DEVICE FOR ANALYZING BEHAVIOR OF CONTINUUM, METHOD FOR ANALYZING BEHAVIOR OF CONTINUUM, AND PROGRAM

Abstract

To analyze behaviors of a plurality of different continuums including a continuum that can perform plastic deformation.SOLUTION: A continuum behavior analyzing device (10) includes: a setting unit (11) that sets a deformable first continuum model divided into numerous factors, a second continuum model contactable with the first continuum model and formed of a set of multiple particles indicating an elastoplastic body or a plastic body that can be plastically deformed, and a contact condition; a rolling and shearing calculation executing unit (12) that executes rolling and shearing calculations for a part of the first continuum model and the second continuum model; and a continuously forming unit (13) that derives an interaction force between the multiple particles of the second continuum model and the factors of the first continuum model, and continuously forms the first continuum model and the second continuum model on the basis of the interaction force between the multiple particles of the second continuum model and the factors of the first continuum model.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present disclosure relates to a continuum behavior analysis device, a continuum behavior analysis method, and a program. [Background technology]

[0002] Conventionally, various numerical analysis simulations have been performed on the motion of continuum bodies such as fluids and solids. In analyzing the behavior of a tire, which includes blocks of elastic material such as rubber as an example of such a continuum, it is important to analyze the area around the road surface with which the tire comes into contact. A technique is known in which the behavior of a tire is analyzed using a numerical analysis method such as the finite element method when an intervening object such as a liquid is present between the tire and the road surface (see, for example, Patent Document 1). Another technique is known in which the behavior of an intervening object such as a liquid is analyzed using a particle method when an intervening object is present between the tire and the road surface (see, for example, Patent Document 2).

[0003] Meanwhile, the objects present between the tire surface and the road surface include not only liquid fluids such as water, but also snow, which is solidified water, and snow behaves differently from liquids.Technologies are known for analyzing the behavior of snow, which behaves differently from liquids, using a numerical analysis method based on the particle method (see, for example, Non-Patent Documents 1 and 2). [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] Alexy Stomakhin, Craig Schroeder, Lawrence Chai, Joseph Teran, Andrew Selle, "A material point method for snow simulation", ACM Transactions on Graphics, Vol.32, No.4, 2013 [Non-patent document 2] JA Nairn, "Material point method calculations with explicit cracks", CMES, Vol.4, No.6, 2003 [Patent documents]

[0005] [Patent Document 1] Japanese Patent Application Laid-Open No. 2011-201390 [Patent Document 2] Japanese Patent Application Laid-Open No. 2011-252748 Summary of the Invention [Problem to be solved by the invention]

[0006] However, when multiple continuums come into contact with each other, at least one of them deforms due to the interaction between them. When analyzing the behavior of a continuum, for example, when analyzing the state of a tire running on a snowy road, it is necessary to consider the interaction between the tire and the plastically deforming snow, treating each of the snow that makes up the snowy road and the tire as a continuum. Therefore, analyzing the behavior of a continuum that includes snow, taking into account factors such as friction, requires a detailed analysis of the contact area between the tire and snow. It is necessary to consider the phase changes of the continuum, which change over time. However, for example, dividing a continuum into meshes and performing a numerical analysis increases the computational load depending on the number of divided elements. Therefore, there is room for improvement in analyzing the behavior of multiple different continuums, including continuums that can undergo plastic deformation.

[0007] Taking the above facts into consideration, the present disclosure aims to provide a continuum behavior analysis device, a continuum behavior analysis method, and a program that can analyze the behavior of multiple different continua, including continua that are capable of plastic deformation. [Means for solving the problem]

[0008] A first aspect of the present disclosure provides a method for producing a continuum model, comprising: a first deformable continuum model of a predetermined shape divided into a large number of elements of a predetermined element size; a second continuum model formed by an assembly of a plurality of particles of a predetermined size that are capable of contacting at least a portion of the first continuum model and that represent a fluid containing at least an elastic-plastic body or a plastic body that is capable of plastic deformation; a setting unit that sets contact conditions related to contact between the first continuum model and the second continuum model; and a control unit that brings a portion of the first continuum model into contact with the second continuum model to produce a continuum model of the first continuum model and the second continuum model. a rolling / shear calculation execution unit that moves a model relatively in a predetermined direction by a predetermined amount of movement and executes rolling and shear calculations based on the contact conditions set by the setting unit; and a coupling unit that derives an interaction force between a plurality of particles of the second continuum model and elements of the first continuum model that occurs between the first continuum model and the second continuum model based on a calculation result of the rolling / shear calculation, and couples the first continuum model and the second continuum model based on the derived interaction force. According to the first aspect, it becomes possible to analyze the behavior of a plurality of different continua, including continua that are capable of plastic deformation.

[0009] A second aspect of the present disclosure is a continuum behavior analysis device according to the first aspect, wherein the first continuum model is a model that can be analyzed using a lattice method, and the second continuum model is a model that can be analyzed using a particle method based on a material point method. According to the second aspect, it becomes possible to analyze a continuum using different analytical methods, namely, the grid method and the particle method.

[0010] A third aspect of the present disclosure is a continuum behavior analysis device according to the second aspect, wherein the first continuum model is a block model representing an elastic body, and the second continuum model is a fluid model representing a fluid containing at least snow. According to the third aspect, it becomes possible to analyze in detail the snowy road surface, which is expressed as an elastic-plastic body or a plastic body capable of plastic deformation.

[0011] A fourth aspect of the present disclosure is directed to the continuum behavior analysis device described in the third aspect, wherein the block model applies a tire model representing a portion of a tire, and the fluid model applies a snowy road surface model representing a snowy road surface. According to the fourth aspect, it is possible to analyze the behavior of a snowy road surface and a tire rolling on the snowy road surface.

[0012] A fifth aspect of the present disclosure is a continuum behavior analysis device according to any one of the first to fourth aspects, wherein a third continuum model formed by an aggregation of a plurality of particles of a predetermined size representing a fluid containing at least an elastic-plastic body or a plastic body capable of plastic deformation is attached to a portion of the first continuum model, and the coupling unit treats the second continuum model and the third continuum model as different continuums with a discontinuity surface between them when a portion of the first continuum model and the second continuum model come into contact. According to the fifth aspect, by treating the second continuum model and the third continuum model in contact with the second continuum model as different continuums, it becomes possible to analyze the behavior of the continuum by taking into account discontinuity surfaces in a fluid that contains at least an elastic-plastic body or a plastic body that can be plastically deformed.

