JP6746971B2 - Composite material analysis method and computer program for composite material analysis - Google Patents

Description

The present invention relates to a composite material analysis method and a composite material analysis computer program, for example, a composite material analysis method and a composite material capable of analyzing the relationship between the dispersion state of a specific substance in the composite material and the material properties of the composite material. A computer program for the analysis of materials.

Conventionally, a method for simulating a polymer material has been proposed which analyzes the dispersibility of a filler compounded in the polymer material (see, for example, Patent Document 1). In this polymer material simulation method, a simulation by molecular dynamics calculation is executed using a filler model and a polymer model arranged in a virtual space by a computer. Then, the dispersion state of the filler is evaluated by obtaining the mean square displacement of the particles having the maximum cutoff distance of the plurality of filler particles from the obtained simulation result.

JP, 2013-238535, A

However, in the polymer material simulation method described in Patent Document 1, for example, when the filler particles orbit relative to a specific point in the virtual space, the position of the filler particles in the virtual space does not change. While small, the mean square displacement may be large. For this reason, the conventional polymer material simulation method cannot always accurately analyze the dispersion and arrangement of the filler particles in the composite material.

The present invention has been made in view of such circumstances, and provides a method for analyzing a composite material and a computer program for analyzing the composite material capable of accurately analyzing the dispersion and arrangement of a specific substance in the composite material. With the goal.

A method for analyzing a composite material according to the present invention is a method for analyzing a composite material using a model for analyzing a composite material created by a molecular dynamics method using a computer, and comprises a plurality of first particles modeled by first particles. The first step of creating an analysis model of a composite material in which a plurality of second material models modeled by the second particles are arranged in the material model, and the numerical analysis is executed by setting the interaction in the analysis model. And a third step of calculating the inter-model distance between the plurality of second substance models based on the reference coordinates of the second substance model after the numerical analysis.

According to the composite material analysis method of the present invention, since the inter-model distance between the second substance models is calculated based on the reference coordinates of the second substance model, the second substance models dispersed in the first substance model are arranged. The distribution and distribution of the material model can be analyzed. Moreover, according to this composite material analysis method, the inter-model distance of the second substance model is directly calculated and analyzed without depending on the displacement of the second substance model. Even when the orbiting motion is performed in step 1, the inter-model distance of the second substance model can be accurately analyzed. Therefore, according to this composite material analysis method, since it is possible to realize a composite material analysis method capable of accurately analyzing the dispersion and arrangement of a specific substance in a composite material, the arrangement and dispersion of the second substance model can be realized. It is possible to evaluate the effect of composite materials on material properties and accelerate the development of fuel-efficient tires.

In the composite material analysis method of the present invention, it is preferable that in the third step, the barycentric coordinates of the second substance model are calculated as the reference coordinates, and the inter-model distance is calculated based on the calculated barycentric coordinates. .. According to this method, since the inter-model distance is calculated based on the barycentric coordinates of the second substance model in the composite material analysis method, the inter-model distance between the second substance models can be analyzed more accurately. ..

In the method for analyzing a composite material of the present invention, in the third step, as the reference coordinates, a second particle in the vicinity of the barycentric coordinates of the second substance model is specified, and the second particle is specified based on the specified second particle. It is preferable to calculate the inter-model distance. With this method, the analysis method of the composite material specifies the second particles in the vicinity of the barycentric coordinates of the second substance model without calculating the reference coordinates of the second substance model in the virtual space for each analysis, Since the inter-model distance of the second substance model can be sequentially calculated, the calculation load can be reduced and the inter-model distance of the second substance model can be easily calculated.

In the composite material analysis method of the present invention, in the third step, the second particles on the surface of the second substance model are specified as the reference coordinates, and the inter-model distance is determined based on the specified second particles. It is preferable to calculate. By this method, the method of analyzing the composite material calculates the inter-model distance based on the surface second particles of the second substance model, so that the inter-model distance between the second substance models can be analyzed more accurately. Becomes

In the composite material analysis method of the present invention, it is preferable that the inter-model distance is calculated under the periodic boundary condition in the third step. With this method, the analysis method of the composite material can calculate the inter-model distance under the periodic boundary condition. Therefore, even when the inter-model distance is calculated under the condition that the virtual space is reduced, the second substance It becomes possible to accurately calculate the distance between the models.

In the composite material analysis method of the present invention, in the first step, a first analysis model and a second analysis model having mutually different parameters are created, and in the third step, the first analysis model and the It is preferable to analyze the inter-model distance of the second analysis model. By this method, the analysis method of the composite material allows the analysis model to be given various parameters such as the strength of the interaction between the first substance model and the second substance model, the volume fraction, and the filler shape such as the aggregation structure. The impact can be evaluated.

In the composite material analysis method of the present invention, it is preferable that in the third step, the inter-surface distance of the second substance model is analyzed based on the model radius of the second substance model. According to this method, the analysis method of the composite material is performed by analyzing the distance between the surfaces of the second substance models, and the analysis of the surface distances of the second substance models is performed. Since it is possible to evaluate the thickness, it is also possible to evaluate the material properties of the composite material from the viewpoint of the thickness of the first substance model.

The method for analyzing a composite material according to the present invention preferably includes a step of executing a simulation by a molecular dynamics method using the analysis model to analyze the inter-model distance. By this method, the analysis method of the composite material can reproduce the behavior of the first substance model in the composite material based on the simulation by the molecular dynamics method, so that the energy loss and the second It is also possible to analyze the relationship with the nanostructure of the composite material based on the distribution and arrangement of the material model.

In the simulation method of the composite material of the present invention, in the simulation, a first inter-model distance that is the inter-model distance at a first analysis time and a second inter-model distance that is the inter-model distance at a second analysis time are used. It is preferable to analyze. With this method, the analysis method of the composite material compares the first inter-model distance with the second inter-model distance to determine the energy loss due to the mechanical deformation of the composite material and the distribution and placement of the second substance model. It is also possible to analyze the relationship between the composite and the nanostructure of the composite material.

