JP6750274B2 - Heterogeneous material simulation method, heterogeneous material simulation device and program - Google Patents

Description

The present invention relates to a method for simulating a heterogeneous material having at least two phases, a simulation device and a program for the heterogeneous material, and in particular, a method for simulating a heterogeneous material that compares the characteristic amount and mechanical property of agglomerates of the heterogeneous material, The present invention relates to a heterogeneous material simulation device and program.

It is known that in rubber materials containing fillers such as carbon black and silica, the viscoelastic properties of the rubber materials change due to the filler distribution (morphology), and the fuel efficiency of the car changes. Has been.
Therefore, in the development of rubber materials for fuel-efficient tires, the relationship between the morphology of the filler (filler) of the rubber material and the mechanical properties such as viscoelasticity of the rubber material that contributes to the fuel efficiency performance or grip performance of the vehicle should be considered. Understanding is very important. Therefore, the creation of a simulation model having parametric morphology, that is, the creation of a simulation model in which the morphology can be changed by changing the numerical values of the parameters, and the simulation using the simulation model are effective means for developing fuel-efficient tires. As a simulation method for evaluating the relationship between the morphology of rubber materials and the viscoelastic properties of rubber materials, various model creation methods have been proposed so far.

In Patent Document 1, a plurality of slice images obtained by slicing a rubber material at a predetermined interval are acquired, the acquired slice images are stacked to generate a three-dimensional image, and the size of the filler in the filler region of the three-dimensional image. Virtual particles of a predetermined size corresponding to the above are virtually arranged, and the area where virtual particles are not arranged in the three-dimensional image is divided as a rubber area into lattice areas of a predetermined size smaller than the size corresponding to the filler. In addition, it is described that a three-dimensional model in which a particle region in which virtual particles are arranged is divided into lattice regions having a size larger than a predetermined size as a filler region is generated.

Patent Document 2 describes a simulation method of a rubber material containing a filler. In Patent Document 2, a measurement step of measuring X-ray and/or neutron scattering data of a rubber material, a visualization step of specifying a three-dimensional structure of a filler in rubber by a reverse Monte Carlo method from the scattering data, and a filler It includes a model setting step of setting a rubber material model based on the three-dimensional structure, and a step of performing deformation simulation based on the rubber material model. In the measurement step, the scattering vector (scattering vector q=4π·sin θ/λ (λ is the wavelength of the electromagnetic wave or particle beam, θ is 1/2 of the scattering angle)) is larger than 10 ⁻⁴ nm ⁻¹ and 10 nm ^−1. Scatter data in the smaller range is obtained.

Japanese Patent No. 4602929 JP, 2013-10880, A

As described above, Patent Document 1 acquires a plurality of slice images of a rubber material and generates a three-dimensional model. Patent Document 2 measures a X-ray and/or neutron scattering data of a rubber material, and visualizes the scattering data to identify the three-dimensional structure of the filler in the rubber by the reverse Monte Carlo method, and the three-dimensional structure of the filler. The rubber material model is set based on, and the rubber material model is set.
However, in both the three-dimensional model of Patent Document 1 and the rubber material model of Patent Document 2, the number and size of the agglomerates are not fixed, and the features of the agglomerates cannot be acquired from parameters and the like.

An object of the present invention is to solve the above-mentioned problems based on the prior art, and to compare the characteristic amount and the mechanical property of the agglomerates of the heterogeneous material with a simulation method for the heterogeneous material, and a simulation apparatus for the heterogeneous material. And to provide the program.

In order to achieve the above object, the present invention provides a step of setting model parameters, a step of creating a material model of a heterogeneous material that can be analyzed by a computer based on the set model parameters, and a material model. In the acquisition process to determine the agglomerates and to obtain the feature amount of the agglomerates, the calculation process to calculate the mechanical properties of the material model, the model parameters and the calculation results of the agglomerate feature amounts and the mechanical properties as data structure information. The present invention provides a method for simulating a heterogeneous material, which comprises a storage step of storing.

When acquiring the characteristic amount of the agglomerate in the acquisition step, it is preferable to divide the material model into a virtual cubic lattice and acquire the characteristic amount of the agglomerate.
When discriminating the agglomerates in the acquisition step, it is preferable that the agglomerates adjacent to each other at the periodic boundaries are regarded as one agglomerate.
Furthermore, it is preferable to have an optimization calculation step that includes the model parameter at the time of creating the material model as the design variable and performs the optimization calculation that includes the mechanical properties of the heterogeneous material as the objective function.
Further, it is preferable to have a visualization step of visualizing a causal relationship between the characteristic amount of the aggregate and the mechanical property.

