JP2008152423A - Deformation behavior simulation method using particle model and program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To highly precisely search deformation behavior of a first structural body in a relatively short time when the first structural body and the second structural body are brought into contact with each other, and the first structural body is deformed, and the contact face between the first structural body and the second structural body is changed. <P>SOLUTION: A first model is generated by reproducing the first structural body as an aggregate of a plurality of particles, and a second model is generated by reproducing the second structural body, and the second model is moved to the first model. When calculating the deformation behavior of the first model, in contact with the second model deformed in a long time, the physical quantity of the second model is not affected by the first model, and the second model is moved to the first model in every predetermined time step, and the speed information of particles whose distances to the second model becomes a predetermined value or less among the plurality of particles configuring the first model is same as the speed information of the second model within a predetermined value, and the deformation of the first model in each time step is calculated. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  In the present invention, the first structure and the second structure come into contact with each other and the first structure is deformed over time, and the contact surface between the first structure and the second structure changes over time. In this method, the deformation behavior of the first structure is obtained, and in particular, the superelastic body such as rubber and the rigid body come into contact with each other to deform the superelastic body, and the contact area between the superelastic body and the rigid body is time It is related with the method of reproducing the deformation | transformation behavior of the 1st structure in what is called a large deformation problem which changes 5% or more over time.

  Unlike the finite element method, the SPH (smoothed particle hydrodynamics) method is a mesh-independent analysis method that represents a substance only by a set of points. Compared with the FEM method that has been widely used, the SPH method is a meshless method, so even a complicated three-dimensional structure in which element creation is difficult can be easily modeled.・ There is no need to select the element type according to the analysis.・ No need for experience and skill in element division with accuracy in mind.・ We can expect a flexible response to large distortion and large deformation problems where analysis is impossible due to element collapse. -Common particle models can be used for structural analysis, thermal analysis, collision analysis, fluid analysis, electromagnetic field analysis, and so on. There are advantages such as. For this reason, application of the SPH method is expected for elasto-plastic analysis, superelastic analysis, and the like in which FEM is mainstream.

  For example, the following Non-Patent Document 1 proposes a solid large deformation elastoplastic analysis method using an SPH analysis method. In contrast to such a solid large deformation elasto-plastic analysis method, the inventor of the present application has proposed an analysis method for a superelastic large deformation problem of a rubber material or the like using the SPH method in Non-Patent Document 2 below. In Non-Patent Document 2, a rubber plate model that is also expressed as a set of a plurality of particles is pressed against a rubber structure model that is expressed as a set of a plurality of particles, and the rubber structure model is quasi-statically deformed. At this time, the deformation behavior of this rubber structure model (reproducing rubber structure) is calculated.

Taketake, Joe Sakai, Akihiko Yamashita “Examination of elasto-plastic analysis method by SPH method (1st report: Two-dimensional small deformation problem)”, Transactions of the Japan Society of Mechanical Engineers (A) 68, 669, p772-778, 2002 Junichi Kawashima, Joe Sakai "Superelastic Analysis of Rubber by Particle Method" Proceedings of the Computational Engineering Lecture Vol.11 No.1 P53- June 2006

  In the conventional methods described in Non-Patent Document 1, Non-Patent Document 2, etc., two structures such as collision of two structures (including a continuum such as fluid) represented by point information such as SPH method In the case of analyzing the deformation of the elastic body based on the contact of each structure, each structure is similarly represented by a particle aggregate model, and the interaction between the particles of each structure model is calculated.

  For example, also in the example described in Non-Patent Document 2, the interaction between a plurality of particles constituting each structure model is calculated, particularly in the contact surface portion between the rubber structure model and the rigid plate model. . However, in the quasi-static deformation of the rubber structure as described in Non-Patent Document 2, the interaction received by the rigid plate is insignificant, and it can be considered that the rigid plate is not deformed at the contact portion. As is well known (premise). However, conventionally, it is known that even when it is desired to calculate only the quasi-static deformation of the rubber structure model, a significant solution cannot be actually obtained along with the deformation behavior of the rubber component. It calculates even the interaction which the contact part of such a rigid plate model receives. For this reason, the conventional deformation behavior simulation method using an aggregate model of particles has a problem in that extra time and cost are required for the calculation.