In the method for analyzing a composite material of the present invention, it is preferable that, in the simulation, the analysis of the inter-model distance using the analysis model is performed a plurality of times to analyze the change in the inter-model distance for each number of times. By this method, the composite material analysis method can analyze the influence of the mechanical deformation of the analysis model on the inter-model distance of the second material model, and the energy loss due to the mechanical deformation of the composite material can be analyzed. It is also possible to analyze the relationship with the nanostructure of the composite material based on the dispersion and arrangement of the second substance model.

A computer program for analyzing a composite material of the present invention is characterized by causing a computer to execute the above-described method for analyzing a composite material.

According to the computer program for analyzing a composite material of the present invention, the inter-model distance between the second substance models is calculated on the basis of the reference coordinates of the second substance model, so that the second substance models are arranged in a dispersed manner in the first substance model. The arrangement and distribution of the second substance model can be analyzed. Moreover, since the inter-model distance of the second substance model is directly calculated and analyzed without depending on the displacement of the second substance model, for example, even when the second substance model makes an orbital motion in the virtual space. , The inter-model distance of the second substance model can be accurately analyzed. Therefore, it is possible to realize a composite material analysis method capable of accurately analyzing the dispersion and arrangement of a specific substance in a composite material, and thus to evaluate the influence of the arrangement and dispersion of the second substance model on the material properties of the composite material. It will also be possible to accelerate the development of fuel-efficient tires.

According to the present invention, it is possible to realize a composite material analysis method and a composite material analysis computer program capable of accurately analyzing the dispersion and arrangement of a specific substance in a composite material.

FIG. 1 is a flow chart showing an outline of a method for analyzing 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 composite material analysis method according to the embodiment of the present invention. FIG. 3 is an explanatory diagram showing an example of a composite material analysis method according to an embodiment of the present invention. FIG. 4 is an explanatory diagram showing another example of the method for analyzing a composite material according to the embodiment of the present invention. FIG. 5: is explanatory drawing which shows the other example of the analysis method of the composite material which concerns on embodiment of this invention. FIG. 6 is an explanatory diagram showing another example of the composite material analysis method according to the embodiment of the present invention. FIG. 7: is explanatory drawing which shows another example of the analysis method of the composite material which concerns on embodiment of this invention. FIG. 8 is a functional block diagram of an analysis device that executes the composite material analysis method according to the embodiment of the present invention. FIG. 9: is a figure which shows the stress strain curve of the 1st analysis model and the 2nd analysis model of the composite material which concerns on the Example of this invention. FIG. 10 is a conceptual diagram showing the dispersed state of the filler particles of the first analysis model before and after the elongation analysis according to the example of the present invention. FIG. 11 is a diagram showing the relationship between the interparticle distance and the frequency of filler particles before and after the elongation analysis according to the example of the present invention. FIG. 12 is a conceptual diagram showing the dispersed state of the filler particles of the second analysis model before and after the elongation analysis according to the example of the present invention. FIG. 13 is a diagram showing the relationship between the interparticle distance and the frequency of filler particles before and after the elongation analysis according to the example of the present invention.

Hereinafter, an embodiment 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 flowchart showing an outline of a method for analyzing a composite material according to this embodiment. As shown in FIG. 1, the composite material analysis method according to the present embodiment is a composite material analysis method using a composite material analysis model created by a molecular dynamics method using a computer. The method of analyzing a composite material is the method of creating an analysis model of a composite material in which a plurality of second substance models modeled by second particles are arranged in a plurality of first substance models modeled by first particles. A model between a plurality of second substance models based on one step ST11, a second step ST12 for setting an interaction in the analysis model and performing a numerical analysis, and the reference coordinates of the second substance model after the numerical analysis. And a third step ST13 for calculating the inter-distance.

FIG. 2 is a conceptual diagram showing an example of the analysis model 1 created by the composite material analysis method according to the present embodiment. As shown in FIG. 2, the analysis model 1 of the composite material according to the present embodiment is arranged in a model creation area A, which is a virtual space of a substantially cubic shape with one side having a distance L, for example. Be converted. The analysis model 1 includes a pair of first filler model (second substance model) 11 and second filler model (second substance model) 12 formed by modeling a plurality of filler particles (second particles) 11a and 12a. , A plurality of polymer models that are arranged around the first filler model 11 and the second filler model 12, and are modeled with a plurality of polymer particles (first particles) 21a and a bonding chain 21b that connects the polymer particles 21a. (First substance model) 21. The first filler model 11 and the second filler model 12 are arranged in the plurality of polymer models 21 so as to be separated from each other. In the example shown in FIG. 2, two first filler models 11 and two second filler models 12 and a plurality of polymer models 21 are shown, but the analysis model 1 has a plurality of models created in the model creation region A. And a plurality of polymer models. 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, or a polyhedral shape. In the present embodiment, an example in which the composite material to be analyzed contains a filler model that is a filler and a polymer that is a polymeric material will be described, but the present invention contains two or more kinds of substances. It is also applicable to composite materials. Further, the present invention can be applied to various composite materials containing other than the polymer and the filler.

The first filler model 11 and the second filler model 12 are modeled in a state in which a plurality of filler particles 11a and 12a are aggregated into 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 by a predetermined distance. In addition, the first filler model 11 and the second filler model 12 may have their outer edges connected to each other by covalent bonding in a state where they are aggregated with each other.

Examples of the filler include carbon black, silica, alumina and the like. The filler particles 11a and 12a are modeled by collecting a plurality of filler atoms. The filler particles 11a and 12a form a filler particle group in which a plurality of filler particles 11a and 12a are aggregated. The relative positions of the filler particles 11a and 12a are specified by a binding chain (not shown) between the plurality of filler particles 11a and 12a. This bond chain (not shown) has a function as a spring in which the equilibrium length, which is the bond distance between the filler particles 11a and 12a, and the spring constant are defined, and binds between the filler particles 11a and 12a. .. The bond chain is a bond in which the relative position of the filler particles 11a and 12a and the potential at which a force is generated by twisting, bending, etc. are defined. The filler models 11 and 12 are numerical data (including mass, volume, diameter and initial coordinates of the filler particles 11a and 12a) for handling the filler by molecular dynamics. Numerical data of the filler models 11 and 12 is input to the computer.

