JP7024593B2 - Composite material analysis method and computer program for composite material analysis - Google Patents

Description

The present invention relates to a method for analyzing a composite material and a computer program for analyzing the composite material, for example, a method for analyzing a composite material and a composite material capable of efficiently and accurately analyzing a network of polymer materials formed in the composite material. Regarding computer programs for 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 method for simulating a polymer material 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 modulus is calculated by dividing the space in which the model is placed into multiple minute regions.

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

By the way, in a composite substance containing two or more kinds of substances such as a polymer and rubber containing a filler, the crystal structure of the polymer existing between the fillers is fully extended (hereinafter, also referred to as a stretched chain). It is expected that the presence or absence will affect the material properties. Further, for example, even if the length of the stretched chain is the same, it is predicted that the material properties will change depending on the state (for example, the force generated) of the stretched chain.

However, in the conventional method for simulating a composite material using a molecular dynamics method, it is difficult to determine whether or not the crystal structure of the polymer existing between the fillers is a stretched chain. Further, there is a problem that the state of the stretched chain cannot be evaluated because it cannot be determined that the chain is stretched.

The present invention has been made in view of such circumstances, and is a method for analyzing a composite material capable of determining whether or not the crystal structure of the polymer existing between the fillers is a stretched chain and evaluating the state thereof. And to provide computer programs for the analysis of composite materials.

Another object of the present invention is to provide a method for analyzing a composite material and a computer program for analyzing the composite material, which can evaluate the crystal structure of the polymer existing between the fillers regardless of whether or not the chain is a stretched chain. do.

The method for analyzing a composite material of the present invention is a method for analyzing a composite material using a model for analyzing the composite material created by a molecular dynamics method using a computer, and a plurality of polymers modeled with a plurality of polymer particles. The first step of creating an analysis model of a composite material including a plurality of filler models modeling the polymer model and the filler of the above, a second step of cross-linking the polymer model by cross-linking analysis, and the analysis after cross-linking analysis. The third step of setting the interaction in the model and performing the numerical analysis, the fourth step of setting the analysis target area around the filler model of the analysis model after the numerical analysis, and the periphery of the first filler model. The first particle belonging to the particle group of a specific polymer model having a part in the first analysis target region set in the above, and the second set around the second filler model different from the first filler model. A fifth step of extracting a polymer pathway from a second particle belonging to the particle group of the specific polymer model, which is partially present in the analysis target region, and two adjacent polymer particles in the polymer pathway. The sixth step of calculating the force generated per unit bond based on the distance, and the seventh step of calculating the force generated in the polymer pathway based on the force generated per unit bond. It is characterized by including steps.

According to the composite material analysis method of the present invention, the state of the interfiller path can be evaluated. Therefore, the network of polymer materials formed in the composite material can be analyzed efficiently and accurately. This makes it possible to analyze the material properties of the composite material with high accuracy, so that 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 enhanced. Can be clarified. In addition, since the stretched chain is more likely to be cleaved than the non-stretched chain, the relationship between the number of stretched chains and the state of the stretched chain and the mechanism such as breakage and breakage is further enhanced. Can be clarified. As a result, detailed analysis of the Mullins effect and stress rise of the composite material can be performed.

The force generated in the polymer pathway is preferably calculated from the force generated per unit bond and the length of the polymer pathway. According to this analysis method, the force generated in the polymer pathway can be calculated more accurately. This makes it possible to further clarify the relationship between the state of the stretched chain and the mechanism such as breakage and breakage.

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 stretched out in a chain based on the distance between the ends and the path length. It is preferable to determine the presence or absence and calculate the force generated in the polymer pathway only when the polymer pathway is the stretched chain. According to this analysis method, the stretched chain is more likely to be cleaved than the non-stretched chain path, so the number of stretched chains, the state of the stretched chain, and the mechanism of breakage, breakage, etc. The relationship with can be further clarified.

When a plurality of the stretched chains are extracted, the sum of the forces generated in the plurality of stretched chains can be calculated, and the average of the forces generated in the plurality of stretched chains can be calculated. preferable. According to this analysis method, it is possible to calculate the sum and the average of the forces generated in the stretched chain included in the entire analysis model. This makes it possible to further clarify the relationship between the state of the stretched chain and the mechanism such as breakage and breakage.

It is preferable to calculate the number of stretched chains and the force generated in the stretched chains in the entire analysis model based on a specific region of the analysis model. According to this analysis method, even if it is a large analysis model, it is possible to evaluate the number of stretched chains and the state of stretched chains in the entire analysis model based on a specific region of the analysis model.

In the method for analyzing a composite material of the present invention, it is preferable to calculate the time history in which the analysis result of the analysis model is associated with the number of stretched chains and the stretched chains. According to this analysis method, it is possible to confirm the change in the number of stretched chains and the change in the state of stretched chains in the analysis process.

In the method for analyzing a composite material of the present invention, it is preferable to visualize and display the time history. According to this analysis method, it is possible to easily confirm the change in the number of stretched chains and the change in the state of stretched chains in the analysis process.

In the method for analyzing a composite material of the present invention, 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. .. By this method, the material properties of the composite material can be evaluated. Further, by this method, it is possible to correlate the change in the material properties of the composite material with the change in the number of stretched chains and the state of the stretched chains.