[0013] A sixth aspect of the present disclosure is a continuum behavior analysis device according to any one of the first to fourth aspects, wherein the contact conditions include a condition indicating that the first continuum model penetrates the second continuum model and a condition related to friction between the first continuum model and the second continuum model, and the coupling unit derives an interaction force including a repulsive force and a frictional force based on the amount of penetration between the first continuum model and the second continuum model. According to the sixth aspect, it is possible to analyze the behavior of the continuum in more detail by taking into consideration the relative buffering portion between the first continuum model and the second continuum model.

[0014] A seventh aspect of the present disclosure is a continuum behavior analysis device according to any one of the first to sixth aspects, wherein the coupling unit applies an adhesion force that causes the particles of the second continuum model to adhere to the surface of the first continuum model when the particles of the second continuum model come into contact with or approach a predetermined distance from the surface of the first continuum model and then move away after the contact or approach. According to the seventh aspect, when the first continuum model and the second continuum model move relative to each other, it becomes possible to analyze the behavior of at least a portion of the second continuum model adhering to the surface of the first continuum model.

[0015] An eighth aspect of the present disclosure is a continuum behavior analysis device according to any one of the first to seventh aspects, wherein the coupling unit calculates an index value of friction performance based on an interaction force between the first continuum model and the second continuum model. According to the eighth aspect, it becomes possible to analyze the frictional performance that occurs when continuums come into contact with each other.

[0016] A ninth aspect of the present disclosure is a method for analyzing behavior of a continuum, in which a computer sets: a deformable first continuum model of a predetermined shape divided into a large number of elements of a predetermined element size; a second continuum model formed by an assembly of a plurality of particles of a predetermined size that is capable of contacting at least a portion of the first continuum model and represents a fluid containing at least an elasto-plastic body or a plastic body that is capable of plastic deformation; and contact conditions related to contact between the first continuum model and the second continuum model; brings a portion of the first continuum model into contact with the second continuum model, moves the first continuum model and the second continuum model relatively by a predetermined movement amount in a predetermined direction, and performs a rolling and shear calculation based on the contact conditions set by the setting unit; derives an interaction force between the plurality of particles of the second continuum model and elements of the first continuum model based on a result of the rolling and shear calculation; and couples the first continuum model and the second continuum model based on the derived interaction force.

[0017] A tenth aspect of the present disclosure is a program for analyzing the behavior of a continuum, the program including: a deformable first continuum model of a predetermined shape divided into a large number of elements of a predetermined element size; a second continuum model formed by an assembly of a plurality of particles of a predetermined size that are capable of contacting at least a portion of the first continuum model and that represent a fluid containing at least an elastic-plastic body or a plastic body that is capable of plastic deformation; and contact conditions related to contact between the first continuum model and the second continuum model; and a program for analyzing the behavior of a continuum by bringing a portion of the first continuum model into contact with the second continuum model. The program causes a computer to execute a process including: performing a rolling and shearing calculation based on the contact conditions set by moving a first continuum model and the second continuum model relatively by a predetermined amount in a predetermined direction; deriving an interaction force between a plurality of particles of the second continuum model and elements of the first continuum model that occurs between the first continuum model and the second continuum model based on a result of the rolling and shearing calculation; and coupling the first continuum model and the second continuum model based on the derived interaction force.

[0018] The storage medium for storing the program of the present disclosure is not particularly limited and may be a hard disk or a ROM. It may also be any of a CD-ROM, a DVD disk, a magneto-optical disk, and an IC card. Furthermore, the program may be downloaded from a server or the like connected to a network. [Effects of the Invention]

[0019] According to the present disclosure, it is possible to easily analyze the behavior of continua when a plurality of different continua, including a phase-changeable continuum, come into contact with each other. [Brief explanation of the drawings]

[0020] [Figure 1] FIG. 1 illustrates an example of a behavior analysis device according to an embodiment. [Figure 2] 1A and 1B are diagrams illustrating examples of a block model and a snow body model. [Figure 3] FIG. 1 is a diagram showing an example of a continuum represented by particles and lattice points. [Figure 4] FIG. 10 is a diagram relating to shear analysis of snow bodies. [Figure 5] FIG. 10 is a diagram showing the analysis process of a snow body model that does not take discontinuity into account. [Figure 6] FIG. 10 is a diagram showing the analysis process of a snow body model taking discontinuity into account. [Figure 7] FIG. 10 is a diagram illustrating the concept of friction between a block model and a snow body model. [Figure 8] FIG. 10 is a diagram showing an example of a configuration of virtual particles representing fluid particles. [Figure 9] FIG. 10 is a diagram showing an example of an analysis result related to friction. [Figure 10] FIG. 1 is a diagram illustrating an example of a block model. [Figure 11] FIG. 1 illustrates the concept of adhesion of fluid particles to a block model. [Figure 12] FIG. 10 is a diagram illustrating an example of a characteristic related to adhesive force. [Figure 13] 10A and 10B are diagrams relating to an analysis of the behavior of a block model and a snow body. [Figure 14] FIG. 1 illustrates an example of a computer configuration that functions as a behavior analysis device. [Figure 15] 10 is a flowchart illustrating an example of the flow of a behavior analysis process. [Figure 16] FIG. 1 is a diagram schematically illustrating a tire moving on a snowy road surface. DETAILED DESCRIPTION OF THE INVENTION

[0021] Hereinafter, embodiments of the present disclosure will be described in detail with reference to the drawings. Note that components and processes that have the same actions and functions will be given the same reference numerals throughout the drawings, and duplicated descriptions may be omitted as appropriate.

[0022] FIG. 1 shows an example of the configuration of a behavior analysis device 10 that analyzes the behavior of a continuum according to an embodiment of the present disclosure.

[0023] In this embodiment, the technology disclosed herein is applied to an analysis process in which at least a portion of a plurality of continua is brought into contact with each other, and the behavior of the plurality of continua that changes due to an interaction force resulting from the deformation of the continua that occurs upon contact is analyzed.

