1. Then, as described above, in this embodiment, for example, the force generated in the first polymer model 21-1 is calculated by multiplying the force per unit bond by the number of bonds present in the first polymer model 21-1. can be calculated and the state of the first polymer model 21-1 can be evaluated. Further, in this 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. Note that the distances L1 to L5 may be the same or different. Moreover, the spring constants k1 to k5 may be the same or different.

When there are N (N is an integer of 2 or more) polymer models 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, the present embodiment may calculate the sum of the forces generated in each of the N polymer models to calculate the force generated in the entire system.

This embodiment is good also considering only the polymer model which is an extended chain among the polymer models which exist between the 1st filler model 11 and the 2nd filler model 12, for example as evaluation object. Specifically, in the case of the example shown in FIG. 7, in this embodiment, among the first polymer model 21-1, the second polymer model 21-2, and the third polymer model 21-3, the extended chain You may calculate the force which has generate|occur|produced only for. In this case, the present embodiment calculates the force generated in the stretched chain extracted between the first filler model 11 and the second filler model 12, and the stretched chain present in the entire system. It is possible to calculate the sum of the forces that As a result, the present embodiment can clarify the mechanism of system stiffness (stress) increase caused by extended chains generated between fillers. In addition, the present embodiment can clarify the morphology of fillers, the nanostructure factors such as filler diameter, and the movement of the polymer, and can clarify the relationship between the nanostructure factors and the mechanical properties of the system. Furthermore, since the present embodiment can quantify the state of elongation of the easily cut extended chain, it is possible to predict the possibility of breakage of the extended chain.

Further, in the present embodiment, it may be determined whether or not the first polymer model 21-1 to the third polymer model 21-3 are extended chains at predetermined time intervals. In this case, the present embodiment may determine the state of the stretched chain at predetermined time intervals. Thereby, the present embodiment can calculate the time history in which the analysis result of the analysis model 1 and the number of extended chains are associated with each other. In addition, this embodiment can calculate a time history in which the analysis result of the analysis model 1 and the state of the stretched chain are associated with each other. There is no particular limitation on the predetermined time interval, and the interval may be set as desired by the user. In addition, this embodiment may evaluate the time history of one analysis result, or may evaluate the time history of different analyses. When evaluating the time history of one analysis result, for example, it is possible to evaluate changes in the stretched chain during the elongation process in the elongation test. When evaluating the time histories of different analyses, it is possible to evaluate the different effects on extended chains depending on the analyses.

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

Further, in the present embodiment, based on the time history of the calculated number of stretched chains, the first analysis result analyzed at the first analysis time and the analysis at a second analysis time different from the first analysis time A difference from the second analysis result may be calculated. This enables the present embodiment to calculate material properties such as hysteresis, hysteresis ratio, and stress softening of the analyzed composite material. At this time, the number of fully extended chains in the first analysis time and the number of fully extended chains in the second analysis time may be calculated. As a result, in the present embodiment, by calculating the difference between the number of fully extended chains in the first analysis time and the number of fully extended chains in the second analysis time, the change in the number of fully extended chains and the material properties can be associated with changes in In the present embodiment, the difference in the number of stretched chains in the case of the same strain is calculated and calculated in the deformation analysis performed under the first analysis condition and the second analysis condition different from the first analysis condition. Preferably, the difference is integrated over time. Further, in this embodiment, the state of the stretched chain at the first analysis time and the state of the stretched chain at the second analysis time may be compared. Thereby, in this embodiment, the change in the state of the extended chain can be associated with the change in the material properties.

In addition, in this embodiment, the number of extended chains included in the comparative analysis model of the polymer model in which parameters different from the analysis model 1 are set is calculated, and the calculated result and the analysis model 1 include The number of extended chains may be compared. Further, in this embodiment, the state of the extended chain included in the analysis model 1 may be compared with the state of the extended chain included in the comparative analysis model. Thus, the present embodiment can evaluate the influence of various parameters of the polymer model on the number of extended chains included in the analysis model 1 and the state of the extended 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 speed in the elongation test.