In the method for analyzing a composite material of the present invention, it is preferable to compare the analysis result of the analysis model with the analysis result of the comparative analysis model having different parameters from the analysis model. According to this analysis method, it is possible to evaluate the influence of the parameter on the number of stretched strands included in the analysis model and the state of the stretched strands.

The analysis computer program of the present invention is characterized in that the computer executes the above analysis method.

According to the computer program for analysis of the present invention, the state of the path between fillers can be evaluated. Therefore, the network of polymer materials formed in the composite material can be analyzed efficiently and accurately. This makes it possible to analyze the material properties of the composite material with high accuracy, so that 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 enhanced. Can be clarified. In addition, since the stretched chain is more likely to be cleaved than the non-stretched chain, the relationship between the number of stretched chains and the state of the stretched chain and the mechanism such as breakage and breakage is further enhanced. Can be clarified. As a result, detailed analysis of the Mullins effect and stress rise of the composite material can be performed.

According to the present invention, a method for analyzing a composite material and a computer program for analyzing the composite material, which can determine whether or not the crystal structure of the polymer existing between the fillers is a stretched chain and evaluate the state, are realized. be able to.

Further, according to the present invention, it is possible to realize a method for analyzing a composite material and a computer program for analyzing the composite material, which can evaluate the crystal structure of the polymer existing between the fillers.

FIG. 1 is a flowchart showing an outline of an analysis method for a composite material according to an embodiment of the present invention. FIG. 2 is a conceptual diagram showing an example of an analysis model created by the method for analyzing a composite material according to an embodiment of the present name. FIG. 3 is an explanatory diagram showing an example of an analysis method for a composite material according to an embodiment of the present invention. FIG. 4 is an explanatory diagram showing an example of an analysis method for a composite material according to an embodiment of the present invention. FIG. 5 is an explanatory diagram showing an example of an analysis method for a composite material according to an embodiment of the present invention. FIG. 6 is an explanatory diagram showing an example of an analysis method for a composite material according to an embodiment of the present invention. FIG. 7 is a diagram showing an example of setting representative points in another example of the analysis method of the composite material according to the present embodiment. FIG. 8 is an explanatory diagram for designating a range of an analysis target region in the composite material analysis method according to the present embodiment. FIG. 9 is an explanatory diagram of the periodic boundary conditions in the analysis model 1. FIG. 10 is an explanatory diagram of an analysis method for a composite material according to the present embodiment. FIG. 11 is a functional block diagram of an analysis device that executes an analysis method for a composite material according to the present embodiment. FIG. 12 is a flowchart showing an outline of an analysis method for a composite material according to another embodiment of the present invention.

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 appropriately modified and implemented.

FIG. 1 is a flowchart showing an outline of an analysis method for a composite material according to the first embodiment of the present invention. As shown in FIG. 1, the method for analyzing a composite material according to the present embodiment is a method for analyzing a composite material using a model for analyzing the composite material prepared by a molecular dynamics method using a computer. This composite material analysis method is a composite material analysis method using a composite material analysis model created by a molecular dynamics method using a computer, and is a plurality of polymers in which a polymer is modeled by a plurality of polymer particles. For the first step ST11 to create an analysis model of a composite material containing a plurality of filler models modeling a model and filler, the second step ST12 to crosslink the polymer model by cross-linking analysis, and the analysis model after cross-linking analysis. The third step ST13 for setting the interaction and performing the numerical analysis, the fourth step ST14 for setting the analysis target area around the filler model of the analysis model after the numerical analysis, and the setting around the first filler model. The first particle belonging to the particle group of a specific polymer model having a part in the first analysis target region and the second analysis target region set around the second filler model different from the first filler model. Based on the distance between the fifth step ST15, which extracts the polymer pathway from the second particle belonging to the particle group of a specific polymer model in which a part is present, and the two adjacent polymer particles in the polymer pathway. , The sixth step ST16 for calculating the force generated per unit bond, and the seventh step ST17 for calculating the force generated in the polymer pathway based on the force generated per unit bond. include. Hereinafter, the first embodiment of the present invention will be described in detail.

FIG. 2 is a conceptual diagram showing an example of an analysis model 1 created by the method for analyzing a composite material according to the present embodiment. As shown in FIG. 2, the composite material analysis model 1 according to the present embodiment is, for example, a model arranged in a model creation area A which is a virtual space having a substantially cubic shape having a side length of L. be. 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 bonded chain 21b. It has a plurality of polymer models 21 which are made of particles. 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. 2, 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 described. 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 any shape such as a spherical shape, an elliptical shape, a rectangular parallelepiped shape, and a polyhedral shape.

The first filler model 11 and the second filler model 12 are modeled in a state where a plurality of filler particles 11a and 12a are each aggregated in a substantially spherical body. Further, the first filler model 11 and the second filler model 12 are arranged in a state of being separated from each other at a predetermined interval. The first filler model 11 and the second filler model 12 may be connected to each other by a covalent bond in an outer edge portion in a state of being mutually aggregated.

