JP4946335B2 - Operation method of simulation apparatus - Google Patents

Description

The present invention relates to an operation method of a simulation apparatus that performs simulation of a heterogeneous material in which a plurality of material phases having different material properties are dispersedly arranged.

  Bulk properties of filler-containing rubber and reinforcing members used for tire tread rubber members, bead filler rubber members and the like affect tire performance. For this reason, simulation calculation of tire performance and simulation calculation of rubber material characteristics are important factors in tire development. Bulk property is a macro property in the state of a mass (bulk) of heterogeneous material in which material phases with different material properties are dispersed, and equivalent material property when the heterogeneous material is regarded as a homogeneous material. is there.

  To evaluate the bulk properties of a heterogeneous material in which a plurality of material phases with different material properties such as the above-mentioned filler-blended rubber are dispersedly arranged by simulation, for example, the representative region (micro region) of the heterogeneous material is a rectangular parallelepiped. Cut into shapes to create a finite element model. And, this finite element model creates a simulation model by giving periodic boundary conditions to the opposing faces of the finite element model so that it forms an infinitely continuous bulk in the vertical, horizontal, and depth directions. Perform the operation.

  In the following Patent Document 1, a structure analysis method and a structure design method using a homogenization method are disclosed. In the structural analysis method, a homogenization method is applied to the composite material when analyzing a composite material in which different kinds of materials are periodically arranged in a uniform inner material and a structure in which other materials are connected to the composite material. Apply and perform structural analysis. At that time, a tensile test is performed by a finite element analysis on a microstructure model which is a model of a micro region of the composite material, and a macro characteristic of the composite material is obtained from a result at that time to perform a structural analysis.

  On the other hand, Non-Patent Document 2 below discloses a simulation method related to uncoupled bidirectional multi-scale simulation. In this method, a so-called micro-macro uncoupled analysis method is used in which material parameters in the macro structure model are obtained from the simulation results of the tensile test obtained with the micro structure model, and simulation is performed using these material parameters in the macro structure model. Has been done.

  Patent Document 3 below proposes a method for simulating a heterogeneous material in order to efficiently perform the simulation calculation of the macro structure and the micro structure. In Patent Document 3, a macro-scale model that reproduces a structure containing a heterogeneous material by determining a superelastic potential and a material constant by deforming a microscale model that reproduces the microstructure of the heterogeneous material and performing a simulation calculation. Is used to perform a macro-simulation calculation based on the superelastic potential and the material constant. Then, the result of the distortion of the representative point of the arrangement part of the heterogeneous material is obtained from the macro simulation calculation result, the displacement of the boundary region in the microscale model is determined from this distortion, and this displacement is used as the boundary condition of the microscale model. It is described that a microscale simulation is performed.

JP 2003-347301 A "Micro-macro disjoint approximate solution of the two-variable boundary value problem in nonlinear homogenization theory", Ikumu Watanabe, Kenjiro Terada, Applied Mechanics, Vol.8, pp.275-285, (August 2005) JP 2006-15866 A

  In any of the above-mentioned documents, the material characteristics of the material phase are often greatly different, as in the configuration in which reinforcing fillers such as carbon black are dispersed in the rubber material in the simulation of the microstructure model. In this case, if the simulation result of the macro structure model is directly input to the micro structure model, the deformation of the model element in the material phase portion where the material constant value indicating the material property is low becomes very large, and a convergent solution is obtained. In some cases, the calculation time becomes long, and in some cases, a convergent solution cannot be obtained.

For example, in Patent Document 3, using the results of the strain of the representative points extracted by the macro-scale simulations, distortion of the representative point, strain _e xx in the following formula _{(1), e xy, e} xz, e yx , E _yy , e _yz , e _zx , e _zy , e _zz, and by substituting the length of one side of a rectangular parallelepiped voxel for Δx, Δy, Δz, a node on the boundary surface of one finite element The displacements Δu _x , Δu _y , and Δu _z of the other node with reference to the above are obtained. This displacement is given as a forced displacement to the nodes on the boundary of the microscale model, and the strain distribution and stress distribution in the representative region are calculated using the same material constants as in the microscale simulation.

For example, when a model (tire model) that reproduces the shape of a tire is created as a macro structure model, and a simulation of rolling the tire model is performed, the deformation and displacement of the macro structure model are relatively large. In such a case, in the macro-scale simulation using the heterogeneous material simulation method described in Patent Document 3, when the large deformation / displacement simulation is performed, the displacements Δu _x , Δu _y , Δu _z of the other node are compared. It will be big. In this case, if the simulation results of the macro structural model are directly input to the micro structural model as displacement boundary conditions, the transition state from the initial state to the final state of the micro model is the actual transition of the heterogeneous material represented by the micro model. There was a case where it was far from the state. In such a case, it takes a long time to obtain a convergent solution, and there may be a problem that the convergent solution cannot be obtained in some cases. For this reason, it is not practically preferable for early design and development of heterogeneous materials.