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

Further, in the present embodiment, the first distance between the representative point P1 and the representative point P2 of the polymer particle 21a at the first analysis time of the composite material analysis model 1 and the second analysis different from the first analysis time A path between a second distance between the representative point P1 and the representative point P2 in time may be analyzed. By analyzing in this way, it is also possible to analyze the change in the path between the representative points P1 and P2 accompanying the movement of the polymer particles 21a during a certain period of time. In this case, the present embodiment may determine whether or not the route between the first distance and the route between the second distance is an extended chain. As a result, the present embodiment can more accurately analyze changes in the path associated with the motion of the polymer particles 21a during a certain period of time. Specifically, in this embodiment, the change in the number of extended chains included in the analysis model 1 can be calculated by determining the change in the paths between all the fillers included in the analysis model 1. can. Also, the present embodiment may evaluate the state of the route between the first distance and the state of the route between the second distance. Thereby, the present embodiment can analyze changes in the state of the path accompanying the movement of the polymer particles 21a for 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 chains 21b included in the path between the representative points P1 and 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. Visualization of the polymer particles 21a and the binding chains 21b may be performed by, for example, coloring all the polymer particles 21a and the binding chains 21b for visualization, or by coloring and visualizing some of the polymer particles 21a and the binding chains 21b. area may be made transparent. In addition, the visualization of the polymer particles 21a and the binding chains 21b may be performed by specifying the same polymer particles 21a and the binding chains 21b for each of a plurality of mutually different analysis times. Polymer particles 21a and binding chains 21b may be visualized. Moreover, it is not always necessary to visualize only the polymer particles 21a and the binding chains 21b, the filler particles 11a may be visualized, and a part of the analysis model 1 may be visualized. Further, in the present embodiment, when an extended chain is detected, it is preferable to color the extended chain in order to easily distinguish between the extended chain and the binding chain that is not the extended chain. This makes it possible to easily confirm whether or not the polymer model 21 is an extended chain. In addition, in this embodiment, when a plurality of stretched chains are detected, it is preferable that different colors are applied according to the state of the stretched chains. As a result, in this embodiment, the state of the extended chain included in the analysis model 1 can be easily confirmed.

Further, in this embodiment, as the polymer model 21, a plurality of first polymer models 21-1 and a plurality of second polymer models 21-2 having different parameters from the first polymer model 21-1 are created, and the first polymer The paths of the representative points of the model 21-1 and the second polymer model 21-2 may be analyzed and evaluated. By analyzing in this way, 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 accompanying changes in the parameters of the polymer model 21 Changes can also be analyzed. Also, in this embodiment, it may be determined whether or not the structures of a plurality of polymer models having different parameters are extended chains. This makes it possible to determine whether or not the polymer model 21 is an extended chain according to the parameters. Further, it becomes possible to analyze the structural change of the polymer model 21 accompanying the parameter change. Also, in this embodiment, the structural state of multiple polymer models with different parameters may be evaluated. This enables evaluation of the state of the polymer model 21 according to the parameters of the polymer model 21 . Further, in this embodiment, the state of the extended chain may be evaluated only when the structure of the polymer model is determined to be the extended chain. This makes it possible to evaluate the state of the extended chain according to the state of the polymer model 21 . Polymer pathways in the matrix can also be similarly evaluated.

As described above, according to the above embodiment, it is possible to evaluate the state of the structure of the searched inter-filler pathway and the state of the structure between the matrices, and the structure of the searched inter-filler pathway and the structure of the matrix. Since it is possible to determine whether or not each of the states is an extended chain, it is possible to analyze the polymer network with higher accuracy. With these, the material properties of composite materials can be analyzed with high accuracy, and the relationship between the material properties (hysteresis) such as energy loss accompanying deformation of composite materials and the mechanism of the nanostructure of composite materials will be further clarified. It becomes possible to

Also, when detecting extended chains, the extended chains may be extracted based on the orientation of the bonds in the polymer pathway. In other words, it is also possible to extract bonds arranged within a predetermined angular range. Here, the orientation angle is preferably 120° or more, more preferably 150° or more. This makes it possible to properly detect the extended chains that generate force within the composite material. In addition, it is preferable to evaluate angles of three or more bonds as the orientation angle. As a result, it is possible to suppress extraction of a polymer path in which a certain number of bonds are not connected at a predetermined angle as an extended chain.