The present invention, a condition setting unit that sets model parameters, a model creating unit that creates a material model of a heterogeneous material that can be analyzed by a computer based on the set model parameters, and identifies agglomerates in the material model. An analysis unit that obtains the characteristic amount of the agglomerate, and a calculation unit that calculates the mechanical properties of the material model and stores the model parameters and the calculation results of the characteristic amount and the mechanical property of the agglomerate in the storage unit as data structure information. A simulation device for a heterogeneous material having the above-mentioned features.

When acquiring the characteristic amount of the agglomerate, the analysis unit preferably divides the material model into a virtual cubic lattice and acquires the characteristic amount of the agglomerate.
When discriminating the agglomerates, the analysis unit preferably sets the agglomerates adjacent to each other at the periodic boundaries to be one agglomerate.
Furthermore, in the condition setting part, the mechanical parameters of the heterogeneous material should be included in the design variables in the model parameters when creating the material model as the objective function, and the computing part should perform the optimization calculation using the design variables and the objective function. Is preferred.
Further, it is preferable that the calculation unit visualizes the causal relationship between the characteristic amount of the aggregate and the mechanical characteristics.

The present invention provides a program for causing a computer to execute each step of the heterogeneous material simulation method of the present invention as a procedure.

According to the present invention, it is possible to compare the characteristic amount and mechanical property of the agglomerate of the heterogeneous material, whereby it is possible to find useful information about the relationship between the morphology and the viscoelastic property of the heterogeneous material, and It can be used to develop new materials for fuel-efficient tires. In addition, the material model creation method can be evaluated by associating the model parameter at the time of creating the material model with the feature amount of the aggregate.

It is a schematic diagram which shows the simulation apparatus used for the simulation method of the heterogeneous material of embodiment of this invention. (A) is a schematic diagram showing an example of a material model, (b) is a schematic diagram showing a first example of an aggregate, and (c) is a schematic diagram showing a second example of an aggregate. , (D) is a schematic diagram showing a third example of an aggregate. (A) is a schematic diagram for explaining an example of the feature amount of the aggregate, and (b) is a schematic diagram for explaining another example of the feature amount of the aggregate. It is a flowchart which shows the 1st example of the simulation method of the heterogeneous material of embodiment of this invention. (A) is a schematic perspective view showing an example of a material model, (b) is a schematic perspective view showing agglomerates of a material model, and (c) is a graph showing a distribution of agglomerates of a material model. is there. (A) is a schematic perspective view showing a first example of an aggregation criterion, (b) is a schematic perspective view showing an example of an aggregation criterion, and (c) is an aggregation criterion. It is a typical perspective view showing the 3rd example of a discriminating standard. It is a typical perspective view for explaining the periodic boundary of an aggregate. It is a flowchart which shows the 2nd example of the simulation method of the heterogeneous material of embodiment of this invention. (A) and (b) are self-organizing maps of design variables, (c) and (d) are self-organizing maps of feature amounts of aggregates, and (e) to (h) are mechanical characteristics. It is a self-organizing map.

Hereinafter, a heterogeneous material simulation method, a heterogeneous material simulation apparatus, and a program according to the present invention will be described in detail based on preferred embodiments shown in the accompanying drawings.
FIG. 1 is a schematic diagram showing a simulation device used in a method for simulating a heterogeneous material according to an embodiment of the present invention.

A simulation device 10 (hereinafter, simply referred to as a processing device 10) shown in FIG. 1 is an example of a device that implements the heterogeneous material simulation method of the present invention. The processing device 10 is configured using hardware such as a computer. The processing apparatus 10 shown in FIG. 1 is used for the method for simulating a heterogeneous material of the present invention. However, if the method for simulating a heterogeneous material can be executed by using hardware and software such as a computer, the processing apparatus 10 is executed. It is not limited.
Heterogeneous materials are at least two-phase materials that have a first material phase and a second material phase. The heterogeneous material is, for example, a rubber material containing rubber as a mother phase (first material phase) and containing a filler (second material phase) such as carbon black or silica.

The processing device 10 includes a processing unit 12, an input unit 14, and a display unit 16. The processing unit 12 includes a condition setting unit 20, a model creation unit 22, an analysis unit 24, a calculation unit 26, a memory 28 (storage unit), a display control unit 30, and a control unit 32. In addition to this, a ROM and the like are provided although not shown.
The processing unit 12 is controlled by the control unit 32. Further, in the processing unit 12, the condition setting unit 20, the model creation unit 22, the analysis unit 24, the calculation unit 26, and the display control unit 30 are connected to the memory 28, and the condition setting unit 20, the model creation unit 22, and the analysis unit 24. , And the data of the calculation unit 26 are stored in the memory 28.