[0024] In this embodiment, snow is numerically modeled around the road surface with which the tire comes into contact, for example, a snowy road surface, and coupled analysis of the snow and tire is performed to predict tire performance on snow (for example, frictional force). In this disclosure, tire performance is predicted from the perspective of the interaction between the tire and snow. This makes it possible to replace part of the tire development cycle that takes into account tire performance on snow with numerical analysis, thereby shortening the development period.

[0025] In the present disclosure, a first continuum among the multiple continuums is a continuously formed material that does not undergo plastic change even when a predetermined pressure is applied. The first continuum includes at least an elastic body. The elastic body may be any material that is continuously formed with elasticity, such as a rubber material, a polyurethane material, or a polymer material. In this embodiment, a case where a hexahedral block of rubber material is used as an example of the first continuum is described. Note that, in this embodiment, a case where a rubber material is used as the first continuum is described, but the first continuum is not limited to a rubber material. Of course, the technology of the present disclosure can be applied to cases where other elastic materials, such as a polyurethane material or a polymer material, are used.

[0026] Furthermore, among the multiple continuum, a second continuum different from the first continuum is a continuously formed material that undergoes plastic deformation when a predetermined energy (e.g., pressure) is applied. Examples of the second continuum include elastic-plastic bodies and plastic bodies, such as snow bodies that contain snow. In this embodiment, a case where a snow body that contains snow is used as an example of the second continuum will be described. Note that in this embodiment, a case where snow or a material that contains snow is used as a continuum that is a snow body will be described, but the second continuum is not limited to a snow body, and it goes without saying that the technology of the present disclosure can be applied to cases where a material that contains other materials that undergo plastic deformation when a predetermined energy is applied is used.

[0027] In this embodiment, a numerical analysis method is used as an analytical process for analyzing the behavior of a continuum. In analyzing the behavior of a rubber material, which is a first continuum, an analysis using a lattice method is performed. In this embodiment, a case where the finite element method (hereinafter referred to as FEM) is applied will be described as an example of the lattice method. Note that a difference method or a boundary element method may be used instead of FEM.

[0028] The behavior of the snow body, which is the second continuum, is analyzed using a particle method. In this embodiment, a case where the Material Point Method (hereinafter referred to as MPM) is applied as an example of the particle method will be described. The MPM applied as the material point method is a well-known technology, and a detailed description will be omitted, but it is a hybrid particle method that takes into account the grid method. Note that the particle method for analyzing the second continuum is not limited to MPM, and other particle methods may also be used.

[0029] In this embodiment, the snow body, which is the second continuum, is exemplified by natural snow during snowfall and soft, compacted snow made from soft snow compacted under a predetermined pressure. In other words, the snow body is applied as an elastic-plastic body capable of plastic deformation or a fluid having at least the properties of a plastic body.

[0030] On the other hand, the snow on the road surface on which a vehicle equipped with tires runs can also be wet snow called snow jam, slush, slush, etc. Therefore, when considering tire performance on snowy roads, it is preferable to reproduce the behavior of fluid on the road surface, such as the behavior of a tire on snow (for example, snow performance).

[0031] Snow bodies are a mixture of snow (which may contain ice in part, for example) and air, or a mixture of snow, air, and water. When a load is applied to snow bodies on the road surface, the internal structure, which is made up of ice and snow crystals and cavities, changes. Furthermore, the internal structure of deformed snow may not recover and return to its original state even after the load is removed. For this reason, snow bodies are treated as plastic bodies when expressed in numerical models, but by incorporating water, they also have the properties of an elastic body.

[0032] Although snow has viscoelastic properties, for simplicity, it is modeled as a non-viscous, elasto-plastic body and as a homogeneous material. In addition, to represent the shear force characteristics of snow, the Mohr Coulomb plasticity model, expressed by the following equation, is used as the plasticity model. σy==c+p·tanφ where σy is the yield stress, p is the pressure, and c and φ are the plasticity parameters. Because the yield stress of a material increases linearly with the pressure, it is possible to express the phenomenon in which snow is compressed and compacted, resulting in an increase in shear stress.

[0033] By using the above model, it becomes easy to treat snow bodies as elastic-plastic bodies. Note that the above model is not limited to the Mohr Coulomb plasticity model, and other models may be used. Also, models expressed by polynomials of third degree or higher, or by functions (such as Fourier series) may be used.

[0034] Furthermore, in this embodiment, a snow body is described as an example of an elastic-plastic or plastic body, but the present disclosure is not limited to snow bodies and can be applied to materials that have elastic-plastic or plastic properties, such as soil and sand that maintain a certain shape and materials that contain moisture, such as partially frozen soil and sand.

[0035] 1, a behavior analysis device 10 includes a model generation unit 11, a rolling / shear analysis unit 12, and a coupled analysis unit 13. The coupled analysis unit 13 includes a discontinuous analysis unit 14, a friction force analysis unit 15, and an adhesion force analysis unit 16.

[0036] The model generation unit 11 is a functional unit that generates a block model and a snow body model by modeling blocks that constitute part of a tire and snow bodies that are soft, compacted snow. The block model is an example of a first continuum, and is formed by dividing it into a large number of elements of a predetermined element size that can be deformed to enable analysis by FEM. The snow body model is an example of a second continuum, and is formed by an aggregation of multiple particles of a predetermined size to enable analysis by MPM.

[0037] An example of the generated block model and snow body model is shown in Figure 2. The example shown in Figure 2 shows a block model in which a block having two sipes is divided into a mesh of rectangular prism-shaped (e.g., hexahedral) elements, and a snow body model in which particles of a predetermined size are arranged vertically, horizontally, and vertically.

[0038] The model generation unit 11 has a function of setting contact conditions related to contact between the block model and the snow body model. The contact conditions include a condition indicating that the block model penetrates into the snow body model and a condition related to friction between the block model and the snow body model. Penetration indicates that after the block model and the snow body model come into contact, an overlapping area is formed when the block model and the snow body model are moved relative to each other while maintaining their respective shapes. An example of a condition indicating penetration (i.e., a penetration condition) is a condition indicating whether or not the block model penetrates into the snow body model. The condition related to friction (i.e., a friction condition) specifies the frictional force generated by contact between the block model and the snow body model, and one example is the use of Coulomb friction. The model generation unit 11 is an example of a setting unit in the present disclosure.