Numerical analysis to be performed in the material analysis method according to the present embodiment includes, for example, relaxation analysis, extension analysis, variable temperature analysis, and transformation analysis. It should be noted that it is preferable to include at least the undeformed state in the evaluation time when the extension analysis is performed. Thus, by comparing the analysis result at the evaluation time in the non-deformed state and the analysis result after the extension analysis, the number of particles that have been peeled off during the extension process can be evaluated. In addition, this embodiment can evaluate the number of stretched chains cut during the stretching process. In addition, this embodiment can evaluate the state of the stretched chain that has changed during the stretching process.

In addition, the material analysis method according to the present embodiment can comprehensively detect polymer pathways by searching for both the main chain and the cross-linking of the polymer pathway, but is not limited to this. FIG. 10 is an explanatory diagram showing an example of the material analysis method according to the embodiment of the present invention. As for the material analysis method, as shown in FIG. 10, only the polymer pathway of the main chain 34 may be extracted without extracting the cross-linking bond (the bond connecting the main chains) as the pathway. This simplifies the route search.

FIG. 11 is an explanatory diagram showing an example of the 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, the polymer particles of the search end particle group 32, and the cross-linking 36 are sandwiched between the cross-linking 36 and the cross-linking 36. A region 50 near the crosslinks 36 of the main chain 34 bound to the polymer pathway may be searched. This makes it possible to search for polymer pathways across crosslinks. In addition, as shown in FIG. 10, it is possible to search for polymer pathways that could not be searched when only the main chain was searched.

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

Next, the material analysis method and the composite material analysis computer program 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 this embodiment.

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

The processing unit 52 includes, for example, a central processing unit (CPU) and memory. The processing unit 52 reads a computer program from the storage unit 54 and develops it in the memory when executing various processes. The computer program deployed in memory executes various processes. For example, the processing unit 52 expands data related to various processes stored in advance from the storage unit 54 into an area allocated to itself on the memory as necessary, and based on the expanded data, the data for composite material analysis is processed. Executes various processes related to model creation and composite material analysis using the composite material analysis model.

The processing unit 52 includes a model creation unit 52a, a condition setting unit 52b, and an analysis unit 52c. Based on the data stored in advance in the storage unit 54, the model creation unit 52a calculates the number of particles, the number of molecules, and the molecular weight of the composite material such as filler and polymer when creating the analysis model 1 of the composite material by the molecular dynamics method. , molecular chain length, number of molecular chains, branching, shape, size, reaction time, reaction conditions, arrangement of constituent elements such as target number of molecules, which is the number of molecules included in the analysis model to be created, setting, number of calculation steps, etc. Coarse-grained model settings and initial conditions for various calculation parameters such as interactions between molecular chains are set.

As calculation parameters for adjusting the interaction between the filler particles 11a and the interaction between the polymer particles 21a, σ and ε of the Leonard-Jones potential represented by the following formula (1) are used and 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 work over long distances. In addition, it is preferable to decrease the parameter of the interaction between the filler particles 11a and the interaction between the polymer particles 21a sequentially until the interaction between the filler particles 11a and the interaction between the polymer particles 21a reach a constant value. By gradually approximating σ and ε of the Leonard-Jones potential from large values to the original values, the particles can approach at a moderate speed that does not lead the molecules to an unnatural state. Also, by gradually decreasing the cutoff distance, the attractive force and the repulsive force can be adjusted within an appropriate range.