The input unit 14 is various input devices such as a mouse and a keyboard for inputting various information according to an operator's instruction. The display unit 16 visualizes, for example, a material model, a characteristic amount of aggregates, calculation results of mechanical properties, data structure information, optimization calculation results, and a causal relationship between aggregate characteristic amounts and mechanical properties, which will be described later. , And the results obtained by the simulation method of the heterogeneous material are displayed, and various known displays are used. The display unit 16 also includes a device such as a printer for displaying various information on an output medium.

The processing device 10 executes a program (computer software) stored in a storage medium such as a ROM by using the control unit 32, so that the condition setting unit 20, the model creation unit 22, the analysis unit 24, and the calculation unit 26. Each part is functionally formed. As described above, the processing device 10 may be configured by a computer in which each part functions by executing a program, or may be a dedicated device in which each part is configured by a dedicated circuit.

The condition setting unit 20 is a model parameter of a heterogeneous material, a discriminant condition of agglomerates, a material, which is necessary in the method for simulating a heterogeneous material according to the present embodiment and is used to create a computer-analyzed material model of the heterogeneous material Various conditions and information such as calculation conditions such as boundary conditions of model mechanical properties, data structure information setting conditions, optimization calculation calculation conditions, optimization calculation approximation models, and visualization calculation calculation conditions are input and set. To do. Various conditions and information are input via the input unit 14. Various conditions and information set by the condition setting unit 20 are stored in the memory 28.

The model parameter of a heterogeneous material is, for example, a parameter necessary to create a material model of a heterogeneous material having a two-phase structure in which a predetermined material phase is dispersed in a matrix phase. It is a parameter necessary to make a material model of a material a simulation model composed of a plurality of unit elements that can be calculated by a computer.
The inhomogeneous material model parameters are the size of the modeling region, information about which material phase is to be the matrix model, information about which material phase is the particle model dispersed in the matrix model, and the matrix Information such as the number of model types, the number of particle model types, the presence/absence of a boundary layer model, the information of the attribute values that define the model of the second material phase, the particle model for controlling the generation position of the particle model. And at least one or more of the material parameters for each material, such as the first material phase and the second material phase, as well as information on control parameters defining relative positions between For example, the first material phase is modeled as a matrix model, and the second material phase is modeled as a particle model. The attribute value that defines the particle model of the second material phase is the shape of the particle model that constitutes the second material phase (information on a spherical model or an ellipsoidal model), the size of the particle model to be created (radius, or (Major axis and minor axis), and information such as volume fraction in the modeling region. The model parameter includes model information of the simulation model (each piece of information of the model by the finite element method or each piece of information of the model by the mesh-free method) and size information of the unit element.
The material parameter includes a value representing the viscoelastic property of the material, for example, a complex elastic modulus of each material, or elastic constants such as Young's modulus and shear rigidity and viscosity constants such as tangent loss tan δ. In assigning such material parameters to the material model, a correspondence table of material attribute values and material parameters for specifying the type of material (material parameter) is set in advance, and this attribute value is assigned to the material model. Including that.

Further, in the condition setting unit 20, design variables are set in model parameters as calculation conditions for optimization calculation, and mechanical characteristics of the heterogeneous material are set as an objective function. Design variables are model parameters when creating a material model. The design variables are, for example, various parameters regarding the filler, such as parameters that control the spatial arrangement of the filler.
As various parameters, model parameters of a material model of a heterogeneous material include, for example, phase constitution, size and arrangement density of each phase, constitution of each phase, and the like. In addition, the model parameters include, for example, the setting value of the phase structure in the material model creation, and the image information of the heterogeneous material including the agglomerates. The image information of the heterogeneous material is, for example, information obtained by acquiring a cross-sectional image of the heterogeneous material using a CT (Computer Tomography) method and combining position information and density information of each pixel forming the cross-sectional image. .. In addition to this, information obtained by combining the position information of each pixel and the density information of the image of the heterogeneous material obtained using X-rays can be used as the image information of the heterogeneous material. Incidentally. The conditions for determining the aggregate will be described in detail later.

The model creating unit 22 creates a computer-analyzed material model of the inhomogeneous material based on the model parameters set in the condition setting unit 20, and an approximate model for optimization calculation based on the various parameters described above. It is a thing.