[0039] The rolling and shear analysis unit 12 shown in FIG. 1 is a functional unit that performs a rolling and shear analysis in which a block model is brought into contact with a snow body model and moves relative to it. The rolling analysis is a process required to analyze physical quantities related to, for example, friction, that change when a block model in contact with a snow body model is moved relative to it by performing a rolling calculation. The shear analysis is a process required to analyze physical quantities related to, for example, shearing of a snow body model by performing a shear calculation. The rolling and shear analysis unit 12 is an example of a rolling and shear calculation execution unit of the present disclosure.

[0040] The rolling and shear analysis unit 12 uses the block model and snow body model generated by the model generation unit 11 to set the amount of penetration that occurs between the block model and snow body model, and the amount of relative movement between the block model and snow body model, based on the set contact conditions. These settings are limitations to maintain accuracy when performing a rolling and shear analysis using FEM in which the block model comes into contact with and moves relative to the snow body model.

[0041] By contacting and moving the block model with the snow body model, information such as stress, strain, and slippage can be obtained for any division element or node. For example, the distribution of frictional performance can be determined by calculating the friction energy from the force and slippage of the nodes on the surface of the block model.

[0042] For example, at least one of the block model and the snow body model is moved in a predetermined direction (e.g., vertically or in the opposite direction, or horizontally) to bring the block model and the snow body model closer together and into contact. As an example, consider the block model approaching the snow body model horizontally (flat pushing). This flat pushing is controlled by a load value or deflection amount. Next, the block model is moved relative to the snow body model in a direction intersecting the above-mentioned predetermined direction (e.g., horizontally) by the above-mentioned set movement amount. The flat pushing and horizontal movement cause friction between the block model and the snow body model. The axis of the block model and the block model are constrained, and as a frictional force is generated between the block model and the snow body model, the constraint on the block model is released and the block model moves (e.g., penetrates and moves horizontally). A detailed explanation of frictional force will be given later.

[0043] The coupled analysis unit 13 is a functional unit that couples the block model and the snow body model by deriving the interaction forces acting between the block model, the snow body model, and the elements of the block model and the particles of the snow body model based on the physical quantities of the analysis results in the rolling / shear analysis unit 12. The coupled analysis unit 13 is an example of a coupling unit in the present disclosure.

[0044] The coupled analysis unit 13 includes a discontinuity analysis unit 14, a friction force analysis unit 15, and an adhesion force analysis unit 16. The discontinuity analysis unit 14 is a functional unit that analyzes discontinuities in the snow body model. The friction force analysis unit 15 is a functional unit that analyzes friction forces in the block model and the snow body model. The adhesion force analysis unit 16 is a functional unit that analyzes the adhesion force of at least a part of the snow body model adhering to the block model.

[0045] Next, we will explain the discontinuity analysis unit 14. The discontinuity analysis unit 14 performs an analysis of discontinuities in the snow body model when the snow body model is expressed using the particle method.

[0046] While it has been possible to analyze partial deformation of snow bodies, analyzing soft, compacted snow, which is prone to large-scale deformation and destruction, such as at least partial collapse, has been difficult. Furthermore, MPM is a method for analyzing continuums, and it has been difficult to represent discontinuities. In other words, MPM is a hybrid method of particle and grid methods, and represents the continuum using fluid particles and structural particles. However, even if the interaction between the fluid particles and structural particles (grid points) is cut off, it is difficult to represent discontinuities. Furthermore, MPM requires consideration of the deformation of discontinuous surfaces due to three-dimensional deformation and deformation of the object surface.

[0047] In other words, MPM, which analyzes continuum, fixes structural particles (grid points) in the background and analyzes a structure in which fluid particles can move freely in space while possessing physical quantities such as stress and strain. However, when analyzing multiple fluid particles together, different objects, such as different snow bodies, are analyzed as a single snow body, making it difficult to analyze discontinuities caused by the different snow bodies.

[0048] Therefore, in this embodiment, discontinuity is expressed by defining the physical quantities at each lattice point, which is the structural particle of the MPM, for each different object and solving the governing equation shown in the following formula (1). The governing equation is an example of an equation for structural analysis using Cauchy's law. Note that, hereinafter, the fluid particles of the MPM may be simply referred to as particles, and the structural particles may be referred to as lattice points. Furthermore, since the lattice points, which are the structural particles of the MPM, and the lattice points in the FEM are calculational lattice points, they may be referred to as lattice points without distinction. When explaining the lattice points of the MPM and the lattice points of the FEM separately, the terms MPM or FEM will be used.

number

[0049] FIG. 3 is a conceptual diagram showing an example of how different continua in an MPM are represented by particles and grid points. FIG. 3 shows two different continua, Body 1 and Body 2, with Body 1 including two fluid particles 21A and 21B and Body 2 including four fluid particles 22A, 22B, 22C, and 22D. FIG. 3 also shows structural particles (grid points) in the MPM as grid points 31. Each fluid particle can move through space, and its velocity, acceleration, mass, and stress can be calculated or set. Physical quantities (e.g., force and mass) at grid points 31 are defined for Body 1 and Body 2, and the governing equations described above are solved for each definition to represent and analyze discontinuities.

[0050] In other words, by deriving the calculation results of the governing equations based on the physical quantities of particles for each object at each fixed grid point in the background, analysis that takes discontinuities into account becomes possible. Therefore, when analyzing with MPM, it is possible to take discontinuities in the snow body model into account without having to define discontinuous surfaces for the snow body model.

[0051] Furthermore, in the discontinuity analysis described above, a condition was set that continuum objects do not penetrate each other. Specifically, when structural particles (lattice points) in an MPM are subjected to, for example, a compressive force, the physical quantities (force, mass) are superimposed, and the condition was set that no penetration occurs between objects. The following equation (2) is used to determine compression.

number

[0052] However, the variables in the formula are

number

[0053] By expressing the discontinuities described above, it becomes possible to perform deformation analysis of snow bodies, such as shear analysis, taking discontinuities into account.

[0054] Figure 4 shows a diagram related to snow shear analysis. Figure 4 shows the relationship between snow depth (density) and shear strength as an analytical result. Figure 4 shows the analytical results of the shear strength generated by applying a specified stress to a snow model with soft, compacted snow applied. As shown in Figure 4, the shear strength increases as the snow depth (density) increases. We confirmed that the characteristics shown in Figure 4 are close to the results of measuring the shear strength generated by applying a specified stress to actual soft, compacted snow.