Therefore, the present invention uses a simulation model of a heterogeneous material in which a plurality of material phases having different material properties are dispersedly arranged to perform large deformation when performing a non-coupled bidirectional multiscale simulation of the heterogeneous material on a computer. Another object of the present invention is to provide a method of operating a simulation apparatus that performs simulation of a heterogeneous material that can be efficiently and quickly simulated even when analyzing large displacements.

To achieve the above object, the present invention, CPU and memory and, and a mouse keyboard, heterogeneous material using a simulation model of the heterogeneous material in which a plurality of material phase having different material characteristics are positioned A method of operating a simulation apparatus for performing the simulation , wherein the CPU creates a simulation model of a structure obtained by modeling a constituent member made of the heterogeneous material by an equivalent model of the homogeneous material; and A physical quantity representing deformation of the structure for each predetermined elapsed stage preset in the memory by input from the mouse / keyboard is performed by applying deformation or external force to the body simulation model to simulate the structure. A macro simulation step to output each and the predetermined elapsed stage obtained Boundary to the heterogeneous material discretization model at each of the predetermined progress stages so that each physical quantity representing the deformation is an average deformation in the simulation model of the heterogeneous material at each of the predetermined progress stages. giving condition, the providing a method of operating characteristics and to Resid simulation apparatus to perform a micro-simulation step of obtaining said predetermined elapsed stage deformation of each respective heterogeneous material.

Further, the CPU determines whether or not a simulation result has converged each time the deformation of each of the predetermined elapsed stages of the heterogeneous material is determined in the micro simulation step, and the determination step includes the determination step. When it is determined that the simulation result has not converged, it is preferable to further subdivide the predetermined progress stage and execute a repetition step of executing the macro simulation step and the micro simulation step.

  In the macro simulation step, it is preferable to obtain at least one of a deformation gradient and a displacement gradient as a physical quantity representing deformation.

  In the micro simulation step, the physical quantity representing the deformation of the structure output in the macro simulation step is decomposed into a rotation component and a stretch component, and the rotation component is an average of the heterogeneous material. It is preferable to give boundary conditions to the simulation model of the heterogeneous material so that the rotation component becomes an average stretch of the heterogeneous material.

  In addition, when a boundary condition is given to the simulation model of the heterogeneous material so that the rotational component is an average rotation of the heterogeneous material, a coordinate axis is defined for the rotational component, and represents a rotation around the determined coordinate axis. It is preferable to calculate a rotation tensor and apply the rotation tensor to the heterogeneous material simulation model.

  Further, in the micro simulation step, the physical quantity representing deformation of the structure is decomposed into a component representing rotation and a stretch component, and the stretch component becomes an average stretch of the heterogeneous material. It is preferable to give only a boundary condition for the stretch component to the simulation model of the material.

  Moreover, it is preferable that the said stretch component is a physical quantity defined by the left stretch tensor or the right stretch tensor. In addition, it is preferable to add a periodic boundary condition to the model in the deformation simulation of the heterogeneous material. Moreover, it is preferable that the model area | region of the said heterogeneous material discretization model is comprised from 1 or more types of material physical properties.

Hereinafter, the operation method of the simulation apparatus of the present invention will be described in detail based on the preferred embodiments shown in the accompanying drawings.

  FIG. 1 is a block diagram functionally showing the configuration of a simulation apparatus 10 that implements the heterogeneous material simulation method of the present invention. The simulation apparatus 10 is a computer including a CPU 12, a memory 14, a ROM 16, and an I / O board 18. The simulation apparatus 10 reads application software stored in the memory 14 or the ROM 16, and creates a model creation unit 20, a periodic boundary condition setting unit 22, The CPU 12 executes respective subroutines of the finite element analysis unit 24, the condition change / setting unit 25, the determination unit 26, and the material parameter identification unit 28. The CPU 12 functions as a control unit that controls the entire simulation method performed by the simulation apparatus 10.

  The simulation apparatus 10 creates a micro structure model (hereinafter referred to as a micro model) and a macro structure model (hereinafter referred to as a macro model), which are finite element models described later, and executes simulation analysis using the finite element method. The simulation apparatus 10 is connected to a display 30, a printer 32, and a mouse / keyboard 34. Information necessary for the finite element model, conditions necessary for the simulation analysis, etc. are input to the simulation apparatus 10 by the mouse / keyboard 34 while the operator views the input screen displayed on the display 30, and the simulation analysis result Is displayed on the display 30 and the printer 32 by numerical values, graphs, or figures. The I / O board 18 is connected to a data supply system such as CAD / CAM (not shown).