The plurality of polymer models 21 are arranged between the first filler model 11 and the second filler model 12. The plurality of polymer models 21 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 the range where the interaction from the second filler model 12 is received. It is arranged in a certain second analysis target area A12. 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.

Fillers include, for example, carbon black, silica, alumina and the like. The filler particles 11a and 12a are modeled by assembling the atoms of a plurality of fillers. 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, bendings, and the like 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, rubber, resins, elastomers and the like. The polymer particles 21a are modeled by assembling a plurality of polymer atoms. The plurality of polymer particles 21a aggregate to form a polymer particle group. If necessary, the polymer is blended with a denaturing agent that enhances the affinity with the filler. The modifying agent 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 a 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, or the like of the polymer particles 21a is defined. This polymer model 21 is numerical data (including 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 analysis method of the composite material according to the present embodiment will be described in detail. FIG. 3 is an explanatory diagram showing an example of an analysis method for a composite material according to the present embodiment. In FIG. 3, the space between the first filler model 11 and the second filler model 12 shown in FIG. 2 is enlarged and shown.

As shown in FIG. 3, in the composite 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 is performed in the region around the first filler model 11. The target area A11 is set, and the second analysis target area A12 is set in the area around the second filler model 12. Then, it exists between the first analysis target area A11 and the second analysis target area A12, and a part thereof exists in the first analysis target area A11 and a part in the second analysis target area A12. The pathways R1-R3 of a particular polymer model 21 contained in a plurality of polymer models 21 in which is present are analyzed. 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 region in the vicinity within the range affected by the action of the polymer model 21. This also applies to the second analysis target region A12.

The polymer model 21 has one end in the first analysis target region A11 and the other end in the second analysis target region A12. The polymer model 21 forms a complex three-dimensional network through cross-linking (not shown) by a plurality of polymer models 21 (not shown in FIG. 3, see FIG. 2). In the present embodiment, among the polymer model 21, a plurality of polymer particles 21a (representative points P1 and points P3) on one end side arranged in the first analysis target region A11 are extracted as the first polymer particle group, and the first polymer particles are extracted. 2 A plurality of polymer particles 21a (representative points P2 and points P4) on the other end side arranged in the analysis target region A12 are extracted as a second polymer particle group. Then, 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 second analysis target. The interfiller path R1 formed by the polymer particles 21a outside the range of the region A12 is searched for. This makes it possible to analyze the inter-filler path R1 of the network of the polymer model 21 formed between the first filler model 11 and the second filler model 12 as the shortest path. In this embodiment, the interfiller pathway is sometimes referred to as a polymer pathway.

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, an 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.

In the present embodiment, the representative point P1 is set to the polymer particles 21a which are the outermost particles existing at the outer edge of the first analysis target region A11, and the representative point P2 exists at the outer edge of the second analysis target region A12. It is preferable to set the polymer particles 21a as the outermost particles. By setting the representative points P1 and P2 in this way, it is possible to analyze the shortest path of the inter-filler path R1 between the representative points P1 and the representative points P2 via the polymer model 21. By analyzing this shortest path, the polymer particles 21a (see, for example, point P3) existing on the first filler model 11 side from the representative point P1 in the first analysis target region A11 in the polymer model 21 and the second analysis target. Search for overlap with the path (for example, the path between the points P3 and P4) between the polymer particles 21a (for example, the point P4) existing on the second filler model 12 side from the representative point P2 in the region A12. Since it can be avoided, it is possible to efficiently analyze the path between the first filler model 11 and the second filler model 12 via the polymer model 21.

In the present embodiment, the bond length between the representative point P1, the representative point P2, the point P3 and the point P4 does not use the linear distance between the representative point P1, the representative point P2, the point P3 and the point P4, and the representative point P1 , The number of particles or the number of bonds of the polymer particles 21a interposed between the representative points P2, P3 and P4 may be used for analysis, and the length of the bond length of the polymer particles 21a due to thermal vibration by temperature change analysis may be used. The analysis may be performed after reducing the fluctuation of. The conditions for the temperature change analysis in this case include, for example, the 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 lengths 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.

In the above-described embodiment, an example of extracting a route between the representative points P1 and the representative point P2 has been described, but the routes include the route between the representative points P1 and the points P4, and the representative points P2 and P3. The route between the points P3 and P4 may be extracted, and even when the route between the points P3 and P4 is extracted, it is possible to prevent the duplicate extraction of the routes. It is possible to analyze the path between the two filler models 12 efficiently and with high accuracy.

FIG. 4 is an explanatory diagram showing another example of the analysis method of the composite material according to the present embodiment. Also in FIG. 4, similarly to FIG. 3, the space between the first filler model 11 and the second filler model 12 shown in FIG. 2 is enlarged and shown. In the example shown in FIG. 4, 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. 4, the representative points P1 and P2 and the points P3 and P4 of the first polymer model 21-1 are extracted in the same manner as in FIG. Of the second polymer model 21-2, the polymer particles 21-2a on one end side existing in the first analysis target region A11 are extracted as the representative point P5, and the other end side existing in the second analysis target region A12 is extracted. 21-2a of the polymer particles of the above are extracted as a representative point P6. Then, the inter-filler path R11 between the representative point P1 and the representative point P2 is analyzed, and the inter-filler path R21 between the representative point P5 and the representative point P6 is analyzed. Subsequently, by comparing the lengths of the inter-filler path R11 and the inter-filler path R21, which of the first polymer model 21-1 and the second polymer model 21-2 is the first filler model 11 and the second filler model 12 It is possible to analyze whether the shortest route between and is included. This makes it possible to analyze the networks of the first polymer model 21-1 and the second polymer model 21-2. In addition to this, for example, it is possible to analyze whether the first polymer model 21-1 or the second polymer model 21-2 is dominant in the influence on the material properties of the composite material before and after the deformation in the deformation analysis. It becomes.