[0055] Furthermore, by expressing the discontinuity described above, it becomes possible to analyze the deformation and at least partial collapse of a snow body as if it were bounded by a discontinuous portion (for example, a surface).

[0056] Furthermore, by expressing discontinuities as described above, the behavior of a snow body caused by the application of a predetermined stress can be reproduced by analysis as the behavior of the snow body model that occurs at the discontinuous surface of the snow body model.

[0057] Figures 5 and 6 show diagrams related to the analysis of the behavior of a snow body model caused by the application of a predetermined stress. Figure 5 shows the results of an analysis of stress application performed on a snow body model made of uniform snow without considering the discontinuity described above, while Figure 6 shows the results of an analysis of stress application performed on a snow body model made by overlapping and integrating two snow body models while representing discontinuity.

[0058] In Figure 5, state 42A shows the natural state at the beginning of the analysis, state 42B shows the compressed state in which partial region 42x of the snow body model has been moved toward the road surface model (stress applied in direction Fd in the example of Figure 5). State 42C shows the tensile state in which partial region 42x of the snow body model has been moved away from the road surface model (stress applied in direction Fu in the example of Figure 5). State 42D shows the shear state in which partial region 42x of the snow body model has been moved in a direction along the road surface model (stress applied in direction Fs in the example of Figure 5).

[0059] In Figure 6, state 43A shows the natural state at the beginning of the analysis, state 43B shows the compressive state with stress applied in the direction Fd, state 43C shows the tensile state with stress applied in the direction Fu, and state 43D shows the shear state with stress applied in the direction Fs. In Figure 6, the two snow body models that make up the snow body model are shown as different continua, body 1A and body 2A. The discontinuity described above is also shown as discontinuity surface 44 at the boundary between body 1A and body 2A. Note that discontinuity surface 44 is not a defined discontinuity surface, but is a virtual part derived by expressing the discontinuity using the governing equations as described above.

[0060] As shown in Figure 5, particles in the uniform snow body model move in unison in response to stress from the subregion 42x. That is, in the compressed state, particles move in response to stress from the subregion 42x, and the snow body model is compressed so that the inter-particle distance becomes shorter than in the natural state. In the tensile state, particles are dispersed so that the inter-particle distance becomes longer than in the natural state. In the shear state, particles move in unison, and the snow body model deforms as a unit.

[0061] On the other hand, as shown in Figure 6, when the above-mentioned discontinuities are taken into account, the analysis results show that particles in the snow model move in response to stress from subregion 42x and discontinuity surface 44 deforms. That is, in the compression state, the snow model is compressed, and the discontinuity surface deforms in response to stress from subregion 43x. In the tension state, particles are dispersed to increase the interparticle distance, resulting in the snow model being divided at discontinuity surface 44, with Body 1A moving in the direction Fu and Body 2A deforming to move in a direction returning to its natural state. In the shear state, the snow model is also divided at discontinuity surface 44, with Body 1A constituting the snow model moving in the direction Fs and Body 2A deforming to move in a direction returning to its natural state. In other words, it is possible to perform an analysis as if two snow models were stacked and integrated, with discontinuity surface 44 set and stress applied to the snow model.

[0062] As shown in Figures 5 and 6, by representing discontinuities in the snow body model, it is possible to analyze the state in which the discontinuous surface deforms due to three-dimensional deformation and deformation of the object surface, or the state in which the model is separated at the discontinuous surface, without setting up a discontinuous surface.

[0063] Next, we will explain the friction force analysis unit 15 shown in Fig. 1. The friction force analysis unit 15 is a functional unit that performs analysis of the friction applied to each particle of the snow body model. The friction force analysis unit 15 applies friction force to each element of the block model and particle of the snow body model.

[0064] When considering the friction that occurs between the block model and the snow body model, it is important to determine how to determine the contact between the block model and the snow body model. In this embodiment, the calculation speed is improved by simulating the state in which the block model penetrates into the snow body model as described above. That is, a physical quantity (hereinafter referred to as a penalty) that indicates the repulsive force that increases as the amount of penetration of the block model into the snow body model increases is derived. Specifically, the penalty that indicates the repulsive force is calculated by multiplying a penalty coefficient derived in advance by an experiment or the like by the amount of penetration. Then, the penalty is calculated from the amount of penetration, and the contact is expressed by applying a penalty to the particles of the snow body model and the elements of the block model. In addition, a physical quantity related to the friction that occurs during this contact (e.g., Coulomb friction) is also derived.

[0065] FIG. 7 is a conceptual diagram showing a state in which friction that occurs when a block model and a snow body model come into contact is taken into consideration.

[0066] FIG. 7 shows fluid particles 23 in the MPM and grid points 32A to 32D, which are structural particles. The friction force analysis unit 15 first determines contact between elements of the block model (e.g., the surface of the block model) and particles of the snow body model using the contact conditions described above, and derives the physical quantities of the fluid particles. In the example shown in FIG. 7, the physical quantities of the fluid particles 23 are derived from the positional relationship between the block model side and the fluid particle 23, which is shown as an FEM. Specifically, the friction force analysis unit 15 calculates the penetration amount, penalty coefficient, and Coulomb friction of the fluid particles 23, which are determined by the relative relationship due to contact or movement between the block model and the snow body model derived by the rolling / shear analysis unit 12.

[0067] Next, the friction force analysis unit 15 performs a process of assigning the penalty of the fluid particle derived from the penetration amount and the penalty coefficient, and the friction force derived from Coulomb friction as an interaction to the surface of the element of the block model (for example, a grid point in the FEM of the block model). Specifically, the friction force analysis unit 15 performs a process of assigning the physical quantity of the fluid particle 23 to, for example, a grid point in the FEM of the block model.

[0068] Next, the friction force analysis unit 15 performs a process of assigning a penalty and a friction force from the fluid particle to the grid points of the MPM. Specifically, as shown by the arrows in Fig. 7, a process of assigning the physical quantity of the fluid particle 23 to the grid points 32A to 32D surrounding the fluid particle 23 is performed. In this way, the friction force analysis unit 15 can improve the calculation speed by performing calculations related to contact between the block model and the snow body model only using the fluid particles, rather than using the grid points of the MPM.

[0069] In this embodiment, taking into consideration the influence of the number of particles in the MPM, for example, the decrease in calculation accuracy that occurs when the number of particles is small, fluid particles in the MPM are treated as virtual particles of a predetermined size.