The material model and the approximation model for the optimization calculation created by the model creation unit 22 are created using the parameters of each type set by the condition setting unit 20, but the material model and the approximation model for the optimization calculation are created. A publicly known creating method can be used for creating. The material model can be created using, for example, the method described in Japanese Patent No. 5854067.
The elements constituting the material model are, for example, a quadrilateral element in a two-dimensional plane, a solid element such as a tetrahedral solid element, a pentahedral solid element and a hexahedral solid element in a three-dimensional body, a shell such as a triangular shell element and a quadrangular shell element. Elements that can be analyzed by a computer, such as elements and surface elements. In the analysis process, the elements thus divided are specified one by one by using the three-dimensional coordinates in the three-dimensional model and the two-dimensional coordinates in the two-dimensional model.

The analysis unit 24 discriminates the aggregate in the material model, obtains the characteristic amount of the aggregate, and acquires the characteristic amount of the aggregate. The analysis unit 24 determines the agglomerate, for example, under the above-described agglomerate determination condition. As a result of the determination of the agglomerate obtained by the analysis unit 24, the feature amount of the agglomerate is stored in the memory 28.

Here, FIG. 2A is a schematic diagram showing an example of a material model, FIG. 2B is a schematic diagram showing a first example of aggregates, and FIG. 2C is a second example of aggregates. It is a schematic diagram which shows, (d) is a schematic diagram which shows the 3rd example of an aggregate. FIG. 3A is a schematic diagram for explaining an example of the feature amount of the aggregate, and FIG. 3B is a schematic diagram for explaining another example of the feature amount of the aggregate.
The material model 40 shown in FIG. 2A shows a heterogeneous material in which a polymer phase such as rubber is dispersed with a polymer phase containing filler.
In the material model 40, the polymer model 44 is dispersed in the matrix model 42. The mother phase model 42 is made of rubber, for example. The polymer model 44 includes a filler model 46 that represents a filler such as carbon black and silica, and between the polymer model 44 and the filler model 46 is a boundary layer model 48 that represents a boundary layer.

When the material model 40 is formed with a plurality of phase structures of at least two phases, an agglomerate can be defined in a material phase containing at least particles such as fillers. For example, island structures such as polymer phases can be defined as agglomerates. Note that the agglomerate includes an island structure such as the above-mentioned polymer phase, and a plurality of particles such as fillers overlapping, but not only a plurality of particles such as fillers overlapping, one particle such as a filler. But it's called an aggregate. The aggregate can be obtained, for example, from the position of the center of gravity of particles such as filler and the radius of particles such as filler.
From the above, the agglomerates are, for example, the polymer model 44 as shown in FIG. 2B, the boundary layer model 48 as shown in FIG. 2C, the filler as shown in FIG. The model 46 may be used. One of the above models is selected as the agglomerate, but the number of agglomerates is different in each model. The polymer model 44 shown in FIG. 2B has 2 aggregates, the boundary layer model 48 shown in FIG. 2C has 11 aggregates, and the filler model shown in FIG. 2D. At 46, the number of agglomerates is 16.

The feature amount of the agglomerate is, for example, the number of agglomerates, the volume of the agglomerates, the surface area of the agglomerates, the diameter or radius of the smallest sphere containing the agglomerates, the size of the ellipsoid containing the agglomerates, and the filler. The number of particles. In addition to this, as the feature amount of the agglomerate, the number of the agglomerates described above, the volume of the agglomerates, the surface area of the agglomerates, the diameter or radius of the smallest sphere containing the agglomerates, the size of the ellipsoid containing the agglomerates, and The maximum value, the average value or the dispersion of the number of particles of the filler or the like can be used.
The diameter of the smallest sphere containing the agglomerates is twice the radius r of the circle 52 that circumscribes the agglomerates 50 as shown in FIG. The size of the ellipsoid containing the aggregate is the length of the major axis a or the minor axis b of the ellipsoid 54 that circumscribes the aggregate 50 as shown in FIG. 3B.

The calculation unit 26 calculates the mechanical characteristics of the material model. The calculation result of the mechanical properties of the material model obtained by the calculation unit 26 is stored in the memory 28.
The calculation method of the mechanical characteristics of the material model in the calculation unit 26 is not particularly limited, and a known method can be appropriately used. For example, a material model is divided into a predetermined mesh, physical property values corresponding to a matrix model and a polymer model are applied, and mechanical properties are calculated using FEM (finite element method). The above-mentioned mechanical properties are, for example, rigidity, maximum stress, maximum strain, strain distribution, or the like. Other mechanical properties include, for example, the maximum value of the rigidity of the heterogeneous material, the average value of the rigidity of the heterogeneous material, the dispersion of the rigidity of the heterogeneous material, and the energy loss of the heterogeneous material.