  When the representative region of the inhomogeneous material is input from a data supply system (not shown), the model creating unit 20 generates a finite element model that reproduces the representative region of the inhomogeneous material by using the finite element, and converts the inhomogeneous material into the constituent member. This is a part for creating a finite element model of a structure provided as a finite element. A finite element model of a representative region of a heterogeneous material is configured by continuously arranging a plurality of finite elements of at least one of tetrahedron, pentahedron, and hexahedron whose shape is characterized by a plurality of discrete points. It is a micro model. A heterogeneous material is a material in which a plurality of material phases and / or voids having different material characteristics are dispersed and arranged, for example, a polymer as a base material, a filler such as carbon black or silica, a fiber such as a steel wire or an organic fiber material. Examples thereof include a reinforcing material and a rubber material in which bubbles are dispersed.

  The representative region (micro region) of the inhomogeneous material is, for example, a hexahedron cuboid shape, and the representative region is divided into meshes in three directions orthogonal to each other, thereby creating a voxel-like continuously arranged finite element model. . The material constants of each material phase in the micro model are set so as to have values of material properties specific to each material phase. At this time, a periodic boundary condition is given to each node on each boundary surface so that the micro model reproduces a state in which the micro regions are continuously arranged in three directions. In addition, a model of a structure including an inhomogeneous material as a constituent material is created as a macro model. In this macro model, the part of the heterogeneous material is modeled as a homogeneous material. That is, the portion of the heterogeneous material is expressed as a homogeneous material equivalent model. In the present embodiment, a tire model is created in which a tire is a structural body and a rubber material such as tread rubber or bead rubber is a heterogeneous material.

  The periodic boundary condition setting unit 22 is a part that determines a periodic boundary condition when a simulation is performed using the created micro model. For example, as a periodic boundary condition, for each of the three directions of the micro model, the nodes on one boundary surface and the same relative on the other boundary surface are reproduced so as to reproduce a state where the micro model is continuously arranged infinitely. Define a relational expression that correlates the behavior between the nodes at the position.

  The finite element analysis unit 24 is a part that performs simulation using a micro model and a macro model using a predetermined periodic boundary condition. The simulation may be linear analysis or non-linear analysis. For the finite element analysis unit 24, a known general-purpose finite element analysis solver, for example, a general-purpose non-finite element analysis program manufactured by ABAQUS, Inc. is used.

  The finite element analysis unit 24 performs a simulation (characteristic simulation) using a micro model for obtaining the mechanical characteristics of the heterogeneous material, for example, a uniaxial tension of a rubber material, a tension test such as a compression test, and a simulation of a compression test. In addition, a deformation behavior simulation (macro simulation) is performed using a tire macro model having a tire made of a rubber material as a structure. Further, the finite element analysis unit 24 simulates the mechanical behavior using a micro model (micro simulation) in order to reproduce the behavior of the micro region of the heterogeneous material at the time of the mechanical behavior of the structure. ). For example, the simulation result using the macro model is given to the micro model, and the deformation and displacement of the micro model are calculated.

  For example, when a tire is used as a structure, the macro simulation includes an internal pressure filling simulation that reproduces the mechanical behavior of the internal pressure filling of the tire and a mechanical behavior when a load is applied by pressing the tire filled with the internal pressure against the ground. Reproduced grounding simulation, free rolling simulation when rolling the tire without loading the tire, and ground rolling simulation when rolling the tire with the tire loaded Done.

  The finite element analysis unit 24 uses the macro structure model to perform a simulation on the behavior of each predetermined progress stage preset in the condition change / setting unit 25 described later, and the deformation behavior of the macro model for each progress stage. Information (physical quantity representing deformation) is output sequentially (for each elapsed stage). Then, the deformation behavior of the macro structure model for each elapsed stage is sequentially input to the micro model, and micro simulation is performed. In this embodiment, a tire model is used as a macro structure model, and free rolling simulation of this tire model is performed as a macro simulation. Then, using the result of the macro simulation, a micro simulation for reproducing the behavior of the micro region of the heterogeneous material when the tire rolls freely is performed. Details of each simulation (characteristic simulation, macro simulation, micro simulation) performed by the finite element analysis unit 24 will be described later.