[0070] FIG. 8 shows an example of the configuration of virtual particles representing fluid particles handled in MPM.

[0071] In the MPM, when a predetermined region with one fluid particle 23 for a snow body model is used as an analysis unit (state 45A shown by four predetermined regions in FIG. 8), contact between the block model and the snow body model is determined by the fluid particle 23 (for example, the center position of the particle) (state 45B). In contrast, in this embodiment, the fluid particle 23 is treated as a virtual particle having a virtual surface 23Vt with a predetermined radius r around it (state 45C). This allows contact determination to be performed on the virtual surface 23Vt of the fluid particle 23 (state 45D), making it possible to determine contact between the block model and the snow body model, and improving calculation speed compared to analysis using only the fluid particle 23. In the following explanation, the virtual particle having the virtual surface 23Vt will be described as a fluid particle.

[0072] Next, the analysis results relating to friction in the friction force analysis unit 15 described above will be verified.

[0073] FIG. 9 shows an example of the analysis results related to friction in the friction force analysis unit 15. FIG. 9 shows the relationship between the relative movement time of the block model and the snow body model and the friction force as the analysis results. FIG. 10 also shows three types of block models used in the analysis. As shown in FIG. 10, the first block model used in the analysis is a plain block 110 whose contact area with the snow body model is flat. The second block model is a divided block 112 in which two blocks are spaced apart. The third block model is a sipe block 114 in which the divided block 112 has multiple sipes (three sipes each in FIG. 10) at the contact area with the snow body model. In FIG. 9, the friction force characteristics of the plain block 110 are shown by curve 110G, the friction force characteristics of the divided block 112 are shown by curve 112G, and the friction force characteristics of the sipe block 114 are shown by curve 114G.

[0074] As shown in Figure 9, the friction force increases from the first block model to the third block model. This confirms that the shape of the contact point between the block model and the snow body model contributes to the friction force; for example, the rougher the contact point, the greater the friction force. We also confirmed that the characteristics shown in Figure 9 are close to the results of measuring the friction force when a similar test was conducted on actual soft, compacted snow.

[0075] Next, we will explain the adhesion force analysis unit 16 shown in Fig. 1. The adhesion force analysis unit 16 is a functional unit that performs analysis on the adhesion of particles of a snow body model to a block model. The adhesion force analysis unit 16 is a functional unit that applies an adhesion force that causes the block model to adhere to particles of the snow body model when the particles of the snow body model approach the block model.

[0076] When snow, especially soft packed snow, comes into contact with an object such as a tire, some of the snow may adhere to the object. For this reason, it is preferable to perform an analysis based on contact between the block model and the snow model, taking into account the adhesion of some of the snow model to the block model. In this embodiment, the adhesion force analysis unit 16 can analyze the behavior of a continuum by taking into account the adhesion between the surfaces of the block model elements (i.e., FEM elements) and fluid particles (i.e., MPM particles).

[0077] In this embodiment, the adhesive force is a force generated when a fluid particle approaches a block model. The adhesive force can be derived, for example, by the following equation (3).

number

[0078] That is, the adhesion force analysis unit 16 can derive the adhesion force by using the above equation (3) to multiply the distance calculated from the time increment of the relative velocity between the fluid particles of the block model and the snow body model by a predetermined adhesion coefficient.

[0079] An example of the concept of adhesion between the elements of the block model and fluid particles is shown in Figure 11. Figure 12 shows an example of the characteristics of the adhesion coefficient k, which is related to the adhesive force.

[0080] As shown in FIG. 11, when a fluid particle 24 of a snow body model is placed at a distance D from a block model, an adhesive force f is generated on the fluid particle 24. As shown in FIG. 12, the adhesion coefficient k decreases as the distance between the element of the block model and the fluid particle increases. Note that FIG. 12 shows a characteristic in which the adhesion coefficient value is constant (k1) up to a predetermined distance D1, but it goes without saying that the characteristic is not limited to that shown in FIG. 12. Meanwhile, the fluid particle 24 constitutes a snow body model and is constrained to the snow body model by a constraining force Ff. Therefore, when the adhesive force f of the fluid particle 24 exceeds the constraining force Ff, the fluid particle adheres to the block model.

[0081] In this embodiment, the adhesive force is not calculated constantly, but is calculated only when a fluid particle approaches the surface of an element of the block model by a certain distance or more and then separates from it, as a condition for deriving the adhesive force. This makes it possible to reduce the calculation load when deriving the adhesive force compared to constantly studying the adhesive force.

[0082] FIG. 13 shows a diagram related to the analysis of the behavior of a block model and a snow body model by taking adhesive forces into account in the adhesive force analysis unit 16. FIG. 13 shows the analysis results when a divided block 112 (FIG. 10) is used as a block model and the block model is brought into contact with and moved against a snow body model representing soft, compacted snow. FIG. 13 also shows four states 46A to 46D representing the state of the snow body model and the block model. The first state 46A shows a state in which the block model and the snow body model are in contact. The first state 46A also shows that adhesion is taken into account for a portion of the block model (a portion 47 indicated by a solid line on the block model in state 46A). The second state 46B shows a state in which the block model is pressed against the snow body model in a predetermined direction (a state after flat pressing in direction Fd from state 46A). Furthermore, state 46C shows a state in which the block model is moved in a different direction (a state after horizontal movement in direction Fs from state 46B). State 46D shows the state in which the block model has been separated from the snow body model (the state after being lifted in the direction Fu from state 46C). As shown in Figure 13, for a snow body model to which soft compacted snow has been applied, it is possible to analyze the state in which particles gradually move during the analysis process in the snow body model and some particles of the snow body model adhere to parts of the block model.

[0083] The above-described behavior analysis device 10 can be realized by a computer system including a control unit configured by a general-purpose computer.

[0084] FIG. 14 shows a schematic configuration of a computer 40 that can function as the behavior analysis device 10.

[0085] 14, a computer 40 functioning as the behavior analysis device 10 includes a computer main body 40A. The computer main body 40A includes a CPU 40B, a RAM 40C, a ROM 40D, an auxiliary storage device 40E such as a hard disk drive (HDD), and an input / output interface (I / O) 40F. The CPU 40B, RAM 40C, ROM 40D, auxiliary storage device 40E, and I / O 40F are connected via a bus 40G so as to be able to exchange data and commands with one another. The I / O 40F is also connected to an input unit 40H such as a keyboard, a display unit 40J such as a display, and a communication unit 40K for communicating with external devices.