Further, the calculation unit 26 causes the memory 28 to store the calculation result of the model parameter, the feature amount of the agglomerate, and the mechanical property as data structure information. The data structure information is a combination of the model parameter at the time of model creation, the feature amount of the aggregate of the material model, and the mechanical characteristics of the material model.

The calculation unit 26 also performs an optimization calculation using the design variables and the dynamic characteristics (objective function) set by the condition setting unit 20 described above. The calculation unit 26 functions by executing a subroutine using a known finite element solver, for example.
The calculation unit 26 uses the non-linear response relationship to calculate the value of the mechanical characteristic in the mechanical characteristic value space configured by the values of the plurality of types of design variables and the mechanical characteristic (objective function). In this case, the calculation unit 26 uses a plurality of types of design variable values and mechanical characteristics (objective function), and creates an approximate model using the value of the mechanical characteristics as an objective function. The calculation unit 26 performs multi-objective optimization calculation using the created approximation model.
The above-mentioned approximate model (meta model) is a mathematical model that approximates the input/output relationship, and various input/output relationships can be approximated by adjusting the parameters. As the above-mentioned approximate model, for example, a polynomial model, kriging, a neural network, a radial basis function or the like can be used.

In addition to this, the calculation unit 26 also calculates the value of the mechanical characteristic by the combination of the design variable and the mechanical characteristic using the finite element method without using the approximate model. As the multi-objective optimization calculation method, for example, a genetic algorithm (GA) which is one of evolutionary calculation methods is used. Examples of the genetic algorithm include, for example, DRMOGA (Divided Range Multi-Objective GA) and NCGA (Neighborhood Cultivation GA) in which a solution set is divided into a plurality of regions along an objective function and a multi-objective GA is performed for each of the divided solution sets. , Known methods such as DCMOGA (Distributed Cooperation model of MOGA and SOGA), NSGA (Non-dominated Sorting GA), NSGA2 (Non-dominated Sorting GA-II), and SPEAII (Strength Pareto Evolutionary Algorithm-II) method. You can

Further, the Pareto solution may be searched for from the multi-objective optimization calculation result using the approximate model, and the Pareto solution may be extracted. In this case, the obtained Pareto solution is stored in the memory 28.
Here, the Pareto solution cannot be said to be superior to any other solution in a plurality of characteristic values (objective function) having a trade-off relationship, but a solution that does not have a better solution cannot be found. Say. Generally, there are a plurality of Pareto solutions as a set. Search for Pareto solutions using Pareto ranking method. Other than this, for example, selection using a vector evaluated genetic algorithm (VEGA), a Pareto ranking method, or a tournament method is performed. Other than the genetic algorithm (GA), for example, the annealing method (SA) or particle swarm optimization (PSO) may be used as the same evolutionary calculation method.

The calculation unit 26 also visualizes the causal relationship between the characteristic amount of the agglomerate acquired by the analysis unit 24 and the mechanical characteristic. For the visualization, for example, a scatter diagram of the characteristic amount and mechanical characteristics of the aggregate, a self-organizing map of the characteristic amount and mechanical characteristic of the aggregate, and the like are used. The self-organizing map can be created using the method described in Japanese Patent No. 4339808, for example. Therefore, the detailed description of creating the self-organizing map is omitted.

The display control unit 30 visualizes the material model, the agglomerate feature amount, the calculation result of the mechanical property, the data structure information, the optimization calculation result, the visualization result of the causal relationship between the agglomerate feature amount and the mechanical property, and the The results obtained by the simulation method for homogeneous materials are displayed. The display control unit 30 displays, for example, a visualization result that visualizes a causal relationship between the material model, the feature amount of the agglomerate, the calculation result of the mechanical property, the data structure information, the optimization calculation result, and the feature amount of the agglomerate and the mechanical property. It is read from the memory 28 and displayed on the display unit 16.

Next, a method for simulating a heterogeneous material according to this embodiment will be described.
FIG. 4 is a flowchart showing a first example of the method for simulating a heterogeneous material according to the embodiment of the present invention. FIG. 5A is a schematic perspective view showing an example of the material model, FIG. 5B is a schematic perspective view showing an aggregate of the material model, and FIG. 5C is a distribution of the aggregate of the material model. It is a graph.
In the present embodiment, a heterogeneous material having a two-phase structure in which aggregates of particles such as filler are dispersed in a mother phase such as rubber will be described as an example. As shown in FIG. 5A, the material model 40 is a matrix model 42 in which a plurality of aggregate model 43 are dispersed.