  The condition change / setting unit 25 sets the details of the simulation conditions of the macro simulation and the micro simulation, in particular, the progress stage. For example, a macro simulation condition (elapsed stage condition) input from an input unit (not shown) is received, and the received macro simulation condition is stored in the memory 14 or the ROM 16. The finite element analysis unit 24 performs the macro simulation based on the conditions stored in the memory 14 and the ROM 16 in this way, and sequentially inputs the deformation behavior (physical quantity representing the deformation) of the input macro model for each elapsed stage ( Input to the micro model (for example, given as a displacement boundary condition or a load boundary condition) and perform a micro simulation. In addition, the condition change / setting unit 25 receives information about the determination result in the determination unit 26 described later, and the progress stage in the simulation is further detailed, for example, when the simulation is stopped halfway without converging the micro simulation result. To divide. For example, the time step is changed to be shorter and reset so that the time step width in the simulation for outputting the result of the macro model becomes shorter. In the condition change / setting unit 25, for example, after accepting an elapsed stage condition input from an input unit (not shown), the accepted unit time step condition is changed according to the micro model, and the elapsed time after the change The stage conditions may be stored in the memory 14 or the ROM 16.

  The determination unit 26 monitors the state of the micro simulation in the finite element analysis unit 24, and determines whether the micro simulation has converged (whether a converged solution can be obtained) for each micro simulation performed in each progress stage unit. . As will be described in detail later, the macro simulation is a simulation that reproduces relatively large deformations and displacements, and the initial state and final state of the micro model in the micro simulation in each progress stage unit are greatly different. Even if the macro simulation result is given to the micro model, the convergence solution may not be obtained in the micro simulation. The determination unit 26 determines whether or not the micro simulation converges. The CPU 12 (the control unit) changes / reset the conditions in the progress stage by the condition change / setting unit 25 as necessary based on the information of the determination result.

  The material parameter identification unit 28 is a part that identifies a material parameter using the result of the characteristic simulation performed to obtain the mechanical characteristics of the heterogeneous material. For example, the parameters of the stress-strain curve results of the characteristic simulation using the micro model are calculated by curve fitting with a superelastic potential function. Such parameters are used to provide the material properties of the model portion of the heterogeneous material in the macro model.

In the simulation apparatus 10 having such a configuration, a non-coupled bidirectional multi-scale simulation which is a simulation method of the present invention as described below is performed.
FIG. 2 is a flowchart illustrating an example of the simulation method of the present invention.
First, the model creation unit 20 creates a micro model (step S100). Here, a representative region (micro region) in a heterogeneous material is defined, and this micro region is a finite element model that reproduces one micro region using a plurality of voxels characterized by a plurality of nodes. A micro model is created. FIG. 3A shows an example of a micro model in which a micro region is defined using a plurality of voxels. Here, it is a model of a heterogeneous material that is divided into three regions according to shading and in which three material phases having different material properties are dispersedly arranged. Of course, a material constant is set for each material phase. Note that one of the material phases may be a void formed of a gas phase.

  Further, a macro model, which is a finite element model of a structure including a heterogeneous material as a constituent material, is created by the model creating unit 20 (step S102). FIG. 3B shows an example of a three-dimensional macro model having a tire as a structure. In the macro model, the constituent member of the heterogeneous material is modeled as a homogeneous material, and the material constant is in an undetermined state. On the other hand, material constants are set for members other than the constituent members of the heterogeneous material. These micro models and macro models are three-dimensional models, but may be two-dimensional models.

  Next, characteristic simulation is performed in the finite element analysis unit 24 (step S106). The property simulation is a simulation of a heterogeneous material that reproduces a tensile or compression test against a micro model in which material constants are set so as to have material properties unique to the material phase, and the micro region is infinitely continuous in three directions. Periodic boundary conditions are given to the boundary surface of the micro model so as to indicate the bulk characteristics (step S104). In this characteristic simulation, in order to obtain a stress-strain curve as a mechanical characteristic, for example, a reproduction of a uniaxial tensile test is performed. Thereby, a stress-strain curve of micro strain is obtained. In the characteristic simulation at this time, the material constant in the micro model is set so as to have the material characteristic peculiar to the material phase, and the micro model is simulated.

  Hereinafter, processing in the present embodiment will be described using a simple micro model. FIG. 4 shows an example of a simple micro model. The micro model shown in FIG. 4 is composed of two types of materials having different mechanical characteristics, and the darker and lighter material is used as a base material, and the darker material is dispersed in the base material. The lighter material is a rubber material, and the darker material is a reinforcing material. The reinforcing material is used as a reinforcing filler of rubber material, and for example, the rigidity differs by about 100 times. For example, for such a micro model as shown in FIG. 4, a characteristic simulation is performed based on a periodic boundary condition. FIG. 5A shows a state where the micro model is stretched in the pulling direction. FIG. 5B shows a result of an example of the stress-strain curve at this time.