In the present embodiment, the representative point P5 is set to the polymer particles 21-2a existing on the outer edge of the first analysis target region A11, and the representative point P6 is the polymer particles 21 existing on the outer edge of the second analysis target region A12. It is preferable to set it to -2a. By setting the representative points P5 and P6 in this way, it is possible to extract the shortest path between the representative points P5 and the representative points P6 via the second polymer model 21-2.

By extracting the shortest path, the polymer particles 21-2a (see, for example, point P7) existing on the first filler model 11 side of the representative point P5 of the second polymer model 21-2 and the second polymer model 21-2 from the representative point P6. 2 Since the overlap calculation with the path between the polymer particles 21-2a (for example, the point P8) existing on the filler model 12 side (for example, the path between the points P7 and P8) can be avoided. It is possible to efficiently analyze the path between the first filler model 11 and the second filler model 12.

In the example shown in FIG. 4, an example of extracting a route between the representative point P5 and the representative point P6 has been described, but the route includes a route between the representative point P5 and the point P8, and a representative point P6 and a point. The route between P7 may be extracted, or the route between points P7 and P8 may be extracted. Even in the case of extraction in this way, it is possible to prevent duplicate extraction of routes, so that it is possible to efficiently analyze the routes between the first filler model 11 and the second filler model 12 with high accuracy. It will be possible. The bond length between the representative points P5, the representative points P6, the points P7 and the points P8 can be measured in the same manner as the representative points P1, the representative points P2, the points P3 and the points P4.

As described above, according to the present embodiment, it is possible to accurately analyze the path generated by the interaction between the polymer model 21, the first filler model 11 and the second filler model 12. As a result, as shown in FIG. 5, in the actual composite material, the first polymer model 21-1 and the second polymer model 21-2 are placed between the pair of the first filler model 11 and the second filler model 12. , 3rd Polymer Model 21-3 ... Even if there are a plurality of polymer models of the Nth Polymer Model 21-N, the shortest path between the 1st filler model 11 and the 2nd filler model 12 It can be specified that the polymer particles 21a contained in a certain interfiller path R11 is the first polymer model 21-1. Therefore, it is possible to identify that the first polymer model 21-1 included in the inter-filler path R11, which is the shortest path, has the greatest effect on the material properties of the compound of the composite material in the deformation analysis of the composite material. Become. Further, by analyzing the path between the first filler model 11 and the second filler model 12, the information of the polymer particles 21a contained between the representative point P1 and the representative point P2 and the representative points P1 and the representative point P2 are obtained. It is possible to analyze the shape of the path between the first filler model 11 and the second filler model 12, and it is also possible to obtain the distance between the first filler model 11 and the second filler model 12.

FIG. 6 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. FIG. 6 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. 6, 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 points P2, the first polymer particles 21a-1 correspond to the points P3, and the sixth polymer particles 21a-6 correspond to the points P4. is 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 the second bond chain 21b-2. The third polymer particles 21a-3 and the fourth polymer particles 21a-4 are bound by the 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 this embodiment, the path length of the polymer pathway connecting the first polymer particles 21a-1 and the sixth polymer particles 21a-6 is calculated. The path 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 path length of the polymer pathway may be calculated based on the calculated average length of each bonded chain 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 this embodiment, for example, when the distance between the ends and the path length of the polymer pathway have a predetermined relationship, it is determined that the first polymer model 21-1 is a stretched chain. In this embodiment, for example, when the distance between the ends is 90% or more of the path length of the polymer path, it is determined that the polymer path is a stretched chain, but the present embodiment is not limited to this.

In the present embodiment, as in the case of 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 are completely stretched chains. Thereby, in this embodiment, the number of stretched chains included in the analysis model 1 can be calculated. As a result, the present embodiment can extract a 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 × 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 binding 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 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 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 bond chain 21b-1 to the fifth bond 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 N polymer models (N is an integer of 2 or more) exist 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. Specifically, in the case of the example shown in FIG. 6, the present embodiment occurs in the first polymer model 21-1, the second polymer model 21-2, and the third polymer model 21-3, respectively. By calculating the sum of the existing forces, the forces generated in the entire system are 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. 6, 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 nanostructured factors such as the filler diameter, and the relationship between the nanostructured factors and the mechanical properties of the system. Furthermore, since the present embodiment can quantify the state of elongation of the stretched chain that is easily cut, it is possible to predict the possibility of breakage of the stretched chain.