  Therefore, in the present invention, the first structure and the second structure come into contact with each other and the first structure is deformed over time, and the contact surface between the first structure and the second structure takes time. An object of the present invention is to provide a deformation behavior simulation method using a particle model, which can obtain the deformation behavior of the first structure when changing in a relatively short time and with high accuracy.

  In order to achieve the above object, according to the present invention, the first structure and the second structure are brought into contact with each other, and the first structure is deformed over time. A first model that reproduces the first structure as an aggregate of a plurality of particles, and a method for obtaining a deformation behavior of the first structure when the contact surface changes with time, and A model generation step of generating a second model reproducing the second structure, and moving the second model with respect to the first model, so that the first model in contact with the second model is And calculating the deformation behavior of the first model and outputting the calculation result. In the step of calculating the deformation behavior, the physical quantity of the second model is No effect from the first model The second model is moved at predetermined time steps with respect to the first model, and the distance from the second model among the plurality of particles constituting the first model each time it is moved The deformation information of the first model at each time step is calculated by setting the velocity information of the particles having a value equal to or smaller than a predetermined value to be the same as the velocity information of the second model in the range equal to or smaller than the predetermined value. We propose a deformation behavior simulation method using a particle model.

  The second model is preferably a model that reproduces the second structure as an aggregate of a plurality of particles. Moreover, it is preferable that the second model is a model that reproduces only a region in the second structure that is likely to have a distance from an arbitrary particle of the first structure equal to or less than the predetermined value. .

  In the step of calculating the deformation behavior, the deformation behavior is calculated based on a particle movement regulation condition that defines the movement of the particle, which is set for each of the particles, and the particle movement regulation condition is It is preferable that the neighborhood region is determined corresponding to each of the particles, and that the condition is determined by approximating the distribution of the physical quantity of interest in this neighborhood region using the physical quantity of interest of the particles included in this neighborhood region. .

The particle movement regulation condition is that the physical quantity desired to be approximated in the model constituted by the particles is x, and the distribution of the physical quantity of interest in the neighboring region is f (x). It is an equation formulated by approximating with the distribution <f (x)> of the approximate physical quantity determined by the following formula (1) using the target physical quantity and the predetermined kernel function of the particles included in the vicinity region. preferable.
However, W (xx ', h) is a kernel function, and h is an influence radius.

  In the present invention, the first structure and the second structure are contacted to deform the first structure over time, and the contact surface between the first structure and the second structure is timed. A program for causing a computer to execute a method for obtaining the deformation behavior of the first structure when changing over time, the first model reproducing the first structure as an aggregate of a plurality of particles, and A model generation step of generating a second model reproducing the second structure, and moving the second model relative to the first model, so that the first model in contact with the second model is timed And calculating the deformation behavior of the first model and outputting the calculation result. In the step of calculating the deformation behavior, the physical quantity of the second model is The first model It is assumed that no action is taken, and the second model is moved with respect to the first model at predetermined time steps, and a plurality of particles constituting the first model at each movement, The velocity information of the particles whose distance from the second model is equal to or smaller than a predetermined value is the same as the velocity information of the second model in the range equal to or smaller than the predetermined value. A deformation behavior simulation program using a particle model characterized by calculating deformation of one model is also provided.

  According to the deformation behavior simulation method and program using the particle model of the present invention, the first structure and the second structure come into contact with each other, and the first structure is deformed over time. The deformation behavior of the first structure when the contact surface with the second structure changes over time can be obtained in a relatively short time and with high accuracy. Further, by reproducing the second model as an aggregate of a plurality of particles, it can be handled as the same model as the first model, and various numerical calculation processes in the simulation are smoothly executed by the same application program. be able to. In addition, the number of particles on the contact surface portion of the second model can be reduced, and it is not necessary to consider extra interactions, so that the time required for the calculation process can be extremely reduced.

