Continuum behavior analysis device, continuum behavior analysis method, and program

Abstract

To improve behavioral analysis accuracy compared to the case that behavioral analysis of a continuum when a plurality of different continua including a continuum capable of phase-changing contact each other, is performed by using FEM and a particle method.SOLUTION: A behavior analysis device 10 is configured to: generate a block model modeled by using a spline function and an ice body model which contacts the block model; execute rolling motion calculation on the basis of application conditions related to friction between the block model and the ice body model; derive heat energy between the block model and the ice body model on the basis of a calculation result of the rolling motion calculation; derive phase change particles in the ice body model by the heat energy; continuously form the ice body model on the basis of an interaction force among the particles of the ice body model; and continuously form the block model and the ice body model on the basis of an interaction force between the plurality of models of the continuously formed ice body model and the block 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] There is a technology that predicts friction on ice due to thermal-fluid-structure coupling using a block model in which the tread portion of a tire with a tread pattern is modeled using the finite element method (FEM) and an ice body model in which the icy road surface is modeled using a particle method (see, for example, Patent Document 1).

[0003] Furthermore, there is a technology that discloses coupling between an object modeled using IGA (Isogeometric Analysis) and an object modeled using a particle method (see, for example, Non-Patent Document 1).

[0004] There is a technology that uses a particle method numerical analysis method to perform a simulation that discretizes the motion of a continuum such as a fluid or a solid into particle motion (see, for example, Non-Patent Document 2). [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Japanese Patent Application Publication No. 2020-168920 [Non-patent literature]

[0006] [Non-Patent Document 1] Wei Gao, Takuya Matsunaga, Guangtao Duan, Seiichi Koshizuka, A coupled 3D isogeometric / least-square MPS approach for modeling fluid-structure interactions, Computer methods in applied mechanics and engineering, 373, (2021). [Non-patent document 2] SA Silling, “Stability of peridynamic correspondence material models and their particle discretizations”, Computer methods in applied mechanics and engineering, Vol. 322, pp. 42-57 (2017) Summary of the Invention [Problem to be solved by the invention]

[0007] For example, when FEM is applied to modeling a three-dimensional object with curved surfaces as shown in Figure 13, it is difficult to represent a complex and smooth object using FEM, so the curved surface is approximated by straight lines as shown in Figure 14. This can result in a problem where the frictional force on the ice between the block model and the ice body model deviates from the actual value.

[0008] Furthermore, in coupling between an object modeled using IGA and an object modeled using particle methods, phase changes in objects modeled using particle methods (e.g., ice models) have not been taken into account until now.

[0009] The present disclosure has been made in consideration of the above facts, and aims to provide a continuum behavior analysis device, a continuum behavior analysis method, and a program that can improve the accuracy of behavior analysis when multiple different continua, including a phase-changeable continuum, come into contact with each other, compared to when the behavior analysis is performed using FEM and a particle method. [Means for solving the problem]

[0010] A first aspect of the present disclosure provides a method for manufacturing a continuum model, the method comprising: generating a first continuum model in which a shape is modeled using a spline function; and generating a second continuum model formed by an assembly of a plurality of particles of a predetermined size that are contactable with at least a portion of the first continuum model and each exhibit a solid phase;

[0011] a rolling analysis 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 amount, and performs a rolling calculation based on an applied condition related to friction between the first continuum model and the second continuum model; a derivation unit that derives thermal energy generated between the first continuum model and the second continuum model based on a calculation result of the rolling calculation, and derives phase change particles in the second continuum model that change from a solid phase to a liquid phase using the derived thermal energy; and a coupling unit that converts the phase of the phase change particles in the second continuum model into a liquid phase, couples the second continuum model based on an interaction force between particles of the second continuum model, and couples the first continuum model and the second continuum model based on an interaction force between the coupled particles of the second continuum model and the first continuum model.

[0012] According to the first aspect, when a plurality of different continua, including a phase-changeable continuum, come into contact with each other, the behavior analysis accuracy can be improved compared to when the behavior analysis is performed using FEM and a particle method.