Examples of the polymer include rubber, resin, and elastomer. The polymer particles 21a are modeled by aggregating atoms of a plurality of polymers. Further, the polymer particles 21a form a polymer particle group by assembling a plurality of polymer particles 21a. If necessary, a modifier that enhances the affinity with the filler is added to the polymer. Examples of this modifier include a hydroxyl group, a carbonyl group, and a functional group of an atomic group. The polymer model 21 is modeled by filling a plurality of polymer atoms and polymer particles 21a, which is an aggregate of a plurality of polymer atoms, in a model creating region A at a predetermined density. The relative position of the polymer particle 21a is specified by the bonding chain 21b between the plurality of polymer particles 21a. 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 bonding chain 21b is a bond in which the relative position of the polymer particles 21a and the potential for generating a force due to twisting, bending, etc. are defined. The polymer model 21 is numerical data (including mass, volume, diameter, initial coordinates, etc. of the polymer particles 21a) for handling the polymer by molecular dynamics. Numerical data of the polymer model 21 is input to the computer.

Next, the method of analyzing the composite material according to the present embodiment will be described in detail. FIG. 3 is an explanatory diagram showing an example of the composite material analysis method according to the present embodiment. In addition, in FIG. 3, the part between the 1st filler model 11 and the 2nd filler model 12 shown in FIG. 2 is expanded and shown typically. As shown in FIG. 3, in the method of analyzing a composite material, between the models of the pair of the first filler model 11 and the second filler model 12 arranged in the predetermined analysis target area A1 in the model creation area A. The arrangement and dispersion of the first filler model 11 and the second filler model 12 are analyzed based on the distance. In the example shown in FIG. 3, the model distance is set by setting the first reference coordinates C1 of the first filler model 11 and the second reference coordinates C2 of the second filler model 12, and setting the first reference coordinates C1 and the second reference coordinates C2. It is calculated based on the distance D1 between the center of gravity points with the coordinate C2. In the example shown in FIG. 3, the first reference coordinate C1 is set to the center of gravity (barycentric coordinate) P1 of the first filler model 11 composed of the plurality of filler particles 11a. Further, the second reference coordinate C2 is set to the barycentric point (barycentric coordinate) P2 of the second filler model 12 composed of the plurality of filler particles 12a.

The center of gravity P1 may be set to the filler particle 11a existing in a region including the center of gravity P1 of the first filler model 11, and when the center of gravity P1 does not include the filler particle 11a, it coincides with the center of gravity P1. You may set to the specific point of coordinates. Similarly, the center of gravity P2 may be set to the filler particles 12a existing in the region including the center of gravity P2 of the second filler model 12, and if the center of gravity P2 does not include the filler particles 12a, the center of gravity P2 may be set. You may set to the specific point of the coordinate which coincides with. By thus setting the first reference coordinates C1 and the second reference coordinates C2 and calculating the distance D1 between the centers of gravity, without being affected by the shapes of the first filler model 11 and the second filler model 12, The arrangement and dispersion of the first filler model 11 and the second filler model 12 can be accurately analyzed. In addition, when the deformation analysis of the analysis model 1 is performed by specifying the filler particles 11a including the coordinates of the center of gravity P1 and the filler particles 12a including the coordinates of the center of gravity P2, respectively, after the predetermined analysis time, It is possible to easily perform the analysis without recalculating the center of gravity P1 of the first filler model 11 and the center of gravity P2 of the second filler model 12.

FIG. 4 is an explanatory view showing another example of the composite material analysis method according to the present embodiment. In addition, in FIG. 4, similarly to the example illustrated in FIG. 3, the first filler model 11 and the second filler model 12 are schematically illustrated. In the example shown in FIG. 4, first, similarly to the example in FIG. 3, the center of gravity P1 of the first filler model 11 is set and the center of gravity P2 of the second filler model 12 is set. Next, the first reference coordinates C1 are set to the specific filler particles 11aX existing near the center of gravity P1 of the first filler model 11. Further, the second reference coordinates C2 are set to the specific filler particles 12aX existing near the center of gravity P2 of the second filler model 12. Then, the arrangement and dispersion of the first filler model 11 and the second filler model 12 are analyzed based on the set filler particle distance D2 between the specific filler particles 11aX and the filler particles 12aX. Thus, by setting the first reference coordinates C1 and the second reference coordinates C2, for example, when a deformation analysis of the analysis model 1 is performed, the first filler particles 11aX and the second filler particles 12aX By tracking the behavior, it is possible to easily perform the analysis without recalculating the center of gravity P1 of the first filler model 11 and the center of gravity P2 of the second filler model 12 after the predetermined analysis time. Further, as shown in FIG. 5, for example, even when the first filler model 11 and the second filler model 12 each perform a rotational movement (see FIG. 5) during deformation analysis of the analysis model 1, The first filler particles 11aX after the rotational movement exist near the center of gravity P1 and the second filler particles 12aX after the rotational movement exist near the center of gravity P2. This makes it possible to reduce the change in the inter-filler particle distance D2 before and after the rotational movement, so that the arrangement and dispersion of the first filler model 11 and the second filler model 12 before and after the rotational movement can be accurately analyzed.