  Hereinafter, a deformation behavior simulation method and program using a particle model of the present invention will be described in detail based on preferred embodiments shown in the accompanying drawings. FIG. 1 is a block diagram showing a schematic configuration of a deformation behavior simulation apparatus 10 (apparatus 10) that implements a deformation behavior simulation method using the particle model of the present invention. In the device 10, for example, a first structure that is a superelastic body such as rubber and a second structure that is a rigid body are in contact with each other, and the first structure is deformed over time, and the first structure and the above-described structure The deformation behavior of the first structure when the contact surface with the second structure changes over time is obtained. The device 10 is connected to a main body device 22 including a model creation unit 12, a movement / compression operation unit 14, a deformation operation unit 16, a memory 18, and a CPU (control unit) 20. An input operation system 24 including a mouse and a keyboard and an output unit 26 such as a printer or a display connected to the main body device 22 are provided. The device 10 is a computer in which each of the above parts functions when the CPU 20 executes a program stored in the memory 18.

  The model creation unit 12 reproduces the first model and the second structure in which the first structure is reproduced as an aggregate of a plurality of particles according to the model creation conditions input using the input operation system 24. Create a second model. FIG. 2 shows an example of a model created by the deformation behavior simulation method of the present invention. The first model 32 shown in FIG. 2 is a model in which a rubber body that is a superelastic body is reproduced by a set of a plurality of particles. Further, the second model 34 shown in FIG. 2 is a model in which a metal body that is much higher in hardness than a rubber body and can be handled as a rigid body is reproduced by a set of a plurality of particles. Hereinafter, an embodiment for reproducing the deformation behavior of the rubber body when the rubber body represented by the first model 32 is compressed at a sufficiently low speed by the metal body flat plate represented by the second model 34 will be described. Such deformation behavior in the present embodiment is a quasi-static deformation behavior, such that the contact area between the rubber body and the metal body increases or decreases by 5% or more compared to the initial state over time. It can be said that it is a problem.

  In this embodiment, at least the first structure is reproduced with a plurality of particles as described above, and the simulation using the SPH method is performed to express the model of the superelastic body being deformed. In the SPH method, a space grid and a finite element are not provided as in the conventional method. Moreover, since the particles of the first model move freely under the particle movement regulation conditions, even if a large deformation is expressed based on Lagrangian described in a coordinate system fixed to the first structure such as a superelastic body. Therefore, an appropriate solution in numerical calculation can be obtained.

As is well known, the behavior of a continuum expressed using particles is expressed using so-called continuity equations, equations of motion, and energy equations as governing equations. The distribution f (x) of the physical quantity of interest such as the velocity (rubber flow velocity) of each part in the superelastic body (x is a physical quantity to be approximated, and in this embodiment represents the three-dimensional position coordinate of the space), As shown in (1), the approximate physical quantity obtained using the target physical quantity f (x ′) and the kernel function W (xx ′, h) (h is an influence radius parameter) at a predetermined position coordinate x ′. It can be approximated by the distribution <f (x)>.

The attention physical quantity f (x) possessed by the particles is discretized using the density ρ ^J of the particles J and the mass m ^{J of the} particles J (J represents the particle number) and is discretized as in the following formula (2). be able to.

The differential system of the formula (2) is expressed as the following formula (3), and the equation of motion of the particles is expressed as the following formula (4) using stress divergence. In Expression (4), σ is a Cauchy stress tensor.

The formula (3) and (4), the equation of motion of particles using Kernel approximation is represented by the formula (5), the particle acceleration ^{a I} particles I of interest are obtained. I indicates the number of the particle of interest among the plurality of particles. Hereinafter, let I denote the particle of interest.

In this way, Expression (5) defined by approximating the distribution f (x) of the target physical quantity such as the velocity using the target physical quantity of the particle J is created. The position and speed of the particle I are obtained by the following formulas (6) and (7). In the present embodiment, a first model is created that includes equations (5), (6), and (7) as particle movement defining conditions that regulate the movement of particles I.

Here, the kernel function W (xx ′, h) is not particularly limited. However, as | x−x ′ | / h = ν, for example, as shown in the following formula (8), a cubic B− Use spline functions.