  Next, using the result of the stress-strain curve, the material parameter identification unit 26 identifies the material parameter as the bulk characteristic of the heterogeneous material (step S108). For example, the material parameter is extracted by curve fitting the curve of FIG. 5B using a known superelastic potential function. Such a material parameter is used as a material constant of a finite element using a heterogeneous material in a macro model described later. Such material parameters when the heterogeneous material is a homogeneous material are given as material constants to the created macro model, and the macro model is a model that can be simulated. Through the steps so far, a macro model and a micro model are created.

  Simulation is performed using such a macro model and a micro model. First, the condition changing / setting unit 25 sets conditions for macro simulation (step S110). Here, the time series deformation or displacement conditions of the structure reproduced by the macro model are set. In the present embodiment, as shown in FIG. 6, conditions are set for the tire model 60, which is a macro model, to freely roll 90 degrees around the tire rotation axis during the required time T. And the predetermined part (target tire model part) on the tire model which calculates | requires a deformation | transformation is implemented by implementing micro simulation. In the present embodiment, for example, a deformation when a tire model is freely rolled by 90 degrees is obtained for a micro model (marked as a target micro model) indicated by a circle in the figure. In this step S110, detailed conditions in the macro simulation such as details of boundary conditions given to the macro model in the macro simulation are also set.

Then, in step S112, it is set for simulation history stage _t 1 ~t _n for outputting a result of the macro model. In the present embodiment, five stages t _{1 to} t ₅ are set for the path through which the target micro model passes until it freely rolls by 90 degrees. Specifically, a stage where the tire model is rotated by 18 degrees is t ₁ , a stage where the tire model is rotated by 36 degrees is t ₂ , a stage where the tire model is rotated by 54 degrees is t ₃ , and a stage where the tire model is rotated by 72 degrees is t ₄ and 90 degrees. The degree of rotation is set to 90 degrees, and macro simulation results (physical quantities representing deformation of the target tire model portion) representing the state after each of t ₁ to t ₅ are set to be output.

Next, the finite element analysis unit 24 performs a macro simulation (step S114). For example, a simulation of freely rolling the tire model 60 shown in FIG. 6 by 90 degrees is performed, and macro simulation results (physical quantities representing deformation of the target tire model portion) are obtained for each of the elapsed stages t _{1 to} t _5. Output. In the macro simulation, as in an analysis using a normal finite element method, a set boundary condition (tire rolling condition) is given to the tire model 60, and the tire model 60 changes with time. Calculate the state (deformation / displacement). That is, in the numerical calculation in the macro simulation, the state of deformation / displacement of the tire model 60 is calculated starting from time 0 and dividing the time for each unit time increment Δt. In the present embodiment, in step S110, among the numerical calculation results of the macro simulation calculated for each unit time increment Δt in this way, calculation is performed at each of the five stages corresponding to the elapsed stages t _{1 to} t _5. The result (physical quantity representing deformation of the target tire model portion) is output.

The physical quantity representing the deformation output in the macro simulation (physical quantity representing the deformation of the target tire model portion) is preferably, for example, a physical quantity represented by a deformation gradient tensor F _ij . As is well known, the deformation gradient tensor is a physical quantity that defines how a line segment in an arbitrary direction starting from a certain point changes before and after deformation, and is preferable as a physical quantity representing deformation. Further, the physical quantity representing the deformation may be a displacement gradient tensor H _ij (= F _ij −I [I is a unit tensor]), and is not particularly limited. The displacement gradient tensor is roughly a physical quantity representing the degree of strain before and after deformation.

In the present embodiment, for example, corresponding to each of the elapsed time _t 1 ~t _5, the deformation gradient tensor _{F ij (1) ~F ij (} 5) is obtained. In the present embodiment, the deformation gradient tensors F _{ij (1) to} F _{ij (5)} are respectively converted, and the following displacement gradient tensors H _{ij (1) to} H _{ij (5)} are output.

Next, in order to analyze the deformation of the micro region of the heterogeneous material, the finite element analysis unit 24 performs micro simulation using the result of the macro simulation (step S116). In the micro simulation, first, the displacement gradient tensor H _{ij (1)} corresponding to the elapsed stage t ₁ is given to the micro model, and the micro simulation is performed. At this time, the boundary of the micro model is set so that the magnitude of deformation represented by the displacement gradient tensor (the magnitude of the pseudo-strain component) becomes the average magnitude of deformation in the micro model (the magnitude of the pseudo-strain component). A simulation is performed to determine the deformation of the micro model given the conditions.

For example, in the present embodiment, when the deformation state at the elapsed stage t _n is obtained, the length of one side of the micro model is substituted into Δx, Δy, Δz in the following formula (2), so that Displacement Δu _x , Δu _y , Δu _z of the other node with respect to the node on the boundary surface is obtained. Then, this displacement is given as a forced displacement to a node on the boundary of the microscale model (given as a displacement boundary condition), and the deformation state of the micromodel is calculated (microsimulation is performed). The micro-simulation at each stage takes the state of the micro model after giving the above-mentioned forced displacement as the final state, and the micro simulation result (the state of the micro model) at the previous stage as the initial state. It is performed by calculating the deformation state of the micro model up to.