[0013] A second aspect of the present disclosure is a behavior analysis device according to the first aspect, wherein the first continuum model is a model that can be analyzed using IGA, and the second continuum model is a model that can be analyzed using a particle method.

[0014] According to the second aspect, it becomes possible to analyze a continuum using different analytical methods such as IGA and particle method.

[0015] A third aspect of the present disclosure is a behavior analysis device according to the second aspect, wherein the first continuum model is a curved surface model representing an elastic body, and the second continuum model is a fluid model that changes phase when thermal energy is applied.

[0016] According to the third aspect, it is possible to analyze the behavior of a deformable elastic body and a phase-changeable fluid.

[0017] A fourth aspect of the present disclosure is the behavior analysis device according to the third aspect, wherein the surface model is a tire model showing a part of a tire, and the fluid model is an icy road surface model showing an icy road surface.

[0018] According to the fourth aspect, it is possible to analyze the behavior of an icy road surface and a tire rolling on the icy road surface.

[0019] A fifth aspect of the present disclosure is a behavior analysis device according to any one of the first to fourth aspects, wherein at least one groove is provided on the contact surface of the first continuum model with the second continuum model, and the rolling analysis unit performs rolling calculations taking into account contact forces with other contact surface elements at integration points provided on contact surface elements constituting the contact surface of the first continuum model divided by the groove.

[0020] According to the fifth aspect, the coefficient of friction when the first continuum model and the second continuum model come into contact can be accurately predicted compared to when rolling calculations are performed without taking into account the contact force between the contact surface elements.

[0021] A sixth aspect of the present disclosure provides a method for generating a first continuum model whose shape is modeled using a spline function, and a second continuum model formed by an assembly of a plurality of particles of a predetermined size that are contactable with at least a portion of the first continuum model and each exhibit a solid phase, bringing a portion 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 amount in a predetermined direction, performing a rolling calculation based on an applied condition related to friction between the first continuum model and the second continuum model, and, based on a result of the rolling calculation, a first continuum model and a second continuum model; a second continuum model that is coupled to the first continuum model based on an interaction force between the first continuum model and the second continuum model; a second continuum model that is coupled to the second continuum model based on an interaction force between the first continuum model and the second continuum model; a second continuum model that is coupled to the second continuum model based on an interaction force between the first continuum model and the second continuum model; a second continuum model that is coupled to the second continuum model based on an interaction force between the first continuum model and the second continuum model; a first continuum model that is coupled to the second continuum model based on an interaction force between the first continuum model and the second continuum model; a second ...

[0022] A seventh aspect of the present disclosure provides a method for generating, in a computer, a first continuum model whose shape is modeled using a spline function, and a second continuum model formed by an assembly of a plurality of particles of a predetermined size that are contactable with at least a portion of the first continuum model and each exhibit a solid phase; bringing a portion of the first continuum model into contact with the second continuum model, and moving the first continuum model and the second continuum model relatively in a predetermined direction by a predetermined movement amount; performing a rolling calculation based on an applied condition related to friction between the first continuum model and the second continuum model; and calculating a rolling coefficient based on a calculation result of the rolling calculation. The program executes a process of deriving thermal energy generated between the first continuum model and the second continuum model based on the thermal energy, deriving phase change particles that change from a solid phase to a liquid phase in the second continuum model using the derived thermal energy, converting the phase of the phase change particles in the second continuum model into a liquid phase, coupling the second continuum model based on an interaction force between particles of the second continuum model, and coupling the first continuum model and the second continuum model based on an interaction force between the first continuum model and a plurality of particles of the coupled second continuum model. [Effects of the Invention]

[0023] According to the present disclosure, the accuracy of behavior analysis can be improved when multiple different continua, including a phase-changeable continuum, come into contact with each other, compared to when the behavior analysis is performed using FEM and particle methods. [Brief explanation of the drawings]