When the cubic B-spline function shown in Expression (8) is used as the kernel function W (xx ′, h), the kernel function W (xx ′, h) becomes 0 when ν is 2 or more. Therefore, when ν is less than 2, a positive value is obtained. Therefore, the behavior of the particle I of interest depends on the particle J located in the range where ν is less than 2. For example, as shown in FIG. 2, the particles L contained in the (near region R ^M that corresponds to this range particles M) spheres within a radius 2h around the particles M, the movement of the particles M defined Is done. This radius 2h is also called a smoothing length. In the present invention, together with the smoothing length, as shown in FIG. 2, a contact condition range C ^N (for the particle M, the contact condition range C ^M ) is set for each particle of the first model 32. The contact condition range ^CN is a range in which the second model and the first model are considered to be in contact when the second model enters the range. In the present embodiment, the contact condition range C is set to the size of the influence radius h. These smoothing lengths and contact condition ranges are not limited to the example of the present embodiment, and arbitrary numerical ranges may be set. In the present invention, such a first model composed of a plurality of particles is created.

In the present embodiment, as shown in FIG. 2, the second model 34 is created as an aggregate of particles in the same manner as the first model 32. The particles constituting the second model 34 are set so as not to receive any action from the second model. Further, the neighboring region R ^K of any particle K of the first model 32 (not specifically illustrated for number "K"), even containing the particles of the second model 34, any particles of the first model The movement of K is not defined by the particles of the second model 34. On the other hand, in the contact condition range C ^K of any particle K of the first model 32, if the entered particles of the second model 34, the velocity vector of any particle K of the first model, the second model 34 Is set to be the same vector as the velocity vector of the particle. Again, the particles of the second model 34 enters the contact condition range C ^K is not subject to any action from the particles of the first model, the velocity vector is also set to not change at all.

  In the present invention, the second model is not particularly limited. For example, the second model may be modeled by a finite element or may be modeled by a function representing a contact surface. However, by reproducing the second model as an aggregate of a plurality of particles, it can be handled as the same model as the first model, and various numerical calculation processes described later are smoothly executed by the same application program. be able to.

In the example shown in FIG. 2, the second model is reproduced for a part of the surface of the metal body that may come into contact with the rubber body, and the particles constituting the surface part are three layers. . In the present invention, the second model only needs to be a model that reproduces only a region of the second structure that may be in contact with the first structure. FIG. 3A is an example of the first model and the second model created by the conventional deformation behavior simulation method, and FIG. 3B is the first model created by the deformation behavior simulation method of the present invention. And another example of the second model. In the model shown in FIG. 3A, for the particles constituting the second model 34a, similarly to the first model 32a, particle movement regulation conditions are set (conditions that can be regarded as a metal body), and the first model This is a model for calculating the deformation of the second model while calculating the interaction between the model and the second model. As described above, conventionally, it is necessary to calculate the second model particle in consideration of the movement regulation condition and the interaction, and the second model includes a plurality of particles in addition to the region in contact with the first model. (Minimum of 2) is required, and the time required for the calculation for each particle has been enormous. In the present invention, the second model may be a model (second model 34b) that reproduces only the region that may contact the first structure as shown in FIG. 3B. In the present invention, particles of the second model has entered the contact condition range C ^N is not subject to any action from the particles of the first model, the velocity vector is also set to not change at all, contact conditions range C ^N By modeling only the particles of the second model that may enter, the surface shape of the second model does not change at all by contacting the first model, and the second model can be handled as a rigid model. . The number of particles of the second model 34a shown in FIG. 3 (a) is 2308, and the number of particles of the second model 34b shown in FIG. 3 (b) is 202. Compared to the case shown in FIG. 3 (a), the number of particles in the case shown in FIG. 3 (b) is simply small, and it is not necessary to consider extra interactions. Few.