Specifically, when calculating the deformation state of the micro model, as a periodic boundary condition, one of each of the three directions of the micro model is reproduced so as to reproduce a state where the micro model is continuously arranged infinitely. A relational expression relating the behavior between the node A on the boundary surface and the node B at the same relative position on the boundary surface facing this one boundary surface is defined. For example, assuming that the position vector of the node A is Y _a , the position vector of the node B is Y _b , the displacement vector of the node A is W _a , and the displacement vector of the node B is W _b , the simulation for obtaining the deformation state at the elapsed stage t _n . Then, a microsimulation is performed by giving a relational expression of the following formula (3) as a periodic boundary condition.
W _b −W _a = H _{ij (n)} · (Y _b −Y _a ) (3)

  The details of the micro simulation in the present invention are not particularly limited. For example, a physical quantity representing deformation obtained by macro simulation may be decomposed into a component representing a rigid body rotation (rotation component) and a component other than the rigid body rotation (stretch component). For each decomposed component, for example, only the stress and strain in the micro model may be analyzed by applying a micro simulation with only the stretch component applied to the micro model. Further, the micro-simulation may be performed by giving the stretch component and the rotation component to the micro model in order. Note that the order in which the stretch component and the rotation component are given to the micro model may be either the order in which the rotation component is given after the stretch component or the order in which the stretch component is given after the rotation component. Thus, by decomposing each component and giving it to the micro model and performing the micro simulation, it is possible to individually grasp the contribution of each component to the deformation of the micro model.

Specifically, the deformation gradient tensor F _ij obtained by the macro simulation may be decomposed into a stretch tensor U _ij and a rotation tensor R _ij representing rigid body rotation. It is well known that the relationship between these tensors is expressed as F _ij = U _ij R _ij , and if F _ij is known, U _ij and R _ij can be easily obtained respectively. When a micro simulation is performed with each component applied to the micro model, for example, the boundary condition may be given to the micro model so that the component representing the rotation is an average rotation of the micro model, and the stretch component is the micro model. A boundary condition may be given to the micro model so as to achieve an average stretch. For example, the micro simulation may be performed in the same manner as the example in which the displacement gradient tensor is provided. When the rotation component is used as a boundary condition, a coordinate axis is determined for the decomposed rotation component, a rotation tensor representing the rotation around the defined coordinate axis (specific coordinate axis) is obtained, and the rotation tensor around the specific coordinate axis is converted into a micro model. You may make it act. For example, the rotation angle around the xyz axis (the coordinate axis shown in FIGS. 6 to 8) of the Cartesian coordinate system representing the macro model and the micro model is calculated from the rotation component. The rotation tensor in this case is expressed by the following formula (4), and α, β, and γ are angles around the x, y, and z axes, respectively.

  When the micro simulation (step S116) is started, the determination unit 26 determines whether the numerical calculation solution for determining the deformation of the micro model has not converged without converging (step S118). Usually, numerical calculation (non-linear analysis, etc.) in micro simulation is continued until the solution converges by repeated calculation. However, in the case of performing a large deformation simulation in the macro model simulation, the numerical calculation in the micro simulation may not be converged even after a long time and the calculation may even stop. This is because, as described above, based on the calculation result in the macro simulation, when the simulation is performed by giving a forced displacement to the node on the boundary of the micro model, the path in the deformation of each node of the micro model is actually The reason is that it is very different from the route.

FIGS. 7A and 7B are diagrams illustrating an example of a result of a simulation performed using a conventional method for simulating a heterogeneous material, and a diagram illustrating an example where a solution of a micro simulation does not converge. In the macro model simulation, the result obtained by performing the micro model simulation by giving the micro model the result in a state in which the tire model 60 is rotated by 90 degrees (that is, the elapsed stage t ₅ ) is described. FIG. 7A is a diagram showing an initial state of the micro model before the micro model simulation is performed, and FIG. 7B is a diagram showing the displacement gradient tensor H _{ij (} result of the elapsed stage t ₅ ). It is a figure which shows an example of the deformation | transformation analysis result of a micro model when ₅₎ is directly given to the micro model in an initial state, and a micro simulation is performed. In this case, if a forced displacement is applied to the node N shown in FIG. 7A by a displacement gradient tensor H _{ij (5)} , which is the result of a simulation of rotating the macro model by 90 degrees, the node N is shown in FIG. It will be displaced to position α. The path through which the node N passes when the macro model actually rolls is the path along the solid line arrow in FIG. However, in the micro simulation, for example, nonlinear analysis is performed so as to linearly interpolate the position of the initial state and the position of the displacement state, and the node N is on a path passing through the broken line arrow in FIG. A numerical calculation is performed on the condition that the movement is performed along the periodic boundary condition. When such a calculation is performed, the deformation in the matrix rubber element is extremely increased. As a result, the convergence is deteriorated, and the calculation is stopped in the state shown in FIG. 7B.