First, the model parameters of the material model are set in the condition setting unit 20 (step S10).
Next, based on the set model parameters, the model creation unit 22 creates a material model 40 (see FIG. 5A) of the heterogeneous material that can be analyzed by a computer (step S12).
Next, the analysis unit 24 determines the aggregate model 43 (see FIG. 5A) in the material model 40, and acquires the feature amount of the aggregate model 43 (step S14). The feature amount of the aggregate is stored in the memory 28.

When acquiring the feature amount of the agglomerate model 43, first, in the material model 40, the mother phase model 42 and the agglomerate model 43 are distinguished, and the agglomerate model 43 is separated from the mother phase model 42. In this case, for example, by changing the color of the aggregate model 43 and the matrix model 42, it is shown that they are separated. Next, the aggregate model 43 is divided into groups. Regarding grouping, for example, the relationship between the size of the agglomerate and the position of the center of gravity is set in advance, and the agglomerate model 43 is divided into groups. At this time, the volume of each aggregate model 43 is also obtained. The material model 40 of FIG. 5A includes 10 agglomerate models 43, and the volume of the largest agglomerate was 3.87% in terms of the total volume ratio. For example, it can be distinguished by changing the color of each aggregate model 43. Thereby, each aggregate model 43 can be visually recognized.
In addition, on the data, for example, by assigning a number to the aggregate model 43, the aggregate can be distinguished. Thereby, the volume ratio of each aggregate shown in FIG. 5C can be obtained, and the feature amount of the aggregate can be obtained.

In FIG. 5C, the volume ratio of the aggregates is normalized with the minimum aggregate volume being 1. The volume of the agglomerate can be obtained, for example, by dividing the material model 40 by a virtual cubic lattice whose size is set in advance and counting the number of cubic lattices.
After that, under the calculation condition set in the condition setting unit 20, the calculation unit 26 calculates, for example, the maximum stress as the mechanical property for the material model 40 by using, for example, FEM (step S16). The calculated maximum stress value is stored in the memory 28 as a mechanical property value.
Next, the calculation unit 26 reads out from the memory 28 the model parameters at the time of model creation, the characteristic quantities of the agglomerates of the material model, and the mechanical properties of the material model, and the model parameters at the time of the model creation Data structure information is created by pairing feature quantities and mechanical properties of material models. The above-mentioned data structure information is stored in the memory 28 (step S18). Specifically, the data structure information is, for example, the structure shown in Table 1 below.

In this way, the agglomerates of the material model and the mechanical properties of the material model can be associated. As a result, the morphology of heterogeneous materials and the viscoelastic properties of heterogeneous materials can be obtained by associating not only the model parameters used when creating a material model, but also the feature quantities of aggregates obtained from the material model and the mechanical properties of the material model. It is possible to find useful information about the relationship with, and it can be useful for the development of new materials for fuel-efficient tires. In addition, the method of creating a material model of a heterogeneous material can be evaluated by associating the model parameter at the time of creating the material model with the feature amount of the aggregate of the heterogeneous material.

When acquiring the feature amount of the aggregate model 43 (step S14), for example, the material model 40 shown in FIG. 5A is divided into virtual cubic lattices. In this case, the cubic lattice includes the agglomerate model or a part of the agglomerate model. By presetting the size of the cubic lattice, by counting the number of cubic lattices, the volume of the agglomerate and the surface area of the agglomerate can be easily obtained from the characteristic amount of the agglomerate.

There are various methods for determining whether or not they are the same aggregate in a cubic lattice. For example, when the cubic lattice 60 is divided as shown in FIGS. 6A to 6C, each cubic lattice 60 becomes the matrix phase model 42 or the aggregate model 43. In FIG. 6A, the cubic lattice 60 of the aggregate model 43 is in surface contact. Thus, when the cubic lattice 60 of the agglomerate model 43 is in surface contact, it is determined as one agglomerate. Further, as shown in FIG. 6B, when the cubic lattice 60 of the agglomerate model 43 is in contact with the side and the cubic lattice 60 of the agglomerate model 43 is in side contact, it is determined as one agglomerate. As shown in FIG. 6C, when the cubic lattice 60 of the agglomerate model 43 is in point contact and the cubic lattice 60 of the agglomerate model 43 is in point contact, it is determined as one agglomerate. By dividing into the cubic lattices 60, it is possible to easily determine whether or not there is one aggregate based on the arrangement state of the cubic lattices 60 of the aggregate model 43.
In this case, by setting the size of the cubic lattice 60 and the determination conditions shown in FIGS. 6A to 6C in the condition setting unit 20, the analysis unit 24 divides the material model 40 into the cubic lattices 60. However, the agglomerate can be discriminated based on the discrimination condition.