  The movement / compression operation unit 14 performs a simulation operation for moving the second model with respect to the first model 32 based on the compression condition input using the input operation system 24. In the present embodiment, a simulation calculation is performed to bring the second model 34 closer to the first model 32 at a constant speed. In the movement / compression calculation unit 14, the second model 34 is brought close to the first model 32 at every unit time interval (time step), and the second of the total particles of the first model 32 at each time interval. Particles considered to be in contact with the model, that is, particles having the second model within the contact condition range are extracted. And about the particle | grains considered that it contacted with the 2nd model, the velocity vector of the 2nd model in the step which contacted is provided as a velocity vector of this particle | grain. The velocity vector (velocity information) is forcibly given unconditionally without depending on physical quantities such as the position and velocity of the particles before contact.

  Specifically, among each particle of the first model 32, the velocity vector of the particle that has entered the second model within the contact condition range C is set as the velocity vector of each particle of the second model. At this time, regarding the particles of the second model, it is considered that there is no interaction due to collision with the first model, and the velocity vector of the second model is not changed at all due to contact / compression. In the quasi-static deformation as in the present embodiment, it can be considered that the moving speed of the second structure in the contact / compression does not change. The contact / compression state of the two structures can be reproduced with sufficient accuracy. In this invention, since it is not necessary to consider the extra interaction concerning a 2nd structure, the time concerning a calculation process is extremely short. At the same time, calculation noise caused by the second model can be reduced. Note that the first model 32 used in the movement / compression calculation unit 14 is a model that is in the compression deformation state at the time point immediately before the time step calculated by the deformation calculation unit 16 described later in the previous time step. It is. The first model 32 used in the first time step uses an initial state, for example, a model in which a plurality of particles are arranged at equal intervals.

  The deformation calculation unit 16 calculates the compression deformation state of the first model at the current time step n using the velocity vector given to the particles at the contact portion of the first model 32 in the movement / compression calculation unit 14 as an external force condition. . In this embodiment, an incompressible viscous fluid analysis method using an algorithm that solves the incompressible condition under a constant volume condition is used. The incompressible viscous fluid analysis method is used for polymer materials such as rubber, which show incompressibility or microcompressibility in which the volume hardly changes even with pressure, but the SPH method is basically a compressive treatment. This is because the uncompressed state cannot be calculated strictly as it is. The deformation behavior simulation using the particle model of the present invention can be applied under either compression condition or non-compression condition, and the algorithm details in the deformation behavior simulation are not particularly limited.

First, a temporary velocity u _i ^* (the following equation (9)) at the current time step n is obtained using the particle velocity and pressure field at the time point when the previous time step (n−1) has elapsed.
Here, u is the particle velocity, P is the pressure, V is the kinematic viscosity coefficient, and f is the body force. Since the temporary particle velocity does not satisfy the continuous equation as it is, the non-rotational velocity field u ′ is used to represent the n-th velocity as shown in Equation (10). Further, the pressure field of the nth step is as shown in Expression (11). Using Equation (9) (10) (11), when obtaining the particle velocity ^{u n} in n steps, so the following equation (12).
In the deformation calculation unit 16, the provisional particle velocity is obtained explicitly by such an expression (12) (deformation substep <na> by external force).

Here, since u ^* must satisfy the continuity equation, taking the divergence of equation (12) yields the Poisson equation for the pressure of equation (13).

When the left side of the Poisson equation is discretized, Equation (14) is obtained. Here, P _ab = P _a −P _b and r _ab = r _a −r _b . The right side of the Poisson equation is discretized as shown in Equation (15).

  The deformation calculation unit 16 implicitly solves the pressure Poisson equation of Equation (13) so as to satisfy the incompressibility condition after moving the particles at the temporary particle velocity obtained in the deformation substep <na> by external force. Solve, find the corrected pressure and velocity, and move the particles (position correction substep <nb>). In the present embodiment, in this way, in one time step, the deformation sub-step <na> and the position correction sub-step <nb> by external force are performed, and the position of the particle at the time step n is obtained.