FIG. 6 is an explanatory diagram showing another example of the composite material analysis method according to the present embodiment. Note that, in FIG. 6, similarly to the example shown in FIG. 3, the first filler model 11 and the second filler model 12 are schematically shown. In the example shown in FIG. 6, the first reference coordinates C1 are set to the specific filler particles 11aY existing near the surface of the first filler model 11. The second reference coordinates C2 are set to the specific filler particles 12aY existing near the surface of the second filler model 12. Then, the arrangement and dispersion of the first filler model 11 and the second filler model 12 are analyzed based on the set inter-surface distance D3 between the specific filler particles 11aY and the filler particles 12aY. By setting the first reference coordinates C1 and the second reference coordinates C2 in this way, for example, the behavior of the first filler particles 11aY and the second filler particles 12aY when a deformation analysis or the like of the analysis model 1 is performed. By tracing, the analysis can be easily performed without recalculating the center of gravity P1 of the first filler model 11 and the center of gravity P2 of the second filler model 12 after a predetermined analysis time. By setting the first reference coordinates C1 and the second reference coordinates C2 in this way, the inter-surface distance D3 can be obtained without calculating the center of gravity P1 of the first filler model 11 and the center of gravity P2 of the second filler model 12. Based on this, it becomes possible to easily analyze the arrangement and dispersion of the first filler model 11 and the second filler model 12. As the first filler particles 11aY, the filler particles 11a existing on the surface of the first filler model 11 may be specified, and the filler particles 11a adjacent to the filler particles 11a existing on the surface of the first filler model 11 are specified. May be. As the second filler particles 12aY, the filler particles 12a existing on the surface of the second filler model 12 may be specified, and the filler particles 12a adjacent to the filler particles 12a existing on the surface of the second filler model 12 may be specified. May be specified. In addition, the first filler particles 11aY and the second filler particles 12aY may directly specify the filler particles 11a and 12a of the coordinates existing at the outermost sides of the first filler model 11 and the second filler model 12.

Further, in the example shown in FIG. 6, the center of gravity P1 and the center of gravity P2 of the first filler model 11 and the second filler model 12 are specified, and the distance D1 between the centers of gravity P1 and P2 of the center of gravity P1 (FIG. Between the first filler model 11 and the second filler model 12 by subtracting the radius r1 of the first filler model 11 and the radius r2 of the second filler model 12 from the distance D1 between the center of gravity points after calculating The inter-surface distance D3 can be obtained. By obtaining the inter-surface distance D3 in this way, the thickness of the polymer model 21 (see FIG. 1) interposed between the first filler model 11 and the second filler model 12 can be obtained, and thus the composite material It is also possible to evaluate the material properties from the viewpoint of the thickness of the polymer model 21.

FIG. 7 is an explanatory diagram showing another example of the composite material analysis method according to the present embodiment. 7, in the example shown in FIG. 7, the first filler model 11 arranged in a predetermined analysis target area A1 (hereinafter, also referred to as “first analysis target area A1”) in the model creation area A. Also, the second filler model 12 and the analysis target area A2 adjacent to the first analysis target area A1 (hereinafter, also referred to as “second analysis target area A2”) are schematically shown.

As shown in FIG. 7, in the composite material analysis method according to the present embodiment, the analysis model 1 in the model creation area A corresponds to the inside of the first analysis target area A1 and the inside of the second analysis target area A2. It becomes a periodic boundary condition having a structure. For this reason, the first filler model 11 and the second filler model 12 in the first analysis target area A1 and the first filler model 111 and the second filler model 112 in the second analysis target area A2 have repeating structures corresponding to each other. Exists as an equivalent model. Therefore, in the example shown in FIG. 7, similarly to the example shown in FIG. 3, the first reference coordinate C1 in the first analysis target area A1 is set to the center of gravity P1 of the first filler model 11, and The reference coordinate C2 is set to the center of gravity P2 of the second filler model 12, and the distance D1 between the centers of gravity is calculated. Next, similarly, the first reference point coordinate 1 in the second analysis target area A2 is set to the center of gravity P11 of the first filler model 111, and the second reference coordinate C2 is set to the center of gravity of the second filler model 112. P12 is set, and the distance D4 between the center of gravity points between the center of gravity P2 in the first analysis target area A1 and the center of gravity P11 in the second analysis target area A2 is calculated. Then, the distance D1 between the center of gravity points in the first analysis target area A1 and the distance D4 between the center of gravity points between the first analysis target area A1 and the second analysis target area A2 are compared to determine the distance D1 between the center of gravity points. If it is smaller, the center-of-gravity point distance D1 is set as the inter-filler point distance, and if the center-of-gravity point distance D4 is smaller, the center-of-gravity point distance D4 is set as the inter-filler distance, and the center-of-gravity point distance D1 and the center-of-gravity point are set. If the inter-distances D4 are equal, one of the centroid point distance D1 and the inter-centroid point distance D4 is calculated as the inter-filler model distance. In this way, by calculating the inter-model distance between the first filler model 11 and the second filler model 12, the inter-model distance can be calculated under the periodic boundary condition, and thus the analysis target areas A1 and A2 are obtained. Even when the inter-model distance is calculated under the condition that the value is reduced, the inter-model distance can be accurately calculated.

The interaction set between the polymer fillers includes filler particles, polymer particles, filler particles and polymer particles, and the like. The interaction does not have to be set for all of these, but can be set appropriately as needed. The interaction between the filler models 11 and 12 and the polymer model 21 may be an interaction such as an intermolecular force or a chemical attractive force such as hydrogen bond, and the filler particles 11a and 12a and the polymer particle 21a may be set. A physical interaction such as a bond between them may be established. When the polymer model 21 is composed of a plurality of types of polymer particles 21a, the above-mentioned chemical and physical interactions may be set between the plurality of types of polymer particles 21a. Further, the interaction between the plurality of types of polymer particles 21a and the filler particles 11a, 12a does not necessarily have to be set to the same interaction, and for example, the interaction between the polymer particles 21aA and the filler particles 11a, 12a. The action and the interaction between the polymer particles 21aB and the filler particles 11a and 12a may be different from each other. Moreover, examples of the numerical analysis include relaxation analysis, extension analysis, temperature change analysis, and voltage transformation analysis. When performing the extension analysis, it is preferable to include at least the undeformed state in the evaluation time. Thus, by comparing the analysis result at the evaluation time in the undeformed state with the analysis result after the elongation analysis, the number of particles separated during the elongation process can be evaluated.

Next, the composite material analysis method and the composite material analysis computer program according to the present embodiment will be described in more detail. FIG. 8 is a functional block diagram of an analysis device that executes the composite material analysis method according to the present embodiment.