Further, the cycle boundary may be taken into consideration in the determination of the aggregate. As a result, it is possible to perform a simulation considering the periodic boundary. Specifically, as shown in FIG. 7, the adjacent material model 40 is virtually added to the material model 40 having the matrix model 42 and the aggregate model 43. As a result, the agglomerate model 43 is configured with the adjacent virtual material model 40. Aggregates that are adjacent to each other at the periodic boundaries are treated as one aggregate.
The volume of the agglomerate model 43 can be obtained only by adding the volumes of the agglomerate models 43 adjacent to each other at the ends of the material model 40. The surface area of the agglomerate model 43 can be obtained by adding the surface areas of the agglomerate models 43 adjacent to each other and then subtracting twice the adjacent area.

Considering the periodic boundary, in the material model 40 shown in FIG. 7, the number of agglomerates is 2, and the size of the largest agglomerates is 1.67% in terms of the total volume ratio of the material model. Is 12.79% in terms of the total surface area of the material model. In contrast, when the material model 40 shown in FIG. 7 does not consider the periodic boundaries, the number of agglomerates is 10, and the maximum agglomerate size is 3.34% in terms of the total volume of the material model. The surface area of the agglomerates is 8.53% based on the total surface area of the material model.

Next, a second example of the simulation method of the heterogeneous material will be described.
FIG. 8: is a flowchart which shows the 2nd example of the simulation method of the heterogeneous material of embodiment of this invention. In the second example of the heterogeneous material simulation method shown in FIG. 8, the detailed description of the same steps as those of the first example of the heterogeneous material simulation method shown in FIG. 2 will be omitted.

The second example of the method for simulating a heterogeneous material shown in FIG. 8 is different in that optimization calculation (step S20), suitability of optimization calculation (step S22), and visualization (step S24) are performed. The steps are the same as in the first example of the method for simulating a heterogeneous material described above.
When performing the optimization calculation (step S20), the condition setting unit 20 sets design variables in the model parameters as calculation conditions for the optimization calculation, and sets the mechanical properties of the heterogeneous material as the objective function.
In the optimization calculation (step S20), the multi-objective optimization calculation using the approximation model for the design variable (input value) and the objective function (output value), with the mechanical properties of the heterogeneous material as the objective function (output value) carry out. The optimization calculation is done in the manner described above.
By utilizing the information of the actual material model in the optimization calculation (step S20), the knowledge extraction after the optimization becomes easy. Further, when an approximate expression is created when the material model is optimized, the design variables to be considered increase, and the accuracy of the approximate expression used for the optimization calculation can be increased.
By creating the approximate model, the calculation time of the optimization calculation (step S20) can be shortened. Also, the morphological characteristics obtained from the material model can be used as an input value (design variable) for the optimization calculation.

As a result of the optimization calculation (step S20), if a predetermined determination condition is satisfied (step S22), visualization is performed (step S24). The visualization is performed with respect to design variables, feature quantities of aggregates, and mechanical properties, and the visualization method may be a scatter diagram or a self-organizing map. For example, the self-organizing map shown in FIGS. 9A to 9H. The result of visualization using can be obtained.

Here, FIGS. 9A and 9B are self-organizing maps of the design variables, FIGS. 9C and 9D are self-organizing maps of the characteristic amount of the aggregate, and FIGS. ) Is a self-organizing map of mechanical properties.
By visualizing, it is possible to clearly recognize the causal relationship between the characteristic amount of the agglomerate, that is, the morphological information and the mechanical property, and to express the mechanical property targeted in material development (the distribution of the agglomerate. Form) can be specified. Further, by using the self-organizing map, when there are multiple design variables (input values) and multiple dynamic characteristics (output values), the causal relationship between the input values (design variables) and the dynamic characteristics (output values) Can be shown.
For example, FIG. 9A shows a first parameter for controlling the spatial arrangement of fillers as a design variable, and FIG. 9B shows a second parameter for controlling the spatial arrangement of fillers as a design variable. FIG. 9C shows the number of aggregates as the characteristic amount of the aggregate, and FIG. 9D shows the size of the aggregate as the characteristic amount of the aggregate. 9(e) shows the maximum value of rigidity as the mechanical characteristic of the heterogeneous material, FIG. 9(f) shows the average value of the rigidity of the heterogeneous material as the mechanical characteristic, and FIG. 9(g) shows the rigidity as the mechanical characteristic. 9H, and FIG. 9H shows energy loss as a mechanical characteristic.