  In this way, in the uncoupled analysis using the macro model and the micro model, the result of the macro simulation is used as a condition that represents the final state of the micro model. In the micro simulation, the transition state from the initial state to the final state of the micro model may be far from the actual transition state of the heterogeneous material represented by the micro model. In such a case, as in the above example, there was even a problem that the calculation of the micro simulation eventually stopped.

In the present invention, in order to avoid such a problem, for example, as in this embodiment, a non-coupled analysis simulation is performed in which the result of a large deformation simulation that rotates the tire model by 90 degrees is input to the micro model. If you, the macro simulation over the required time T of the entire required for rolling, leave divided for each predetermined elapsed step t _n, the result of the macro simulation of each course stage (physical quantity representing the deformation of the structure) Are output respectively. Then, the result of the macro simulation for each elapsed stage (in this embodiment, the magnitude of the pseudo-strain component represented by the displacement gradient tensor H _ij ) is sequentially set so as to be the average deformation and displacement magnitude in the micro model. A simulation is performed to determine the deformation of the micro model by giving boundary conditions to the micro model. In this way, giving the result of the macro simulation to the micro model at each progress stage simply means that the condition of the transition state when the micro model is deformed, that is, the condition of the deformation path of each node of the micro model is simply linear. Rather, it means that the conditions are more approximate to the actual route. Thereby, even in the micro simulation, the actual smooth deformation and rotation experienced by the micro model can be reproduced, and the convergence of the numerical calculation solution can be improved. In addition, for problems with deformation path dependency, the deformation result of the micro model can be obtained more correctly.

FIGS. 8A to 8E are examples of the result of the micro simulation in the present embodiment, and FIG. 8A shows the displacement gradient tensor H _{ij (1)} corresponding to the elapsed stage t ₁ as a micro model. This is the result of micro simulation. In step S118, when the determination unit 26 confirms that the calculation of the nonlinear analysis calculation does not converge and the calculation stops as in the example illustrated in FIG. 7B (the determination in step S118 is performed). In the case of No), the elapsed stages t _{1 to} t _n are set again. For example, finer than 5 steps, 90 degree rotation is divided into 10 steps, for example, and physical quantities (deformation gradient tensor, displacement gradient tensor, etc.) representing deformation in each state where the macro model is rotated by 9 degrees are output. Then, step S114 to step S118 are repeated.

As shown in FIG. 8, in the present embodiment, the deformation in the matrix rubber element is not increased and the convergence is not deteriorated, and the state of the micro model at the elapsed stage t ₁ (ie, the state rotated by 18 degrees). Is obtained as a simulation result. As shown in FIG. 8, in the case of this embodiment, when the displacement gradient tensor H _{ij (1)} corresponding to the elapsed stage t ₁ is given to the micro model and the micro simulation is performed, the solution of the micro model is not converged without convergence. Since the deformation could be obtained, the determination in step S118 is Yes.

Such micro simulation (step S116) and the determination (step S118) for all the elapsed phase _t 1 ~t _n set in step S112, is repeated (step S120, and step S122). 8 (b) to 8 (e) show that the magnitude of the pseudo-strain component represented by each of the displacement gradient tensors H _{ij (1) to} H _{ij (5)} corresponding to each of the elapsed stages t _{2 to} t ₅ is microscopic. This is a result of performing a simulation for obtaining deformation of the micro model by sequentially giving boundary conditions to the micro model so that the average pseudo-strain component in the model has a magnitude.

  Finally, as a result of the micro simulation, for example, a diagram showing the deformation state of the micro model (for example, a diagram as shown in FIGS. 8A to 8B), numerical data representing such deformation, etc. The data is output to the display 30 and the printer 32 (step S124). According to the method of the present invention, the conventional method cannot obtain a convergent solution as shown in FIGS. 7A and 7B. As shown in e), the final deformation state of the micro model can be obtained accurately.

In this embodiment, prior to the execution of the macro simulation, the elapsed stages t _{1 to} t _n are set in advance. For example, after the macro simulation is performed, the progress is made according to the result of the macro simulation. Stages may be set. For example, once the macro simulation is performed using the macro model, the rotation component of the target area to be micro-simulated is sequentially obtained during the macro simulation, and the elapsed stage is determined at the timing when the rotation component enters a predetermined range. It may be set.