[0086] The auxiliary storage device 40E stores an analysis program 40EP for causing the computer main body 40A to function as the behavior analysis device of the present disclosure. The CPU 40B reads the analysis program 40EP from the auxiliary storage device 40E, loads it into the RAM 40C, and executes the processing. As a result, the computer main body 40A that has executed the analysis program 40EP operates as the behavior analysis device of the present disclosure.

[0087] Various values ​​used in the behavior analysis process are stored as setting values ​​40ED in the auxiliary storage device 40E. The analysis program 40EP may be provided on a recording medium such as a CD-ROM.

[0088] Next, the behavior analysis process in the behavior analysis device implemented by a computer will be described.

[0089] 15 shows an example of the flow of behavior analysis processing by the analysis program 40EP executed in the computer 40. The behavior analysis processing shown in FIG.

[0090] First, in step S101, the CPU 40B models an elastic block made of rubber material to generate a block model, and models an elasto-plastic or plastic snow body to generate a snow body model. That is, the block model, which is a first continuum, is formed by dividing it into a large number of elements of a predetermined element size that can be deformed to enable analysis by FEM. Furthermore, the snow body model, which is a second continuum, is formed by a collection of multiple particles (fluid particles and grid points that are structural particles) of a predetermined size to enable analysis by MPM. Furthermore, in step S101, the process of setting the contact conditions described above is also executed.

[0091] The process of step S101, i.e., the process of generating the block model and the snow body model, may be performed in parallel or sequentially. Also, at least one of the block model and the snow body model may be generated in advance, and the generated data may be acquired instead of the model generation process.

[0092] In step S102, a rolling and shearing analysis is performed in which the block model is brought into contact with the snow body model and moved relative to it. The rolling and shearing analysis analyzes changes, particularly physical quantities related to friction, when the block model in contact with the snow body model is moved relative to it.

[0093] Next, CPU 40B performs a coupled analysis of the block model and the snow body model based on the physical quantities of the rolling and shearing analysis results. That is, coupling is performed by deriving the interaction forces acting between the elements of the block model and the particles of the snow body model. Specifically, by executing at least one of the following steps S103, S104, and S105, the coupled analysis of the block model and the snow body model is performed taking into account the above-mentioned functions.

[0094] In step S103, a discontinuity analysis is performed. The discontinuity analysis in step S103 is an analysis of discontinuities in the snow body model described above. In step S104, a friction force analysis is performed. The friction force analysis in step S104 is an analysis of friction applied to each particle of the snow body model described above. In step S105, an adhesion force analysis is performed. The adhesion force analysis in step S105 is an analysis of adhesion of particles of the snow body model described above to the block model.

[0095] Next, in step S106, a coupled analysis is performed on the structure of the block model and snow body model based on the results of executing at least one of the processes in steps S103 to S105. That is, the element surfaces of the FEM and the particles in the particle method are coupled by the interaction force derived in the MPM method. For example, the structural coupling between the block model and the snow body model is performed by the interaction force between the surface of the block model and the particles of the snow body model, for example, taking into account the pressure gradient.

[0096] The coupled block model and snow body model may be output as described above. In this case, data showing each model may be output to the display unit 40J or to an external device. The output process for outputting the block model and snow body model may be included in each of the above steps or in a specific step.

[0097] The processing process of step S101 shown in FIG. 15 is an example of the function of the model generation unit 11 shown in FIG. 1, and the processing process of step S102 is an example of the function of the rolling / shear analysis unit 12. Furthermore, the processing processes of steps S103 to S106 are an example of the function of the coupled analysis unit 13. The processing process of step S103 is an example of the function of the discontinuity analysis unit 14, the processing process of step S104 is an example of the function of the friction force analysis unit 15, and the processing process of step S105 is an example of the function of the adhesion force analysis unit 16. Furthermore, the processing process of step S106 is an example of the basic processing function of the coupled analysis unit 13.

[0098] The behavior analysis device 10 of the present disclosure may output the interaction force, such as a physical quantity such as a friction force, derived between the first continuum model and the second continuum model in correspondence with a predetermined index value of friction performance.

[0099] As described above, the behavior analysis device of this embodiment makes it possible to, for example, clarify the behavior mechanism of snow bodies in terms of patterns and block friction on the snow bodies, examine partial collapse of snow bodies, and also clarify friction phenomena.

[0100] [Variations] In the above embodiment, a case where a block made of rubber material formed into a hexahedron is used as an example of the first continuum has been described, but the present invention is not limited to a single block. It can also be applied to a tire model that models a tire.

[0101] Figure 16 shows a schematic diagram of a tire moving on a snowy road surface. As shown in Figure 16, when a tire moves on a snowy road surface, only a part of the tire comes into contact with the snowy road surface. Therefore, by modeling the tire instead of a block, cutting out a part of the tire model, and rotating and moving the cut-out block model of the tire, it becomes possible to analyze the behavior of the tire model rolling and shearing on a snowy road surface by performing an analysis in the same way as in the above embodiment.

[0102] In the above embodiment, an example of application to a display device such as a display has been described as the display unit 40J, but the display unit 40J may be an audio output device, or a display device and an audio output device may be combined.

[0103] Although the technology of the present disclosure has been described above using embodiments, the technical scope of the technology of the present disclosure is not limited to the scope described in the above embodiments. Various changes or improvements can be made to the above embodiments without departing from the gist of the technology, and forms incorporating such changes or improvements are also included in the technical scope of the disclosed technology.

[0104] In the above embodiment, the processing is performed by executing a program stored in an auxiliary storage device, but at least a part of the processing of the program may be realized by hardware. The processing flow of the program described in the above embodiment is also an example, and unnecessary steps may be deleted, new steps may be added, or the processing order may be changed within the scope of the gist.

[0105] Furthermore, in order to execute the processing in the above-described embodiment by a computer, a program in which the above-described processing is written in code that can be processed by a computer may be stored on a storage medium such as an optical disk and distributed.