Further, in the present embodiment, determination as to whether or not the first polymer model 21-1 to the third polymer model 21-3 are completely stretched chains may be performed at predetermined time intervals. In this case, in the present 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 depending on 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 stretch of the chain. The horizontal axis may be, for example, the number of steps in a 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 time history of the calculated 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. Thereby, 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 characteristics Can be associated with changes in. In this embodiment, the difference in the number of stretched chains when the strain is 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 in the first analysis time and the state of the stretched chain in the second analysis time may be compared. 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 this embodiment, the number of stretched chains included in the comparative analysis model of the polymer model in which the 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. The parameters are, for example, the volume fraction of the filler, the diameter of the filler, the distance between the fillers, the amount of the bound rubber, the thickness of the bound rubber, the morphology of the filler, the crosslinked structure of the polymer, the temperature, and the elongation rate in the stretching test.

FIG. 7 is a diagram showing an example of setting representative points in another example of the analysis method of the composite material according to the present embodiment. As shown in FIG. 7, the representative points P1 and the representative points P2 do not necessarily have to be set in the polymer particles 21a which are the particles in the first analysis target region A11, and are predetermined from the center point P of the first filler model 11. It may be set to a distance. In the example shown in FIG. 7, in the polymer model 21 arranged in the first analysis target region A11, one end side is folded back in the first analysis target region A11 and the end portion is arranged outside the first analysis target region A11. .. In such a case, when a predetermined position of the polymer model 21 is set from the center point P of the first filler model 11, two representative points P11 and P12 are formed with respect to the polymer particles 21a existing at equidistant L1 and L2. Set. By analyzing in this way, it is also possible to analyze whether or not the polymer model 21 has a folded structure in the first analysis target region A11.

FIG. 8 is an explanatory diagram for designating a range of an analysis target region in the composite material analysis method according to the present embodiment. As shown in FIG. 8, in the present embodiment, it is not always necessary to specify the polymer particles 21a in the entire region of the first analysis target region A11 of the first filler model 11 as the analysis target. As for the analysis target range of the polymer particles 21a in the first analysis target region A11, for example, even if the region projected on the second filler model 12 side paired with the first filler model 11 is designated as the first specific region A111. Often, a range in which the vector of the polymer particles 21a is equal to or less than a predetermined angle θ with respect to the vector between the center point P of the first filler model 11 and the center point P of the second filler model 12 is designated as the second specific region A112. You may.

Further, in the present embodiment, the polymer particles 21a to be analyzed in the first analysis target region A11 are the polymer particles 21a in the first analysis target region A11 and the polymer particles 21a in the second analysis target region A12 described above. A predetermined bond length, number of bonds, and linear distance thresholds may be set and specified between the two. By designating the polymer particles 21a to be analyzed in this way, the number of the polymer particles 21a designated as the analysis target can be reduced, so that the arithmetic processing becomes easy. As a result, the number of stretched chains to be extracted can be reduced, which facilitates arithmetic processing.

Further, in the present embodiment, the shortest path between the representative point P1 and the representative point P2 of the polymer model 21 may be analyzed in consideration of the periodic boundary condition of the analysis model 1. FIG. 9 is an explanatory diagram of the periodic boundary conditions in the analysis model 1. As shown in FIG. 9, in the analysis model 1, the pair of the first filler model 11 and the second filler model 12 and the polymer model 21 existing between the first filler model 11 and the second filler model 12 Exists as a model that is repeatedly equivalent over a plurality of regions AX and AY included in the model creation region A. Therefore, for example, when analyzing the shortest path of the bond length between the pair of adjacent first filler models 11 and the second filler model 12, the first filler model 11 and the second filler model in the region AX are analyzed. In addition to the polymer model 21A between 12 and there is a polymer model 21B that exists between the second filler model 12 in the region AX and the first filler model 11 in the region AY. The total length of the polymer model 21B is the sum of the polymer model 21B1 in the region AX and the polymer model 21B2 in the region AY. Here, considering that the region AX and the region AY are equivalent models, the total length of the polymer model 21B exists in the total length of the polymer model 21B1 in the region AX and the region AX corresponding to the polymer model 21B2. The length is the sum of the total length of the polymer model 21C. By comparing the paths of the polymer model 21 existing between the first filler model 11 and the second filler model 12 in the region AX in this way, it becomes possible to easily carry out the arithmetic processing. Further, in the present embodiment, by adding such a periodic boundary condition, the distance between the ends of the polymer model 21B and the path length are compared, and whether or not the structure of the polymer model 21B is a stretched chain. Can be determined. Thereby, in the present embodiment, the number of stretched chains included in the analysis model 1 can be calculated based on the number of stretched chains contained in a specific region such as the region AX and AY. Further, in the present embodiment, the state of the polymer model 21B can be evaluated by adding the periodic boundary condition. Thereby, in this embodiment, the state of the stretched chain included in the analysis model 1 can be evaluated based on the state of the stretched chain contained in a specific region such as the region AX and AY.

Further, in the method for analyzing a composite material according to the present embodiment, a plurality of pathways between the first polymer particle group and the second polymer particle group are extracted, and the polymer particles belonging to the first polymer particle group are extracted from the extracted pathways. The route between the fillers and the route between the polymer particles belonging to the second polymer particle group are excluded as overlapping routes, and the route between the fillers is searched.