On the other hand, as a result of the optimization calculation (step S20), when the predetermined determination condition is not satisfied (step S22), the process returns to the model parameter setting (step S10) and the model parameter is set again. After that, the creation of the material model (step S12), the acquisition of the characteristic amount of the agglomerate (step S14), the calculation of the mechanical properties (step S16), the saving of the data structure (step S18) are repeated, and the optimization calculation is performed again ( Step S20). The above process is repeated until the result of the optimization calculation satisfies the predetermined determination condition (step S22).
The visualization step (step S24) may be omitted. After the optimization calculation (step S20), the visualization may be performed without performing the determination (step S22).

The present invention is basically constructed as described above. Although the heterogeneous material simulation method, the heterogeneous material simulation apparatus, and the program of the present invention have been described above in detail, the present invention is not limited to the above-described embodiments, and various modifications are possible without departing from the gist of the present invention. Of course, improvements or changes may be made.

10 Simulation device (processing device)
12 processing unit 14 input unit 16 display unit 20 condition setting unit 22 model creating unit 24 analysis unit 26 computing unit 28 memory 30 display control unit 32 control unit 40 material model 42 mother phase model 43 aggregate model 44 polymer model 46 filler model 48 Boundary layer model 50 Aggregate 60 Cubic lattice

Claims (11)

Computer
Setting model parameters,
A creation step of creating a material model of a heterogeneous material that can be analyzed by a computer based on the set model parameters,
An acquisition step of determining an agglomerate in the material model and acquiring a characteristic amount of the agglomerate,
An operation step of calculating mechanical properties of the material model,
A method for simulating a heterogeneous material, which comprises performing a saving step of saving the model parameter, the feature amount of the agglomerate, and the calculation result of the mechanical property as data structure information. In the acquisition step of the computer executes, when the computer acquires the characteristic quantity of said agglomerates in claim 1 which divides the material model to a virtual cubic lattice, it obtains a feature amount of the agglomerates A method for simulating a heterogeneous material as described. The heterogeneous material according to claim 1 or 2, wherein, in the acquisition step executed by the computer, when the computer determines the agglomerates, the agglomerates adjacent to each other at periodic boundaries are regarded as one agglomerate. Simulation method. The method according to claim 1, further comprising: an optimization calculation step in which the model parameter at the time of creating the material model is included in a design variable, and the computer performs an optimization calculation including the mechanical property of the heterogeneous material in an objective function. The method for simulating a heterogeneous material according to any one of items. The method for simulating a heterogeneous material according to any one of claims 1 to 4, wherein the computer executes a visualization step of visualizing a causal relationship between the characteristic amount of the aggregate and the mechanical property. A condition setting part that sets model parameters,
Based on the set model parameters, a model creation unit that creates a material model of a heterogeneous material that can be analyzed by a computer,
An analysis unit that determines an aggregate in the material model and acquires a feature amount of the aggregate,
A heterogeneous material comprising: a calculation unit that calculates mechanical properties of the material model, and stores the model parameters, the feature amount of the agglomerate, and the calculation result of the mechanical properties in a storage unit as data structure information. Simulation device. The simulation device for a heterogeneous material according to claim 6, wherein, when acquiring the feature amount of the agglomerate, the analysis unit divides the material model into a virtual cubic lattice and acquires the feature amount of the agglomerate. .. The heterogeneous material simulation apparatus according to claim 6 or 7, wherein the analysis unit, when determining the agglomerates, treats the agglomerates adjacent to each other at the periodic boundaries as one agglomerate. Furthermore, in the condition setting unit, the model parameters at the time of creating the material model are included in the design variables, and the mechanical properties of the heterogeneous material are used as an objective function, and the arithmetic unit uses the design variables and the objective function. The simulation apparatus for a heterogeneous material according to any one of claims 6 to 8, wherein the optimization calculation is performed by using. The heterogeneous material simulation device according to any one of claims 6 to 9, wherein the calculation unit visualizes a causal relationship between the characteristic amount of the aggregate and the mechanical property. A program for causing a computer to execute each step of the heterogeneous material simulation method according to any one of claims 1 to 5 as a procedure.