As shown in FIG. 8, the analysis method of the composite material according to the present embodiment is realized by the 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 the input/output device 51 having the input means 53. The input unit 53 processes various physical property values of a polymer and a filler that are targets for creating an analysis model of a composite material, an actual measurement result of an extension test result using a composite material containing the polymer and the filler, and boundary conditions in the analysis. Input to the unit 52 or the storage unit 54. As the input unit 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: CentraL1 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 loaded 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 in an area appropriately allocated to itself in the memory as needed, and analyzes the composite material based on the expanded data. Various processes relating to the creation of a model and the analysis of a composite material using the model for analysis of a composite material are executed.

The processing unit 52 includes a model creating unit 52a, a condition setting unit 52b, and an analyzing unit 52c. The model creation unit 52a uses the data stored in advance in the storage unit 54 to count the number of particles, the number of molecules, and the molecular weight of the composite material such as a filler and a 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, and the number of constituent steps such as target molecule number, which is the number of molecules included in the analytical model 1 to be created, number of setting and calculation steps Set coarse-grained models such as, and set initial conditions for various calculation parameters such as interactions 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 Leonard-Jones potential represented by the following formula (1) are used, and these are adjusted. By increasing the upper limit distance (cutoff distance) for calculating the potential, it is possible to adjust the attractive force and repulsive force that have worked to a long distance. It is preferable that the parameters of the interaction between the filler particles 11a and the interaction between the polymer particles 21a be successively decreased until the interaction between the filler particles 11a and the interaction between the polymer particles 21a reach a constant value. By gradually bringing the σ and ε of the Leonard-Jones potential from large values to the original values, particles can be approached at a moderate speed that does not lead the molecule to an unnatural state. Further, the attractive force and the repulsive force can be adjusted within an appropriate range by gradually reducing the cutoff distance.

The condition setting unit 52b sets various analysis conditions such as various numerical analyzes such as bridge analysis, relaxation analysis, extension analysis, temperature change analysis and voltage transformation analysis. The analysis unit 52c executes a 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. In addition, the analysis unit 52c sets the center of gravity P1 of the first filler model 11 as the first reference coordinate C1, sets the center of gravity P2 of the second filler model 12 as the second reference coordinate C2, and sets the center of gravity P1. The distance D1 between the center of gravity points between the center of gravity and the center of gravity P2 is calculated as the distance between the first filler model 11 and the second filler model 12. In addition, the analysis unit 52c identifies and sets the filler particles 11a in the vicinity of the center of gravity P1 of the first filler model 11 as the first reference coordinates C1, and sets the center of gravity of the second filler model 12 as the second reference coordinates C2. The filler particles 12a near the point P2 are specified and set, and the filler particle distance D2 between the specified filler particles 11a and the filler particles 12a is calculated as the model distance. The analysis unit 52c also specifies and sets the filler particles 11a near the surface of the first filler model 11 as the first reference coordinates C1, and sets the filler particles 11a near the surface of the second filler model 12 as the second reference coordinates C2. The particles 12a are specified and set, and the surface distance D3 between the specified filler particles 11a and the filler particles 12a is calculated as the model distance. Here, the analysis unit 52c identifies the filler particles 11a and the filler particles 12a near the surface by using the center of gravity P1 and the radius r1 of the first filler model 11 and the center of gravity P2 and the radius r2 of the second filler model 12. May be. Then, the analysis unit 52c analyzes the distribution and arrangement of the first filler model 11 and the second filler model 12 using the calculated inter-model distance.

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

In the storage unit 54, data of a filler model such as rubber carbon black, silica, and alumina, which is data for creating an analysis model of a composite material to be analyzed via the input unit 53, rubber, resin, and Stores data of polymer models such as elastomers, stress-strain curves that are preset physical quantity histories, and methods for creating a composite material analysis model according to this embodiment, and computer programs for realizing the composite material analysis method. Has been done. This computer program may be one that can realize the composite material analysis method according to the present embodiment in combination with a computer program already recorded in a computer or a computer system. The “computer system” mentioned here includes an OS (Operating System) and hardware such as peripheral devices.

The display unit 55 is, for example, a display device such as a liquid crystal display device. The storage unit 54 may be included in another device such as a database server. For example, the analysis device 50 may access the processing unit 52 and the storage unit 54 by communication from a terminal device including the input/output device 51.

Next, referring again to FIG. 1, the method for analyzing the composite material according to the present embodiment will be described in more detail. First, the model creation unit 52a uses a plurality of polymer models 21 each including a polymer particle 21a and a bonding chain 21b in a predetermined model creation region A, a composite material analysis model including a first filler model 11 and a second filler model. 1 is created (step ST11). Here, the model creation unit 52a creates a plurality of filler models other than the first filler model 11 and the second filler model 12 as necessary. Next, the model creation unit 52a performs balancing 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 until various components after initialization reach an equilibrium state. 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, which 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. The various conditions include the position and number of the filler model 11 for performing the analysis, the position and number of the filler atom, the filler atomic group, the filler particles 11a and 12a, and the filler particle group, the filler particle number, and the position of the molecular chain of the polymer model 21. And number, polymer atom, polymer atomic group, position and number of polymer particle 21a and polymer particle group, polymer particle number, position and number of bonding chain 21b and bonding chain 21b, number of bonding chain 21b, preset physical quantity history Includes a certain stress-strain curve and fixed values that do not change the conditions.

Next, the analysis unit 52c sets the interaction in the analysis model 1 based on the condition set by the condition setting unit 52b and performs various numerical analyzes (step ST12). As the interaction here, , For example, the interaction between the filler particles 11a and 12a, the polymer particles 21a, the interaction between the filler particles 11a and 12a and the polymer particles 21a, and the state in which the filler particles 11a and 12a and the polymer particles 21a are bonded by a bonding chain 21b. Interactions are mentioned, but it is not necessary to set all of them. In addition, the analysis unit 52c, for example, according to the type of the polymer model 21 to be created, the first interaction between the polymer particles 21a and the filler particles 11a constituting the first polymer model 21 and the second polymer model. The second interaction between the polymer particles 21a constituting 21 and the filler particles 11a may be set as a different interaction. In addition, as the numerical analysis, relaxation analysis, extension analysis, temperature change analysis, transformation by molecular dynamics method using the analysis model 1 of the composite material including the filler model 11 and the polymer model 21 created by the model creation unit 52a Numerical analysis by motion analysis such as analysis and deformation analysis such as shear analysis can be used.