Moreover, in this embodiment, the deformation | transformation calculating part 16 calculates | requires a deformation | transformation gradient for every substep of deformation | transformation substep <na> and a position correction substep <nb>, and calculates | requires the stress of each particle | grain in the time step n. In the present embodiment, the deformation gradient tensor F _ij at the time step n is obtained using the Update Lagrangian method. The deformation gradient tensor F based on the Update Lagrangian method is the deformation gradient tensor updated up to the previous step <n−1>, that is, the deformation gradient from the initial state to the end of step <n−1> is F ^{Assuming that <n−1>} , the deformation gradient tensor at the current step is f ^<n> , and the deformation gradient tensor F ^<n> at the end of the current step ^<n> is expressed by the following equation (16). ^<N> = f ^<n> F ^<n-1> (16)

In the present embodiment, as described above, one step is divided into two sub-steps: a deformation sub-step <na> by an external force based on the SPH method, and a position correction sub-step <nb> for constant particle density. Further, a deformation gradient is obtained for each sub-step, and the stress is calculated. Specifically, the deformation gradient tensor at the end of step <n-1> is set as F ^<n-1> , and the deformation gradient tensor at the deformation substep <na> is set as f _a ^<n>. The deformation gradient tensor F _a ^{<n> is obtained} by the following equation (17).
F _a ^<n> = f _a ^<n> F ^<n−1> (17)

Then, the deformation gradient tensor F _b ^<n> up to the end of this substep is set as the deformation gradient tensor F _b ^<n> at the position correction substep <nb> for fixing the particle density as f _b ^<n>. n> Deformation gradient tensor F at the end F ^<n> is obtained by the following equation (18).
F _b ^<n> = f _b ^<n> F _a ^<n> = F ^<n> (18)

  Based on the deformation gradient tensor thus obtained, the stress of each particle at the end of each step is obtained. For example, a Cauchy stress tensor expressed using a Mooney-Rivlin body as an elastic potential function may be obtained. In this way, the deformation calculation unit 16 calculates the compression deformation state of the first model at the current time step n, for example, the position and stress of each particle of the first model. The derivation of the Cauchy stress tensor expressed using the Mooney-Rivlin body and details of each of the above-described processes are described in Non-Patent Document 2, for example.

  The output unit 26 is a known printer or display, and outputs the calculation result of the deformation calculation unit 16. For example, the compression deformation state and stress distribution of the first model at each time step n are displayed and output as an image. Also, numerical information of physical quantities such as the position of each particle and velocity stress may be displayed and output. In addition, it is possible to sequentially output the progress of processing of each unit, such as model creation processing in the model creation unit 12 and movement / compression simulation in the movement / compression operation unit 14.

  FIG. 4 is a flowchart of an example of a deformation behavior simulation method using the particle model of the present invention. In the deformation behavior simulation method using the particle model of the present invention, first, simulation conditions are set (step S100). For example, compression conditions such as the size and shape of the first structure and the second structure, the moving speed of the second structure relative to the first structure (how much speed, how much time step, how much compression) Etc.) and various conditions necessary for the simulation, such as particle conditions. Next, in the model creation unit 12, as described above, according to the model creation conditions input using the input operation system 24, the first model that reproduces the first structure as an aggregate of a plurality of particles, and Then, a second model reproducing the second structure is created (step S102).

  Next, the movement / compression operation unit 14 performs a simulation operation for moving the second model with respect to the first model 32 based on the compression condition input using the input operation system 24 (step S104). In the present embodiment, the second model 34 is moved to the first model 32 at a constant speed (for example, approaching at 10 mm / sec), and the second model is moved at the same speed after the contact to compress the first model. A simulation calculation is performed (step S104). In this step, the second model 34 is brought closer to the first model 32 by a predetermined unit time interval (time step). The movement / compression calculation unit 14 determines that the particles that are in contact with the second model among all the particles of the first model 32 at the time when the movement / compression processing for the time interval is completed, that is, the contact condition range. Particles containing the second model are extracted. As described above, for the particles that are considered to be in contact with the second model, the velocity vector of the second model at the stage of contact is assigned as the velocity vector of the particles (step S106). The velocity vector (velocity information) is forcibly given unconditionally without depending on physical quantities such as the position and velocity of the particles before contact.