FIG. 10 is an explanatory diagram of an analysis method for a composite material according to the present embodiment. In the example shown in FIG. 10, the polymer model 21 existing between the first filler model 11 and the second filler model 12 is a polymer particle 21a belonging to the first polymer particle group and a polymer belonging to the second polymer particle group. A plurality of paths are extracted from the particles 21a. These paths include, for example, an interfiller path including the interfiller paths R11 and R13 between the representative points P1 and P3 of the polymer particles 21a, and a filler between the representative points P1 and P4 of the polymer particles 21a. Inter-filler path including inter-filler path R11, R13, R12, inter-filler path including inter-filler path R13 between representative points P2 and P3 of polymer particles 21a, representative points P2 and points P4 of polymer particles 21a. Inter-filler paths between and between, including inter-filler paths including R13, R12.

In the example shown in FIG. 10, the interfiller path R11 between the representative points P1 and the representative points P2 of the polymer particles 21a belonging to the first polymer particle group and the points P3 and P4 of the polymer particles 21a belonging to the second polymer particle group. The inter-filler path R12 between and is excluded as an overlapping path. Therefore, in the example shown in FIG. 10, the route including the inter-filler paths R11 and R12 is excluded from the plurality of extracted paths, and the filler containing the inter-filler path R13 between the representative points P2 and the points P3 of the polymer particles 21a. Intermediary routes are extracted. Then, the inter-filler routes R11 and R12, which are overlapping routes, are set as exclusion routes and registered in the exclusion list. As a result, the routes between the polymer particles in the first analysis target region and the second analysis target region are excluded as overlapping routes, so that re-searching of the overlapping routes can be prevented when searching for the inter-filler route, and the inter-filler route can be prevented. Can be searched efficiently. The inter-filler route R11 does not necessarily have to be excluded as an overlapping route. Further, when the path exists in the analysis target region set in the filler model other than the first filler model 11 and the second filler model 12, the search for the distance between the fillers is terminated. This route may or may not be set as an exclusion route.

Further, in the present embodiment, the first distance between the representative point P1 and the representative point P2 of the polymer particles 21a in the first analysis time of the model 1 for analysis of the composite material, 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 analyzing in this way, it is also 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, the present embodiment can analyze the change of the pathway accompanying the movement of the polymer particles 21a in a certain period 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 contained in the analysis model 1. 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 method for analyzing a composite material according to the present embodiment, it is possible to visualize at least one of the polymer particles 21a and the bound chain 21b included in the path between the representative point P1 and the representative point P2 of the polymer particles 21a. preferable. 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 bound chain 21b may be, for example, by coloring and visualizing all the polymer particles 21a and the bound chain 21b, or by coloring and visualizing some of the polymer particles 21a and the bound chain 21b. The area of may be made transparent. Further, the visualization of the polymer particles 21a and the bound chain 21b may be visualized by designating the same polymer particles 21a and the bound 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 bound chains 21b may be visualized. Further, it is not always necessary to visualize only the polymer particles 21a and the bound 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 is 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. This makes it possible to easily confirm the state of the stretched chain included in the analysis model 1 in the present embodiment.

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 the representative points of the model 21-1 and the 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 of the parameters of the polymer model 21 Changes can also be analyzed. Further, in the present embodiment, it may be determined whether or not 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 a stretched chain according to the parameters of the polymer model 21. In addition, it becomes possible to analyze changes in the structure of the polymer model 21 due to changes in parameters. Further, in the present embodiment, the structural state of a plurality of polymer models having 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.

As described above, according to the above embodiment, it is possible to evaluate the state of the structure of the searched inter-filler route, and determine whether or not the structure of the searched inter-filler route is a stretched chain. Therefore, 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.

Examples of the numerical analysis to be performed in the composite material analysis method according to the present embodiment include relaxation analysis, extension analysis, temperature change analysis, and transformation analysis. When performing the stretch analysis, it is preferable to include at least the non-deformation state in the evaluation time. Thereby, 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. Further, this embodiment can evaluate the number of stretched chains broken in the stretching process. Further, this embodiment can evaluate the state of the stretched chain changed in the stretching process.

Next, the method for analyzing the composite material and the computer program for analyzing the composite material according to the present embodiment will be described in more detail. FIG. 11 is a functional block diagram of an analysis device that executes an analysis method for a composite material according to the present embodiment.

As shown in FIG. 11, the method for analyzing a composite material according to the present embodiment is realized by an analysis device 50 which is a computer including a processing unit 52 and a 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, the boundary condition in the analysis, and the like. Input to the unit 52 or the 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. Create a model and analyze the composite material Perform various processes related to the analysis of the composite material using the model.

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 fillers and polymers 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. Set the initial conditions of various calculation parameters such as the coarsening model of and the interaction between molecular chains.

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 and repulsive forces that have 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 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. Further, 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 on 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 the representative point P1 or the like 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 a path between the fillers 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 interfiller 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. do. The analysis unit 52c determines, for example, whether or not the structure of the interfiller 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. Further, 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.

Further, the analysis unit 52c evaluates the state of the structure of the interfiller 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 a hard disk device, a magneto-optical disk device, a non-volatile memory such as a flash memory and a CD-ROM that can only be read, and a RAM (Random Access Memory). Volatile memory, which is a possible recording medium, is appropriately combined.