The condition setting unit 52b sets various analysis conditions such as bridge analysis and various numerical analyzes such as relaxation analysis, extension analysis, variable temperature analysis, and transformation analysis. The analysis unit 52c performs 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. Moreover, the analysis part 52c sets 2nd analysis object area|region A12 around the 2nd filler model 12 while setting 1st analysis object area|region A11 around the 1st filler model 11. FIG. In addition, the analysis unit 52c extracts a specific polymer model 21 that partially exists in the first analysis target area A11 and the second analysis target area A12. Furthermore, the analysis unit 52c sets the representative point P1 and the like to the polymer particles 21a of the first polymer particle group within the first analysis target area A11 of the specific polymer model 21, and sets the second analysis target within the second analysis target area 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 within the second analysis target area A12.

In addition, the analysis unit 52c determines whether the structure of the inter-filler path between the polymer particles in the first analysis target area A11 and the polymer particles in the second analysis target area A12 is an extended chain. do. The analysis unit 52c, for example, determines 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 an extended chain. In this case, the analysis unit 52c calculates the end-to-end distance between 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 also 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 end-to-end distance and the path length, and determines that the structure of the inter-filler path is an extended chain when the end-to-end distance and the path length have a predetermined relationship. For example, when the end-to-end distance is 90% or more of the path length, the analysis unit 52c determines that the structure of the inter-filler path is an extended chain.

In addition, the analysis unit 52c evaluates the state of the structure of the path between fillers between the polymer particles in the first analysis target area A11 and the polymer particles in the second analysis target area A12. Specifically, the analysis unit 52c calculates the force generated in the inter-filler path. The analysis unit 52c, for example, calculates the force generated per unit bond based on the distance between adjacent polymer particles existing in the path between fillers. In this case, the analysis unit 52c calculates the force occurring in the inter-filler path by multiplying the number of bonds between the polymer particles by the force occurring 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 an extended chain.

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

In the storage unit 54, data for fillers such as rubber carbon black, silica, and alumina, which are data for creating an analysis model of a composite material to be analyzed via the input means 53, rubber, resin, and elastomer Polymer data such as, a method for creating a stress-strain curve that is a history of preset physical quantities, a method for creating an analysis model of a composite material according to the present embodiment, a computer program for realizing a material analysis method, etc. are stored. This computer program may realize the material analysis method according to the present embodiment by combining with a computer program already recorded in a computer or computer system. The "computer system" here includes an OS (Operating System) and hardware such as peripheral devices.

The display means 55 is, for example, a display device such as a liquid crystal display. Note that 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 through communication from a terminal device equipped with the input/output device 51 .

Next, with reference to FIG. 2 again, the material analysis method according to the present embodiment will be described in more detail. The same applies to the case of FIG. 1, except that no filler particles are included and no comparison is made between fillers and between matrices.

As shown in FIG. 2, the model creation unit 52a creates the uncrosslinked polymer model 21 in a predetermined model creation region A and creates the first filler model 11 (step ST11). The uncrosslinked polymer model 21, as shown in FIG. 3, is formed by connecting a plurality of polymer particles 21a with binding chains 21b. Here, the model creation unit 52a creates a plurality of first filler models 11 and a plurality of polymer models 21 as necessary. Next, the model creation unit 52a creates the analysis model 1 of the composite material by arranging the uncrosslinked polymer model 21 in the created first filler model 11 . Here, the model creating unit 52a performs balancing calculation after setting the initial conditions. In the equilibration calculation, the molecular dynamics calculation is performed at a predetermined temperature, density and pressure for a predetermined time for the various constituent elements after initial setting to reach an equilibrium state. Then, the model creation unit 52a includes the polymer particles 21a and the bond chains 21b in the model creation area A that creates the analysis model of the composite material set in the calculation area after the initial condition setting and the equilibration calculation process. The 1st filler model 11 containing the polymer model 21 and the filler particle 11a is created. In addition, the model creating unit 52a may mix a modifier such as a hydroxyl group, a carbonyl group, and a functional group of an atomic group that enhances the affinity with the filler into the polymer, if necessary.