[0106] In the above-described embodiment, a CPU is used as an example of a general-purpose processor. However, in the above-described embodiment, the term "processor" refers to a processor in a broad sense, and includes general-purpose processors (e.g., CPU: Central Processing Unit, etc.) and dedicated processors (e.g., GPU: Graphics Processing Unit, ASIC: Application Specific Integrated Circuit, FPGA: Field Programmable Gate Array, programmable logic device, etc.).

[0107] Furthermore, the operation of the processor in the above-described embodiments may not only be performed by a single processor, but may also be performed by multiple processors working together, or may be performed by multiple processors located in physically separate locations working together.

[0108] All publications, patent applications, and technical standards mentioned in this specification are herein incorporated by reference to the same extent as if each individual publication, patent application, or technical standard was specifically and individually indicated to be incorporated by reference. [Explanation of symbols]

[0109] 10. Continuum behavior analysis device 11 Model Generation Unit 12 Rolling and Shear Analysis Section 13 Coupled analysis section 14 Discontinuous Analysis Section 15 Friction force analysis section 16 Adhesion force analysis section 40 Computer 40E Auxiliary Storage Device 40EP Analysis Program

Claims

1. a setting unit that sets a deformable first continuum model of a predetermined shape divided into a large number of elements of a predetermined element size, a second continuum model formed by an assembly of a plurality of particles of a predetermined size that are capable of contacting at least a portion of the first continuum model and that represent a fluid that includes at least an elastic-plastic body or a plastic body capable of plastic deformation, and a contact condition related to contact between the first continuum model and the second continuum model; a rolling / shearing calculation execution unit that brings a part of the first continuum model into contact with the second continuum model, moves the first continuum model and the second continuum model relatively in a predetermined direction by a predetermined movement amount, and executes a rolling / shearing calculation based on the contact condition set by the setting unit; a coupling unit that derives an interaction force between a plurality of particles of the second continuum model and an element of the first continuum model, which occurs between the first continuum model and the second continuum model, based on a calculation result of the rolling / shearing calculation, and couples the first continuum model and the second continuum model based on the derived interaction force; Equipped with A third continuum model formed by a collection of a plurality of particles of a predetermined size representing a fluid including at least an elastic-plastic body capable of plastic deformation or a plastic body is attached to a portion of the first continuum model; The coupling portion is when a part of the first continuum model and the second continuum model are brought into contact with each other, the second continuum model and the third continuum model are treated as different continua with a discontinuity surface therebetween. Continuum behavior analysis device.

2. The first continuum model is a model that can be analyzed using a lattice method; The second continuum model is a model that can be analyzed using a particle method based on a material point method. The apparatus for analyzing behavior of a continuum according to claim 1 .

3. The first continuum model applies a block model representing an elastic body, The second continuum model applies a fluid model representing a fluid including at least snow. The apparatus for analyzing behavior of a continuum according to claim 2 .

4. The block model is a tire model showing a part of a tire, The fluid model applies a snowy road surface model representing a snowy road surface. The apparatus for analyzing behavior of a continuum according to claim 3.

5. The contact condition is a condition indicating that the first continuum model penetrates the second continuum model; and a condition related to friction between the first continuum model and the second continuum model; The coupling portion is Deriving an interaction force including a repulsive force and a frictional force based on an amount of penetration between the first continuum model and the second continuum model. The behavior analysis device for a continuum according to any one of claims 1 to 4.

6. The coupling portion is The particles of the second continuum model are in contact with or at a predetermined distance from the surface of the first continuum model. and applying an adhesive force that causes the particles of the second continuum model to adhere to the surface of the first continuum model when the particles of the second continuum model approach each other and then separate from each other after contact or approaching each other. The behavior analysis device for a continuum according to any one of claims 1 to 5.

7. The coupling unit obtains an index value of friction performance based on an interaction force between the first continuum model and the second continuum model. The behavior analysis device for a continuum according to any one of claims 1 to 6.

8. The computer setting a deformable first continuum model of a predetermined shape divided into a large number of elements of a predetermined element size, a second continuum model formed by an assembly of a plurality of particles of a predetermined size that are capable of contacting at least a portion of the first continuum model and that represent a fluid that includes at least an elastic-plastic body or a plastic body capable of plastic deformation, and a contact condition related to contact between the first continuum model and the second continuum model; a rolling and shearing calculation is performed based on the contact condition set by bringing a part of the first continuum model into contact with the second continuum model and relatively moving the first continuum model and the second continuum model by a predetermined movement amount in a predetermined direction; deriving an interaction force between a plurality of particles of the second continuum model and an element of the first continuum model that occurs between the first continuum model and the second continuum model based on a calculation result of the rolling / shear calculation, and coupling the first continuum model and the second continuum model based on the derived interaction force; A third continuum model formed by a collection of a plurality of particles of a predetermined size representing a fluid including at least an elastic-plastic body capable of plastic deformation or a plastic body is attached to a portion of the first continuum model; When the first continuum model and the second continuum model are coupled, when a part of the first continuum model and the second continuum model are brought into contact with each other, the second continuum model and the third continuum model are treated as different continua with a discontinuity surface therebetween. A method for analyzing the behavior of continuums.

9. A program for analyzing the behavior of a continuum, comprising: setting a deformable first continuum model of a predetermined shape divided into a large number of elements of a predetermined element size, a second continuum model formed by an assembly of a plurality of particles of a predetermined size that are capable of contacting at least a portion of the first continuum model and that represent a fluid that includes at least an elastic-plastic body or a plastic body capable of plastic deformation, and a contact condition related to contact between the first continuum model and the second continuum model; a rolling and shearing calculation is performed based on the contact condition set by bringing a part of the first continuum model into contact with the second continuum model and relatively moving the first continuum model and the second continuum model by a predetermined movement amount in a predetermined direction; deriving an interaction force between a plurality of particles of the second continuum model and an element of the first continuum model that occurs between the first continuum model and the second continuum model based on a calculation result of the rolling / shear calculation, and coupling the first continuum model and the second continuum model based on the derived interaction force; A third continuum model formed by a collection of a plurality of particles of a predetermined size representing a fluid including at least an elastic-plastic body capable of plastic deformation or a plastic body is attached to a portion of the first continuum model; When the first continuum model and the second continuum model are coupled, when a part of the first continuum model and the second continuum model are brought into contact with each other, the second continuum model and the third continuum model are treated as different continua with a discontinuity surface therebetween. A program for causing a computer to execute processes including the above.

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