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 an analysis method of a composite material, and the like are stored. .. This computer program may be capable of realizing the method for analyzing a composite material according to the present embodiment in combination with a computer or a computer program already recorded in 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, with reference to FIG. 1 again, the method for analyzing the composite material according to the present embodiment will be described in more detail.

As shown in FIG. 1, the model creation unit 52a creates an uncrosslinked polymer model 21 and a first filler model 11 in a predetermined model creation region A (step ST11). As shown in FIG. 2, 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 a model 1 for analysis of the composite material. 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 creating unit 52a includes the polymer particles 21a and the bonded chain 21b in the model creating region A for creating the analysis model of the composite material set in the calculated 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 cross-linking analysis, numerical analysis, and motion analysis (simulation) by the molecular dynamics method using the model 1 for analysis of the composite material 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 position and number of the filler atom, the filler atom group, 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 the like. 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 performs 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 model 1 for analysis of the composite material, 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 and 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 bond 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 method using the first filler model 11 created by the model creation unit 52a and the model 1 for analysis of the composite material 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 sets an analysis target region around the first filler model 11 of the analysis model 1 after the numerical analysis (step ST14). Here, the analysis unit 52c sets the range in which the polymer model 21 is affected by the interaction by the first filler model 11 as the analysis target region.

Next, the analysis unit 52c uses the polymer particles 21a of the specific polymer model 21 having a part in the first analysis target region A11 set around the first filler model 11 as the second particles (for example, a representative point). The polymer particles 21a of the specific polymer model 21 set as P1) and partially present in the second analysis target region A12 set around the second filler model 12 different from the first filler model 11 are second. It is set as a particle (for example, representative point P2) and the path between the representative point P1 and the representative point P2 is analyzed (step ST15). Here, the analysis unit 52c sets the representative point P1 (first particle) to the polymer particle 21a which is the outermost particle existing on the outer edge of the first analysis target region A11, and sets the representative point P2 (second particle) to the first. 2 The polymer particles 21a (second particles), which are the outermost particles existing on the outer edge of the analysis target region A12, may be set.

Next, the analysis unit 52c calculates the distance between the ends between the first particle and the path between the second particles and the path length (step ST16). Here, the analysis unit 52c calculates, for example, the distance between the ends of the first particle and the second particle based on the coordinates specified for each of the first particle and the second particle. Further, the analysis unit 52c calculates, for example, the path length between the first particle and the second particle based on the length of the binding chain existing between the first particle and the second particle. The analysis unit 52c may calculate the path length between the first particle and the second particle based on the number of particles and the number of bonds of the polymer particles existing between the first particle and the second particle. good. More specifically, the analysis unit 52c may calculate the path length based on the number of unit bonds existing in the path and the equilibrium length of the bound chain, or directly measure and calculate the path length. You may.

Next, the analysis unit 52c determines whether or not the structure of the path between the first particle and the second particle is a stretched chain based on the distance between the ends and the path length (step). ST17). Here, the analysis unit 52c compares, for example, the distance between the ends and the path length, and when the distance between the ends and the path length have a predetermined relationship, the first particle and the second particle are used. It is determined that the structure of the path between them is a stretched chain. In this case, the analysis unit 52c determines that the structure of the path between the first particle and the second particle is a stretched chain when the distance between the ends is 90% or more of the path length.

Next, the analysis unit 52c calculates the force generated per unit bond in the extracted stretched chain (step ST18). Here, the analysis unit 52c is a unit bond in the extracted stretch chain based on the elongation of the bond chain between adjacent particles from the equilibrium length and the spring constant defined in the bond chain. Calculate the winning force.

Next, the analysis unit 52c calculates the force generated in the entire stretched chain based on the force generated per unit bond in the extracted stretched chain (step ST19). Here, the analysis unit 52c calculates the force generated in the entire extracted stretch chain by adding the forces per unit bond in the extracted pathway. Then, the analysis unit 52c stores the analysis result of the analyzed composite material in the storage unit 54.

It is preferable that the analysis unit 52c calculates the force generated in all the stretched chains existing between the first filler model 11 and the second filler model 12. As a result, the analysis unit 52c can calculate the force generated in the entire system by adding the forces generated in all the stretched chains. The analysis unit 52c may calculate the forces of all the stretched chains existing between the first filler model 11 and the second filler model 12, and calculate the average thereof.

Further, the analysis unit 52c may calculate the force for the path extracted between the first filler model 11 and the second filler model 12, not limited to the stretched chain.

FIG. 12 is a flowchart showing a flow of processing in which the analysis unit 52c calculates the force generated by the extracted path between the first filler model 11 and the second filler model 12.

Since steps ST21 to ST25 shown in FIG. 12 are the same as steps ST11 to ST15, the description thereof will be omitted.

Next, the analysis unit 52c calculates the force generated per unit bond in the extracted path (step ST26). Here, the analysis unit 52c per unit bond in the extracted pathway, based on the elongation of the bond between adjacent particles from the equilibrium length and the spring constant defined for the bond. Calculate the force. Here, it is desirable that the analysis unit 52c calculates the force of each unit bond constituting the extracted path, and calculates the average value of the forces generated per unit bond. In this case, it is desirable that the analysis unit 52c uses the calculated average value of the forces as the force per unit bond of the path.