Next, the condition setting unit 52b sets various conditions for executing cross-linking analysis, numerical analysis, and 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 unit 53 and the information stored in the storage unit 54. FIG. Various conditions include the position and number of the first filler model 11 to be analyzed, the position and number of the filler atom, the filler atomic group, the filler particle 11a and the filler particle group, the filler particle 11a number, the position of the molecular chain of the polymer and number, polymer atoms, polymer atomic groups, positions and numbers of polymer particles 21a and polymer particle groups, polymer particle numbers, positions and numbers of bonding chains 21b and bonding chains 21b, numbers of bonding chains 21b, and preset physical quantity histories. Fixed values that do not change the stress-strain curve and conditions are included.

Next, the analysis unit 52c executes cross-linking analysis in the uncross-linked polymer model in the composite material analysis model 1 to create cross-linking points (step ST12). Here, the model creation unit 52a specifies predetermined polymer particles 21a in the uncrosslinked polymer model 21 to create crosslink points. As a result, a large polymer model 21 after cross-linking is created from a plurality of polymer models 21 in the composite material analysis model 1 . The term "crosslinking" as used herein refers to forming a polymer model 21 including polymer particles 21a formed by connecting three or more binding chains 21b.

Next, the analysis unit 52c performs various numerical analyzes by setting interactions in the analysis model 1 after the cross-linking analysis (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 bound by a binding chain. Interactions are included, but need not be set for all of them. As the numerical analysis, relaxation analysis by the molecular dynamics method using the composite material analysis model 1 including the first filler model 11 and the polymer model 21 created by the model creation unit 52a, extension analysis, variable temperature analysis, transformation analysis, and numerical analysis by motion analysis such as deformation analysis such as shear analysis. In addition, the analysis unit 51c acquires various physical quantities such as motion displacement and nominal stress obtained as a result of motion analysis by numerical analysis, or nominal strain obtained by calculating motion displacement.

Next, the analysis unit 52c selects a polymer group to be evaluated (step ST14). Here, the analysis unit 52c selects at least some polymer particles from the polymer group within the analysis area. 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 starting point group. For example, the free end particles are extracted and used as the polymer particles of the search starting point group. Alternatively, the polymer particles of the search starting point group may be determined based on data input by the operator. The analysis unit 52c sets a search end point group from the polymer group (step ST16), and sets some polymer particles of the selected polymer group as polymer particles of the search end point group. For example, the free end particles are extracted and used as the polymer particles of the search end point group. Alternatively, the polymer particles of the search end point group may be determined based on data input by the operator. The analysis unit 52c extracts the polymer paths at the start point and the end point (step ST17), and determines whether the path search for the extracted particles is completed (step ST18). The analysis unit sequentially selects the polymer particles in the search start point group and repeats the search for the polymer paths until the search for the paths of the particles in the particle group satisfies the end conditions.

If the analysis unit 52c determines that it is not completed, it returns to step ST17, and if it is determined that it is completed, it evaluates the composite material based on the route search result (step ST19). For example, the analysis unit 52c identifies whether the polymer path between the polymer particles of the search start point group and the polymer particles of the search end point group is between fillers or in the matrix. Furthermore, the analysis unit 52c calculates the end-to-end distance between the polymer particles in the search start point group and the path between the polymer particles in the search end point group and the path length, and calculates the end-to-end distance and the path length. 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 an extended chain. Furthermore, the analysis unit 52c calculates the force generated per unit bond in the extended chain extracted in each region in the matrix between the fillers, and in the extracted extended chain, the unit bond Based on the force generated in the hit, the force generated in the entire extension 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. As a result, the present embodiment provides a mechanism for increasing the stiffness (stress) of the system due to the state of the paths between the fillers, a mechanism for increasing the stiffness (stress) of the system due to the state of the paths in the matrix, and furthermore, It is possible to clarify the relationship between the paths in the matrix and the paths in the matrix.