  The heterogeneous material simulation method of the present invention has been described in detail above, but the present invention is not limited to the above-described embodiment, and various improvements and modifications may be made without departing from the spirit of the present invention. Of course.

It is a block diagram of the structure of the simulation apparatus which implements the simulation method of the heterogeneous material of this invention. It is a flowchart figure of an example of the simulation method of the heterogeneous material of this invention. (A) is a figure which shows an example of the micro model created with the simulation method of the heterogeneous material of this invention, (b) shows an example of the macro model of a tire when a tire is used as a structure. FIG. It is a figure which shows the other example of the micro model created with the simulation method of the heterogeneous material of this invention. (A), (b) is a figure which shows an example of the result of having performed simulation using the simulation method of the heterogeneous material of this invention. It is a figure explaining the conditions of macro simulation in the simulation method of the heterogeneous material of this invention. (A) And (b) is an example of the result of having performed simulation using the simulation method of the conventional heterogeneous material, and is a figure explaining the example in which the solution of micro simulation does not converge. (A)-(e) is an example of the result of the micro simulation in the simulation method of the heterogeneous material of this invention.

Explanation of symbols

10 Simulation device 12 CPU
14 Memory 16 ROM
18 I / O board 20 Model creation unit 22 Periodic boundary condition setting unit 24 Finite element analysis unit 25 Condition change / setting unit 26 Judgment unit 28 Material parameter identification unit 30 Display 32 Printer 34 Mouse / Keyboard 60 Tire model

Claims (9)

CPU,
Memory,
Mouse and keyboard
The provided, a method of operating a simulation apparatus for simulating a heterogeneous material using a simulation model of the heterogeneous material in which a plurality of material phase having different material characteristics are positioned,
The CPU is
Creating a simulation model of a structure in which the structural member made of the heterogeneous material is modeled by an equivalent model of the homogeneous material;
A physical quantity representing the deformation of the structure for each predetermined progress stage preset in the memory by performing deformation or external force on the simulation model of the structure to simulate the structure and input from the mouse / keyboard Each of the macro simulation steps to output,
The inhomogeneity for each of the predetermined progress stages is such that each physical quantity representing the deformation for each of the predetermined progress stages is an average deformation in the simulation model of the heterogeneous material for each of the predetermined progress stages. the material discretized model given boundary conditions, the predetermined elapsed stage method of operating characteristics and to Resid simulation apparatus to perform a micro-simulation step, the obtaining the deformation of each respective heterogeneous materials. Furthermore, the CPU
A determination step of determining whether or not the simulation result has converged each time the deformation of each of the predetermined progress stages of the heterogeneous material is determined in the micro simulation step;
When the simulation result is determined not converged in the determination step, and further subdividing the predetermined elapsed stage, and repeatedly performing a said micro simulation step and the macro simulation step, to the execution operating method of the simulation apparatus according to claim 1, wherein. And in the macro simulation step, as a physical quantity representing the deformation work method for simulation apparatus according to claim 1 or 2, characterized in that for obtaining at least one of the deformation gradient or displacement gradient. In the micro simulation step, the physical quantity representing the deformation of the structure output in the macro simulation step is decomposed into a rotation component and a stretch component, and the rotation component becomes an average rotation of the heterogeneous material. Further, to the stretch component becomes average stretch of the heterogeneous material, simula- according to any one of claims 1 to 3, characterized in providing a boundary condition in the simulation model of the heterogeneous material The operation method of the installation device . When a boundary condition is given to the simulation model of the heterogeneous material so that the rotational component is an average rotation of the heterogeneous material, a coordinate axis is defined for the rotational component, and a rotation tensor that represents a rotation around the determined coordinate axis calculates operates method of simulation apparatus according to claim 4, wherein the rotation tensor, characterized in that the action on the heterogeneous material simulation model. In the micro-simulation step, a physical quantity representing deformation of the structure is decomposed into a component representing rotation and a stretch component, and the stretch component is an average stretch of the heterogeneous material so that the stretch component becomes an average stretch of the heterogeneous material. the simulation model, the operation method of the simulation apparatus according to any one of claims 1 to 5, characterized in that only provide boundary conditions for the stretch components. The stretch components act method of simulation apparatus according to claim 6, characterized in that the physical quantity defined by the left stretch tensor or right stretch tensor. Wherein when the deformation simulation of heterogeneous materials, operating method of the simulation apparatus according to claim 1, characterized in that the addition of periodic boundary conditions in the model. Operating method of the simulation apparatus according to claim 1, characterized in that the model area of the heterogeneous material discrete model is composed of one or more material properties.

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