Next, 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 (step ST27). Here, the analysis unit 52c is generated in the entire stretched chain extracted by adding the forces per unit bond in the extracted pathway and by adding the forces per unit bond in the extracted pathway. Calculate the force.

It is preferable that the analysis unit 52c calculates the force generated in all the paths existing between the first filler model 11 and the second filler model 12. As a result, the analysis unit 52c can calculate the force generated in the entire system by adding the forces generated in all the paths. The analysis unit 52c may calculate the forces of all the paths existing between the first filler model 11 and the second filler model 12, and calculate the average thereof.

The analysis unit 52c extracts a plurality of first particles in the first analysis target region A1 of the specific polymer model 21 to form a first particle group, and extracts a plurality of second particles in the second analysis target region A2. It is preferable to analyze the path between the plurality of first particles belonging to the first particle group and the plurality of second particles belonging to the second particle group, respectively. Then, it is preferable that the analysis unit 52c evaluates the state of the path by calculating the force generated in the path between the first particle and the second particle. Thereby, the present embodiment can clarify the mechanism of the increase in the rigidity (stress) of the system due to the state of the path between the fillers.

The analysis unit 52c evaluates the state of the stretched chain by extracting the stretched chain from the pathways between the fillers and evaluating the generated force only for the extracted stretched chain. You may. Thereby, the present embodiment can clarify the mechanism of the increase in the rigidity (stress) of the system due to the state of the path between the fillers. Further, in the present embodiment, the calculation amount of the analysis unit 52c can be reduced by limiting the evaluation target to the stretched chain.

(Example)
Next, an example carried out for clarifying the effect of the present invention will be described. The present invention is not limited to the following examples.

In this example, stretch analysis was performed on multiple models with the same filler arrangement and different interactions between the filler and the polymer. Then, the state of the stretched chain of each model was evaluated. It was found that the stronger the interaction between the filler and the polymer, the longer the length per unit bond and the greater the number of stretched chains. That is, it was found that the stronger the interaction between the filler and the polymer, the greater the force generated in the stretched chain. As a result, it was found that the stronger the interaction between the filler and the polymer, the higher the rigidity of the system.

1 Analytical model 11 1st filler model 12 2nd filler model 11a, 12a Filler particles 21 Polymer model 21a Polymer particles 21a-1 1st polymer particles 21a-2 2nd polymer particles 21a-3 3rd polymer particles 21a-4 4 Polymer particles 21a-5 5th polymer particles 21a-6 6th polymer particles 21b Bonding chain 21b-1 1st binding chain 21b-2 2nd binding chain 21b-3 3rd binding chain 21b-4 4th binding chain 21b- 5 Fifth coupled 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 region

Claims (10)

It is a method for analyzing composite materials using a model for analyzing composite materials created by molecular dynamics using a computer.
The first step in creating an analytical model for a composite material that includes multiple polymer models that model polymers with multiple polymer particles and multiple filler models that model fillers.
The second step of cross-linking the polymer model by cross-linking analysis,
The third step of setting the interaction in the analysis model after the cross-linking analysis and performing the numerical analysis,
The fourth step of setting the analysis target area around the filler model of the analysis model after the numerical analysis, and
Around the first particle belonging to a specific polymer model particle group having a part in the first analysis target region set around the first filler model and the second filler model different from the first filler model. The fifth step of extracting the polymer pathway between the second particle belonging to the particle group of the specific polymer model having a part in the second analysis target region set in
In the polymer pathway, the sixth step of calculating the force generated per unit bond based on the distance between two adjacent polymer particles,
A method for analyzing a composite material, comprising a seventh step of calculating the force generated in the polymer pathway based on the force generated per unit bond. The method for analyzing a composite material according to claim 1, wherein the force generated in the polymer pathway is calculated from the force generated per unit bond and the length of the polymer pathway. 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 stretched out in a chain based on the distance between the ends and the path length. The method for analyzing a composite material according to claim 1 or 2, wherein it is determined whether or not the polymer pathway is present, and the force generated in the polymer pathway is calculated only when the polymer pathway is the stretched chain. When a plurality of the stretched chains are extracted, the sum of the forces generated in the plurality of stretched chains is calculated, and the average of the forces generated in the plurality of stretched chains is calculated. Item 3. The method for analyzing a composite material according to Item 3. The composite material according to claim 3 or 4, which calculates the number of stretched chains and the force generated in the stretched chains in the entire analytical model based on a specific region of the analytical model. analysis method. The item according to any one of claims 3 to 5, wherein a time history in which the analysis result of the analysis model is associated with the number of stretched chains and the force generated in the stretched chains is calculated. Analysis method for composite materials. The method for analyzing a composite material according to claim 6, wherein the time history is visualized and displayed. The method for analyzing a composite material 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. .. The method for analyzing a composite material according to any one of claims 3 to 8, 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 a composite material, which comprises causing a computer to execute the method for analyzing the composite material according to any one of claims 1 to 9.

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