FIG. 14 is a graph in which the number of stretched chains and strain are associated with each other over time. FIG. 15 is a graph showing the correspondence between the stretched chain length and strain over time. FIG. 16 is a graph in which the elongation and strain of an extended chain are associated with each other over time. Analysis by the analysis unit 52c is performed, and the time change of the extended chain and strain etc. is analyzed between the fillers and in the matrix, respectively. Changes in relationships can be analyzed.

1 Analysis Model 11 First Filler Model 12 Second Filler Model 11a, 12a Filler Particle 21 Polymer Model 21a Polymer Particle 21b Binding Chain 50 Analysis Device 51 Input/Output Device 52 Processing Part 52a Model Creation Part 52b Condition Setting Part 52c Analysis Part 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)

A material analysis method using a material analysis model created by a molecular dynamics method using a computer,
creating a model for analysis of the material comprising a plurality of polymer models in which the polymer is modeled by a plurality of polymer particles;
cross-linking the polymer model by cross-linking analysis;
a step of setting an interaction in the analysis model after the cross-linking analysis and performing a 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 each particle of the start particle and the end particle an extracting step of performing a process of extracting paths and extracting polymer paths of all paths between the particles of the search start point group and the particles of the search end point group ;
In the extracting step, when the search for polymer paths of all paths of one particle of the search start point group is completed, the process of extracting by searching the polymer paths of all paths of another particle of the search start point group is repeated. A method of analyzing a material, characterized by: 2. The method of 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 a filler is modeled. 3. The material analysis method according to claim 1, further comprising an evaluation step of evaluating the length of the polymer path calculated in the extraction step using the number of bonds or the number of particles included in the path. In the evaluating step, an end-to-end distance from one end to the other end of the polymer pathway and a path length of the polymer pathway are calculated, and based on the end-to-end distance and the pathway length, the polymer pathway 4. The method for analyzing a material according to claim 3, wherein it is determined whether or not is an extended chain. 5. The method of analyzing a material according to claim 3, wherein said evaluation step performs a path search in a low temperature state by variable temperature analysis. 6. A material analysis method according to any one of claims 3 to 5, wherein said evaluating step evaluates results at least two times. 7. The material analysis method according to claim 6, wherein the time history is visualized and displayed. 8. The material analysis method according to claim 6 or 7, wherein a difference between an analysis result of a first analysis time and an analysis result of a second analysis time different from the first analysis time in the time history is calculated. . calculating the force generated per unit bond based on the distance between two adjacent polymer particles in the polymer path;
and calculating the force exerted on the polymer path based on the force exerted per unit bond. Method. 10. The method of analyzing a material according to any one of claims 1 to 9, wherein the extracting step searches for polymer paths with a breadth-first search. The particles of the search starting point group are free terminal particles,
The material analysis method according to any one of claims 1 to 10, wherein the particles of the search end point group are free end particles. The particles of the search starting point group are particles that were free terminal particles of polymer chains at the time before crosslinking,
12. The method of analyzing a material according to any one of claims 1 to 11, wherein the particles of the search endpoint group are particles that were free-end particles of polymer chains at a time prior to cross-linking. 12. The material analysis method according to any one of claims 1 to 11, wherein, in said extraction step, the search is terminated when a route that merges with a polymer route that has already been searched. 13. The method of analyzing a material according to any one of claims 1 to 12, wherein the extraction step searches for polymer pathways in the main chain. 13. The method of analyzing a material according to any one of claims 1 to 12, wherein the extraction step searches for polymer pathways across crosslinks. 13. A method of material analysis according to any one of claims 1 to 12, wherein the extraction step terminates the search for polymer pathways through cross-links. The material analysis method according to any one of claims 1 to 16, wherein an analysis result of the analysis model is compared with an analysis result of a comparative analysis model different from the analysis model. A computer program for material analysis, characterized by causing a computer to execute the material analysis method according to any one of claims 1 to 16.

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