[0024] [Figure 1] FIG. 1 illustrates an example of the configuration of a behavior analysis device. [Figure 2] 1 is a schematic cross-sectional view showing an example of main components constituting a patterned tire. FIG. [Figure 3] This is an example of a block model and an ice body model. [Figure 4] FIG. 10 is an explanatory diagram relating to the derivation of the interaction force acting between the elements of the block model and the particles of the ice body model. [Figure 5] FIG. 10 is an image diagram showing an example of a phase change model. [Figure 6] FIG. 1 is a conceptual diagram of thermal coupling between a block model and an ice body model. [Figure 7] FIG. 1 is a conceptual diagram of the structural coupling between a block model and an ice body model. [Figure 8] FIG. 1 is a block diagram illustrating an example of a schematic configuration of a computer that functions as a behavior analysis device. [Figure 9] 10 is a flowchart illustrating an example of the flow of a behavior analysis process. [Figure 10] FIG. 10 is a perspective view of a block model and an ice body model when moved on the ice body model. [Figure 11] FIG. 10 is a diagram showing an example of contact force between sipes. [Figure 12] FIG. 10 is a diagram showing an example of the coefficient of friction on ice predicted by coupling a block model and an ice body model. [Figure 13] 1A and 1B are diagrams illustrating examples of the shape of a three-dimensional object having a curved surface. [Figure 14] FIG. 1 is a diagram showing an example of the shape of a three-dimensional object having a curved surface modeled by FEM. DETAILED DESCRIPTION OF THE INVENTION

[0025] Hereinafter, the present embodiment will be described with reference to the drawings. The same components and processes are denoted by the same reference numerals throughout the drawings, and duplicated explanations will be omitted. The dimensional proportions in the drawings are exaggerated for the sake of explanation, and may differ from the actual proportions.

[0026] 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.

[0027] In this embodiment, a case will be described in which the technology of the present disclosure 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 a plurality of continua, including a specific continuum that undergoes a phase change due to thermal energy caused by forces such as frictional forces that occur during the contact, is analyzed.

[0028] Among the multiple continuum, a first continuum is a continuously formed material that does not undergo a phase change upon application of energy, for example, at room temperature. The first continuum includes at least an elastic body. The elastic body may be any material having 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 will be described (details will be described later). Note that, in this embodiment, a case where a rubber material is used as the first continuum will be described, but the first continuum is not limited to a rubber material, and the technology of the present disclosure can of course be applied to cases where other elastic bodies, such as a polyurethane material or a polymer material, are used.

[0029] Furthermore, among the multiple continua, a second continuum different from the first continuum is formed continuously from a material that undergoes a phase change upon application of a predetermined energy, for example, from a solid phase to a liquid phase. The second continuum may be, for example, a rigid body such as ice or an elastic body such as a rubber material. In this embodiment, as an example of the second continuum, a case is described in which a rigid body that becomes ice when liquid water solidifies under a normal predetermined temperature environment is formed into a plate-like ice body having an ice surface. Note that, although this embodiment describes a case in which an ice body is used as the second continuum, the second continuum is not limited to an ice body, and the technology of the present disclosure can of course be applied to cases in which a material containing another material that undergoes a phase change upon application of a predetermined energy is used. Furthermore, in this embodiment, a case is described in which a second continuum made of a material that undergoes a phase change from a solid phase to a liquid phase is used, but the phase change is not limited to a solid phase to a liquid phase, and the technology of the present disclosure can of course be applied to a material that undergoes a phase change between any two of a solid phase, a liquid phase, and a gas phase.

[0030] In this embodiment, a numerical analysis method is used for the analysis process of analyzing the behavior of the continuum. Isogeometric analysis (IGA) is used to analyze the behavior of the rubber material, which is the first continuum.

[0031] IGA uses spline functions to represent the shape of an object whose behavior is to be analyzed. IGA has a high affinity with CAD (Computer-Aided Design), and not only can it reduce the time and effort required for element division compared to FEM, but it can also analyze the shape expressed in CAD as is, which improves the reproducibility of the object's shape and improves the accuracy of the analysis.

[0032] A particle method is used to analyze the behavior of ice bodies, which are the second continuum. When analyzing ice bodies, solid-phase ice bodies are analyzed using the Peridynamics method (details will be described later). On the other hand, melted liquid-phase ice bodies are analyzed using the Moving Particle Simulation (MPS) method (details will be described later). The particle method for analyzing the second continuum is not limited to the Peridynamics method and the MPS method, and other particle methods may also be used.