  Then, as described above, the deformation calculation unit 16 uses the velocity vector applied to the particles at the contact portion of the first model 32 in the movement / compression calculation unit 14 as an external force condition, and at the time when the current time step is completed. Then, the compression deformation state (the position and stress of each particle) of the first model is calculated (step S108). When the calculation of the compression deformation state in the deformation calculation unit 16 is completed, it is determined whether or not the compression deformation state has been calculated for all time steps defined by a predetermined compression condition (step S110). Such a determination may be performed by the CPU 20, for example. If the calculation of the compression deformation state for all time steps is not completed, the time step is changed to the next time step (if step <n>, the step is changed to step <n + 1>) (step S112). The processes of S104 to S110 are repeatedly performed. Such processing is repeated until the compression state is calculated for all time steps.

  When the compression state is calculated for all time steps, the output unit 26 outputs a simulation result (step S114). For example, by continuously displaying the deformation state of the first model at the end of each time step for each time step, the first model and the second model are compressed until the first model is compressed. The deformation behavior of the first model is displayed as an animation. The deformation behavior simulation method using the particle model of the present invention is performed in this way.

FIGS. 5A to 5D are examples of results of the deformation behavior simulation method using the particle model of the present invention. The cylindrical first structure, which is a rubber body, is replaced with a substantially rigid second structure. It is the result of having carried out the reproduction simulation of the deformation behavior of the 1st structure at the time of compressing with a body. In the example shown in FIGS. 5A to 5D, a first model 42 made of a plurality of particles, which reproduces the first structure, is formed using a rubber body (superelastic material) of φ100 mm as the first structure. Then, a second model 44 that reproduces a flat, substantially rigid body was created. Then, the second model 44 (one of them) was moved at a speed of 10 mm / sec from the upper side to the lower side in the figure with respect to the first model 42, and the compression deformation state of the first model 42 was calculated. In the calculation of the compression deformation state, the position and stress of each particle in each compression state (that is, in each time step) were obtained. In determining the stress, a Mooney-Rivlin body was used as the elastic potential function of the first model 42. The Mooney-Rivlin constants c ₁ = 1.0, c ₂ = 0.04, and the volume change coefficient α of the finely compressed material were set to 7.5.

FIG. 5A shows an initial state in which the first model 42 and the second model 44 are partially in contact with each other, and both models are stopped. FIG. FIG. 5C shows the result of the compression deformation state in the state in which the first model 42 is compressed 25% in the vertical direction in the drawing. d) is a result of the compression deformation state in a state where the first model 42 is compressed by 40% in the vertical direction in the figure. 5A to 5D, the thinner the color, the stronger the stress in the compression direction, and the darker the color, the stronger the stress in the pulling direction. As shown in FIGS. 5A to 5D, the deformation behavior of the first structure, which is a superelastic body, is determined in detail for each compression state by the deformation behavior simulation method using the particle model of the present invention. Can do. FIG. 6A is an enlarged view showing a part of the first model in the state shown in FIG. FIG. 6B shows a model obtained by reproducing a first structure and a second structure similar to those shown in FIGS. 5A to 5D using a mesh model, and FEM (finite element method) is used. These are the results of the same compression deformation analysis as in the case shown in FIGS. FIG. 6B shows the result of the compression deformation state in the state where the first model is compressed by 40% in the vertical direction in the figure, similarly to FIG. 5D. The simulation results of the present invention shown in FIG. 6 (a) (FIG. 5 (d)) are in good agreement with the analysis results by the finite element method shown in FIG. 6 (b). The deformation behavior simulation method using the particle model of the present invention can analyze a large deformation problem such as a rubber body with sufficient accuracy.

  As described above, the deformation behavior simulation method and program using the particle model of the present invention have been described in detail. However, the present invention is not limited to the above-described embodiment, and various improvements and modifications can be made without departing from the spirit of the present invention. Of course.