Next, the analysis unit 52c acquires various physical quantities such as the nominal displacement obtained by calculating the nominal displacement or the nominal stress or the dynamic displacement obtained as a result of the motion analysis by various numerical analyses. By such a numerical analysis, the change of the segment state such as the bond length and polymer particle velocity of the polymer molecule, the velocity between the cross-linking points and the free end, the physical amount such as the bond length and the orientation, etc., which changes with the analysis time. The relationship between the numerical value and strain, the relationship between the numerical value and the pressure or analysis time, which represents the change in the state of the segment such as the bond length of the polymer molecule and the polymer particle velocity, which changes with each analysis time, and the polymer that changes with each analysis time. Since it is possible to evaluate the relationship between the numerical value indicating the state change of the segment such as the bond length of the molecule and the polymer particle velocity and the temperature or the analysis time, it is possible to analyze the local molecular state change of the polymer molecule in more detail.

Next, the analysis unit 52c calculates the inter-model distance between the first filler model 11 and the second filler model 12 of the created analysis model 1. Here, the analysis unit 52c sets the first reference coordinates C1 of the first filler model 11 and the second reference coordinates C2 of the second filler model 12, and sets the set first reference coordinates C1 and second reference coordinates C2. The inter-model distance between the first filler model 11 and the second filler model 12 is calculated based on the distance between them. Then, the analysis unit 52c analyzes the arrangement and dispersion of the first filler model 11 and the second filler model 12 based on the calculated inter-model distance. The analysis unit 52c also stores the analysis result of the analyzed composite material in the storage unit 54.

In the above-described embodiment, the analysis unit 52c sets the first reference coordinates C1 at the center of gravity P1 of the first filler model 11 configured by the plurality of filler particles 11a and configured by the plurality of filler particles 12a. It is preferable to set the second reference coordinate C2 at the center of gravity P2 of the second filler model 12. Accordingly, the composite material analysis method calculates the inter-model distance based on the inter-center-of-gravity distance D1 of the first filler model 11 and the second filler model 12, so that the first filler model 11 and the second filler model 12 It becomes possible to analyze the distance between the models between them more accurately. Here, the analysis unit 52c may set the barycentric coordinates to the filler particles 11a existing in the region including the barycentric point P1 of the first filler model 11, and when the filler particles 11a do not exist at the barycentric point P1, The barycentric coordinates may be set at a specific point whose coordinates coincide with the barycentric point P1. Similarly, the analysis unit 52c may set the barycentric coordinates for the filler particles 12a existing in the area including the barycentric point P2 of the second filler model 12, and when the barycentric point P2 does not have the filler particles 12a, The barycentric coordinates may be set at a specific point whose coordinates coincide with the barycentric point P2. By thus setting the first reference coordinates C1 and the second reference coordinates C2 and calculating the inter-model distance, the analysis unit 52c is affected by the shapes of the first filler model 11 and the second filler model 12, and the like. Without this, the arrangement and dispersion of the first filler model 11 and the second filler model 12 can be accurately analyzed. In addition, the analysis unit 52c specifies the filler particles 11a including the coordinates of the center of gravity P1 and the filler particles 12a including the coordinates of the center of gravity P2, thereby performing the deformation analysis of the analysis model 1 and the like, It is possible to easily perform the analysis without recalculating the center of gravity P1 of the first filler model 11 and the center of gravity P2 of the second filler model 12 after the predetermined analysis time.

Further, in the above-described embodiment, the analysis unit 52c sets the first reference coordinates C1 to the specific filler particles 11aX existing in the vicinity of the center of gravity P1 of the first filler model 11, and the second filler model 12 The second reference coordinates C2 are set for the specific filler particles 12aX existing near the center of gravity P2. Then, the analysis unit 52c calculates the inter-model distance between the first filler model 11 and the second filler model 12 based on the set inter-filler particle distance D2 between the specific filler particles 11aX and the filler particles 12aX, and arranges and It is preferable to analyze the variance. Thereby, the analysis unit 52c identifies the filler particles 11a and 12a in the vicinity of the barycentric coordinates of the first filler model 11 and the second filler model 12, and thereby the first filler model 11 and the second filler model in the virtual space A. Since the inter-model distances of the first filler model 11 and the second filler model 12 can be sequentially calculated without calculating the reference coordinates C1 and C2 of the model 12 for each analysis, the calculation load can be reduced. It becomes possible to easily calculate the inter-model distance between the filler model 11 and the second filler model 12. The analysis unit 52c traces the behavior of the first filler particles 11aX and the second filler particles 12aX, for example, when the deformation analysis of the analysis model 1 is performed, so that the first filler model after a predetermined analysis time. It is possible to easily perform the analysis without recalculating the center of gravity P1 of 11 and the center of gravity P2 of the second filler model 12.

Further, in the above-described embodiment, the analysis unit 52c sets the first reference coordinates C1 to the specific filler particles 11aY existing in the vicinity of the surface of the first filler model 11 to determine the surface of the second filler model 12. The second reference coordinate C2 is set to the specific filler particles 12aY existing in the vicinity, and based on the surface distance D3 between the specific filler particles 11aY and the filler particles 12aY that have been set, the first filler model 11 and the second filler model Twelve locations and variances may be analyzed. Accordingly, the analysis unit 52c calculates the inter-model distance based on the filler particles 11a and 12a on the surfaces of the first filler model 11 and the second filler model 12, so that the first filler model 11 and the second filler model 12 are separated from each other. It is possible to analyze the inter-model distance of the model with higher accuracy. Further, the analysis unit 52c sets the first reference coordinates C1 and the second reference coordinates C2 in this way, so that, for example, when performing a deformation analysis of the analysis model 1, the first filler particles 11aY and the first filler particles 11aY By tracking the behavior of the two filler particles 12aY, the center of gravity point P1 of the first filler model 11 and the center of gravity point P2 of the second filler model 12 after a predetermined analysis time are not calculated again, and based on the inter-surface distance D3. It is possible to easily analyze the arrangement and dispersion of the first filler model 11 and the second filler model 12.

The analysis unit 52c may specify the filler particles 11a existing on the surface of the first filler model 11 as the first filler particles 11aY, and the filler adjacent to the filler particles 11a existing on the surface of the first filler model 11 may be specified. The particles 11a may be specified. The analysis unit 52c may specify the filler particles 12a existing on the surface of the second filler model 11 as the second filler particles 12aY and is adjacent to the filler particles 12a existing on the surface of the second filler model 12. The filler particles 12a to be used may be specified. In addition, the analysis unit 52c directly specifies the filler particles 11a and 12a of the coordinates existing on the outermost sides of the first filler model 11 and the second filler model 12 as the first filler particles 11aY and the second filler particles 12aY. Good. Furthermore, the analysis unit 52c identifies the center of gravity P1 and the center of gravity P2 of the first filler model 11 and the second filler model 12, and after calculating the distance D1 between the centers of gravity P1 and P2. , The distance d3 between the surfaces between the first filler model 11 and the second filler model 12 is obtained by subtracting the radius r1 of the first filler model 11 and the radius r2 of the second filler model 12 from the distance D1 between the centers of gravity. May be. Accordingly, the analysis unit 52c can obtain the thickness of the polymer model 21 interposed between the first filler model 11 and the second filler model 12 based on the inter-surface distance D3, and thus the material properties of the composite material. Can be analyzed from the viewpoint of the thickness of the polymer model 21.

Further, in the above-described embodiment, it is preferable that the analysis unit 52c calculate the inter-model distance between the first filler model 11 and the second filler model 12 under the periodic boundary condition. As a result, the analysis unit 52c can calculate the model-to-model distance under the periodic boundary condition. Therefore, even when the model-to-model distance is calculated under the condition that the analysis target area is small, the first filler model 11 The inter-model distance between the second filler model 12 and the second filler model 12 can be accurately calculated.

Further, in the above-described embodiment, the analysis unit 52c uses the first analysis model and the second analysis model, which are the analysis models 1 having different parameters created by the model creation unit 52a, to perform the first analysis. It is preferable to analyze the inter-model distances of the analysis model and the second analysis model. Thereby, the analysis unit 52c evaluates the influence of various parameters such as the strength of the interaction between the first substance model and the second substance model, the volume fraction, the filler shape such as the aggregation structure, and the like on the analysis model. can do.

Further, in the above-described embodiment, the analysis unit 52c may analyze the inter-model distance by executing a simulation by the molecular dynamics method using the created analysis model 1. Accordingly, the analysis unit 52c can reproduce the inter-model distance between the first filler model 11 and the second filler model 12 in the composite material based on the simulation by the molecular dynamics method, so that the mechanical deformation to the composite material or the like can be performed. It is also possible to analyze the relationship between the accompanying energy loss and the nanostructure of the composite material based on the dispersion and arrangement of the first filler model 11 and the second filler model 12.

Further, in the above-described embodiment, the analysis unit 52c performs the simulation by the molecular dynamics method using the created analysis model 1 between the first filler model 11 and the second filler model 12 at the first analysis time. It is preferable to analyze the first inter-model distance and the second inter-model distance between the first filler model 11 and the second filler model 12 at the second analysis time. As a result, the analysis unit 52c compares the first inter-model distance with the second inter-model distance to determine the energy loss associated with mechanical deformation of the composite material and the first filler model 11 and the second filler model 12. It is also possible to analyze the relationship of the composite material to the nanostructure based on dispersion and placement.

Further, in the above-described embodiment, the analysis unit 52c uses the created analysis model 1 in the simulation by the molecular dynamics method to analyze the first filler model 11 and the second filler model 12 using the analysis model 1. It is preferable that the analysis of the inter-model distance between and is performed multiple times to analyze the change in the inter-model distance for each number of times. Accordingly, the analysis unit 52c can analyze the influence of the mechanical deformation of the analysis model 1 on the inter-model distance between the first filler model 11 and the second filler model 12, and the mechanical deformation of the composite material, etc. It is also possible to analyze the relationship between the energy loss due to and the nanostructure of the composite material based on the dispersion and arrangement of the second substance model.

As described above, according to the present embodiment, the first filler model 11 and the second filler model are based on the first reference coordinates C1 of the first filler model 11 and the second reference coordinates C2 of the second filler model 12. Since the inter-model distance to 12 is calculated, the arrangement and dispersion of the first filler model 11 and the second filler model 12 dispersedly arranged in the polymer model 21 can be analyzed. Moreover, according to this composite material analysis method, the inter-model distance between the first filler model 11 and the second filler model 12 is directly measured without depending on the displacement of the first filler model 11 and the second filler model 12. Since it is calculated and analyzed, for example, even when the first filler model 11 and the second filler model 12 make an orbital motion within the model creation region A, the first filler model 11 and the second filler model 12 It is possible to accurately analyze the distance between the models. Therefore, according to the composite material analysis method according to the present embodiment, a composite material analysis method capable of accurately analyzing the dispersion and arrangement of the first filler model 11 and the second filler model 12 in the composite material is realized. Therefore, the effect of the arrangement and dispersion of the first filler model 11 and the second filler model 12 on the material properties of the composite material can be evaluated, and the development of fuel-efficient tires can be accelerated.

(Example)
Next, examples carried out to clarify the effects of the present invention will be described. The present invention is not limited to the following examples.

The present inventors created two types of first analysis model and second analysis model with different compound compounds using two types of fillers with different mechanical responses, and created the first analysis model and the second analysis model. 2 The inter-model distance of the filler model 11 in the extension analysis of the analysis model was analyzed and evaluated. The contents investigated by the present inventors will be described below.