It is a block diagram which shows the structure of the outline of the deformation behavior simulation apparatus which implements the deformation behavior simulation method using the particle | grain model of this invention. It is an example of the model produced by the deformation | transformation behavior simulation method of this invention. (A) is an example of a model created by a conventional deformation behavior simulation method, and (b) is another example of a model created by the deformation behavior simulation method of the present invention. It is a flowchart figure of an example of the deformation behavior simulation method using the particle | grain model of this invention. (A)-(d) is an example of the implementation result of the deformation | transformation behavior simulation method using the particle | grain model of this invention, and the deformation | transformation behavior of the 1st structure when the 1st structure is compressed by the 2nd structure It is the result of having performed the simulation which reproduces. (A) is a figure which expands and shows a part about the 1st model of the state shown in Drawing 5 (d). FIG. 5B is a diagram obtained by reproducing a first structure and a second structure similar to those shown in FIGS. 5A to 5D using a mesh model, and using FEM (finite element method). It is the result of having implemented the simulation which reproduces the deformation behavior similar to the case shown in (a)-(d).

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Simulation apparatus 12 Model preparation part 14 Movement / compression calculating part 16 Deformation calculating part 18 Memory 20 CPU
22 Main Device 24 Input Operation System 26 Output Units 32, 42 First Model 34, 44 Second Model

Claims (6)

When the first structure and the second structure come into contact with each other and the first structure deforms over time, and the contact surface between the first structure and the second structure changes over time. A method for determining the deformation behavior of the first structure,
A model generation step of generating a first model that reproduces the first structure as an aggregate of a plurality of particles, and a second model that reproduces the second structure;
Calculating the deformation behavior of the first model when the first model in contact with the second model is deformed over time by moving the second model relative to the first model; When,
Outputting the calculation result, and in the step of calculating the deformation behavior, the physical quantity of the second model is not affected by the first model, and The second model is moved at predetermined time steps, and the distance from the second model among a plurality of particles constituting the first model is less than or equal to a predetermined value each time the second model is moved. Using the particle model, wherein the velocity information of the particle is the same as the velocity information of the second model in the range of the predetermined value or less, and the deformation of the first model is calculated for each time step. Deformation behavior simulation method.   The deformation behavior simulation method using a particle model according to claim 1, wherein the second model is a model in which the second structure is reproduced as an aggregate of a plurality of particles.   The second model is a model that reproduces only a region of the second structure that is likely to have a distance from an arbitrary particle of the first structure equal to or less than the predetermined value. A deformation behavior simulation method using the particle model according to claim 1. In the step of calculating the deformation behavior, the deformation behavior is calculated based on a particle movement regulation condition that regulates the movement of the particles set for each of the particles,
The particle movement regulation condition is determined by approximating the distribution of the target physical quantity in the neighboring area using the target physical quantity of the particles included in the neighboring area while the neighboring area is determined corresponding to each of the particles. The deformation behavior simulation method using the particle model according to any one of claims 1 to 3, wherein the conditions are defined. The particle movement regulation condition is that a physical quantity to be approximated in a model constituted by the particles is x, a distribution of the attention physical quantity in the neighboring area is f (x), and the distribution f (x) of the attention physical quantity is the neighboring area. 5. An equation formulated by approximating the distribution of approximate physical quantities <f (x)> determined by the following formula (1) using a target physical quantity and a predetermined kernel function of particles included in A deformation behavior simulation method using the described particle model.
However, W (xx ', h) is a kernel function, and h is an influence radius. When the first structure and the second structure come into contact with each other and the first structure deforms over time, and the contact surface between the first structure and the second structure changes over time. A program for causing a computer to execute a method for determining the deformation behavior of the first structure,
A model generation step of generating a first model that reproduces the first structure as an aggregate of a plurality of particles, and a second model that reproduces the second structure;
The step of calculating the deformation behavior of the first model when the first model in contact with the second model is deformed over time by moving the second model relative to the first model. When,
Outputting the calculation result, and
In the step of calculating the deformation behavior, the physical quantity of the second model is not affected by the first model, and the second model is moved with respect to the first model at predetermined time steps. The velocity information of the particles whose distance from the second model is equal to or less than a predetermined value among the plurality of particles constituting the first model each time the movement is performed is within a range equal to or less than the predetermined value. A deformation behavior simulation program using a particle model, characterized in that the deformation of the first model is calculated for each time step as the same as the velocity information of the second model.