FIG. 9 is a diagram showing stress-strain curves of the first analysis model 200 and the second analysis model 300 of the composite material according to the example of the present invention. As shown in FIG. 9, when the stress-strain curves of the first analysis model 200 and the second analysis model 300 are compared, the increase in strain due to the increase in stress is reflected in the first analysis model 200 (see the solid line). On the other hand, it can be seen that the second analysis model 300 (see the dotted line) is relatively smaller. This result shows that the interaction between the filler particles 201 (see FIG. 10) used in the first analysis model 200 is different from the interaction between the filler particles 301 (see FIG. 12) used in the second analysis model 300. It is considered that the first analysis model 200 is strongly aggregated between the filler particles 201 with respect to the second analysis model 300, and thus the strain increases with the increase in stress in the first analysis model 200.

FIG. 10 is a conceptual diagram showing the dispersed state of the filler particles 201 of the first analysis model 200 before and after the elongation analysis, and FIG. 11 shows the relationship between the interparticle distance and the frequency of the filler particles 201 before and after the elongation analysis. It is a figure. As shown in FIGS. 10 and 11, since the filler particles 201 of the first analysis model 200 before the elongation analysis are strongly aggregated in the analysis target area A1, the filler particles 201 are densely packed. Within the range, there is a range R1 indicating a short distance between particles and a range R2 indicating a long distance between particles of the filler particle group. In addition, in the filler particles 201 of the first analysis model 200 after the elongation analysis, the distance between the filler groups increases in a state where the filler particles are kept in a dense state. As a result, the inter-particle distance after the elongation analysis does not change significantly in the inter-particle distance within the range R1 representing the short-distance inter-particle distance, and the distribution of the inter-particle distance within the range R2 representing the long-distance inter-particle distance. Will grow.

FIG. 12 is a conceptual diagram showing the dispersed state of the filler particles 301 of the second analysis model 300 before and after the extension analysis, and FIG. 13 shows the relationship between the interparticle distance and the frequency of the filler particles 301 before and after the extension analysis. It is a figure. As shown in FIGS. 12 and 13, since the filler particles 301 of the second analysis model 300 before the elongation analysis have weak interaction and are widely dispersed in the analysis target region A, the interparticle distance is wide range R3. It is distributed all over. Further, in the filler particles 301 of the second analysis model 300 after the elongation analysis, the filler particles 301 are further diffused, so that the distance between the filler particles 301 increases and the interparticle distance is distributed in a wider range R4. From these results, it is possible to analyze the change in the distribution of the inter-particle distance by using the first analysis model 200 and the second analysis model 300 that use the filler models having mutually different interactions, and It turns out that the layout can be analyzed.

As described above, according to the above-described example, by changing the filler type used as the filler model to create the analysis model, the analysis result of the interparticle distance reflecting the interaction of the filler model can be obtained. I understand. From this, it is understood that according to the present embodiment, the dispersion and arrangement of the specific substance in the composite material can be accurately analyzed.

1 Analysis Model 11 1st Filler Model 11a Filler Particles 12 2nd Filler Model 12a Filler Particles 21 Polymer Model 21a Polymer Particles 21b Bonding Chain 50 Analyzing Device 51 Input/Output Device 52 Processing Unit 52a Model Creating Unit 52b Condition Setting Unit 52c Analyzing Unit 53 input means 54 storage section 55 display means A model creation area A1 analysis target area (first analysis target area)
A2 analysis target area (second analysis target area)
D1 Distance between important points D2 Distance between filler particles D3 Distance between surfaces

Claims (11)

A method for analyzing a composite material using a model for analysis of a composite material created by a molecular dynamics method using a computer,
A first step of creating an analysis model of a composite material in which a plurality of second substance models modeled by the second particles are arranged in a plurality of first substance models modeled by the first particles;
A second step of setting an interaction in the analysis model and performing a numerical analysis;
A third step of calculating inter-model distances between the plurality of second substance models based on the reference coordinates of the second substance model after the numerical analysis,
In the third step, a method for analyzing a composite material , characterized in that the inter-model distance is calculated under a periodic boundary condition . In the first step, a first analysis model and a second analysis model having mutually different parameters are created, and in the third step, the model-to-model distance between the first analysis model and the second analysis model. The method for analyzing a composite material according to claim 1, wherein the analysis is performed. A method for analyzing a composite material using a model for analyzing a composite material created by a molecular dynamics method using a computer,
A first step of creating a model for analysis of a composite material in which a plurality of second substance models modeled by the second particles are arranged in a plurality of first substance models modeled by the first particles;
A second step of setting an interaction in the analysis model and performing a numerical analysis;
A third step of calculating inter-model distances between the plurality of second substance models based on the reference coordinates of the second substance model after the numerical analysis,
In the first step, a first analysis model and a second analysis model having mutually different parameters are created, and in the third step, the inter-model distance between the first analysis model and the second analysis model. A method for analyzing a composite material, which comprises: In the third step, the calculated barycentric coordinates of the second material model as a reference coordinate, and calculates the distance between the model based on the calculated center of gravity coordinates, in any one of claims 1 to 3 Method for analyzing the described composite material. In the third step, as the reference coordinates, to identify the second particles in the vicinity of the center of gravity coordinates of the second material model, and calculates the distance between the model based on the specified second particles from claim 1 The method for analyzing the composite material according to claim 3 . 4. In the third step, the second particles on the surface of the second substance model are specified as the reference coordinates, and the inter-model distance is calculated based on the specified second particles . The method for analyzing a composite material according to any one of items . The analysis of the composite material according to any one of claims 1 to 6, wherein in the third step, a surface distance of the second substance model is analyzed based on a model radius of the second substance model. Method. The method for analyzing a composite material according to claim 1, wherein a simulation by a molecular dynamics method is performed using the analysis model to analyze the inter-model distance. The composite material according to claim 8, wherein, in the simulation, a first inter-model distance that is the inter-model distance at a first analysis time and a second inter-model distance that is the inter-model distance at a second analysis time are analyzed. Analysis method. The analysis of the composite material according to claim 8 or 9, wherein in the simulation, the analysis of the inter-model distance using the analysis model is executed a plurality of times, and the change in the inter-model distance for each number of times is analyzed. Method. A computer program for analyzing a composite material, which causes a computer to execute the method for analyzing a composite material according to any one of claims 1 to 10.

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