[0033] As shown in FIG. 1, the behavior analysis device 10 includes a model generation unit 11, a rolling analysis unit 12, a thermal analysis unit 13, a thermal coupling analysis unit 14, a phase change particle derivation unit 15, a particle coupling analysis unit 16, and a structural coupling analysis unit 17.

[0034] The model generation unit 11 is a functional unit that models blocks and ice bodies on a frozen road surface to generate block models and ice body models, and is an example of a generation unit in the present disclosure. The blocks are objects that make up, for example, the tread portion 58 of a patterned tire.

[0035] An example of the structure of a patterned tire will now be described. Fig. 2 is a schematic cross-sectional view showing an example of main components that form a patterned tire 60.

[0036] As shown in Fig. 2, the patterned tire 60 has a carcass ply 42 for maintaining an internal pressure shape. The carcass ply 42 is made of, for example, organic fiber cords and forms the framework of the tire 60. The carcass ply 42 is also called a "carcass" or a "ply." Hereinafter, the carcass ply 42 will be referred to as a "ply 42."

[0037] The ply 42 is folded back by a bead core 44 for fixing the patterned tire 60 to a rim (not shown). In the patterned tire 60, a bead rubber 46 is arranged radially inward of the bead core 44, thereby forming a bead portion 48 at the tip end on the radially inward side of the tire. In the patterned tire 60, a bead filler 50 that maintains the rigidity of the bead portion 48 is arranged within a triangular region formed by folding back the ply 42, and a side tread 52 for protecting the ply 42 is arranged on the outer side of the ply 42. In the patterned tire 60, a belt 54 is arranged radially outward of the ply 42, and a tread 56 is arranged on the radially outer surface of the belt 54. In the tread 56, the region where a pattern (also referred to as a "tread pattern") is formed forms a tread portion 58. As an example of the patterned tire 60, a tubeless tire is used, and an inner liner (not shown) for maintaining internal pressure airtightness is arranged inside the ply 42.

[0038] At least one groove (hereinafter referred to as a "sipe") is provided on the contact surface of the tread portion 58 that comes into contact with the ice model, increasing the contact area with the ice model and increasing frictional force.

[0039] The model generation unit 11 models the block model, which is the first continuum, using a spline function. The spline function used for modeling is not particularly limited, but examples include a Bezier curve, a T-spline, and a B-spline. A Bezier curve is an N-1 degree curve obtained from N control points (also called "control points"). A T-spline is a type of mathematical model used to generate free-form surfaces in computer graphics, and has T-shaped control points. A B-spline is a smooth curve defined by a given number of control points and knot vectors.

[0040] The second continuum, the ice model (also called the "ice road surface model"), is formed by a collection of multiple particles of a predetermined size to enable analysis using the particle method. The ice model uses the Peridynamics method, which is a particle method. The Peridynamics method uses non-ordinary state-based peridynamics, which has no restrictions on constitutive laws, but when it is necessary to add a stabilization term, a well-known stabilization method (see, for example, Non-Patent Document 2) is used (see the following equation).

[0041]

number

[0042] where ρ is the density, V is the volume, b is the volume force, w is the weight function, r is the parametric coordinate, P is the first-order Kirchhoff stress, B is the shape tensor, G is a constant, and H is the deformation gradient tensor.

[0043] For the molten liquid (water) described later, the MPS method, which is one of the particle methods, is used. There are two types of MPS methods: the semi-implicit MPS method, which solves the pressure gradient term of the Navier-Stokes equations semi-implicitly, and the explicit MPS method, which solves it explicitly. In this embodiment, coupling with the IGA and Peridynamics method is considered, so the explicit MPS method, which is easy to couple, is used.

[0044]

number

[0045] Here, c is not the speed of sound but a fictitious value.

[0046] Fig. 3 shows an example of a block model and an ice body model generated by the model generation unit 11. The example shown in Fig. 3 shows a block model in which two hexahedrons are connected on a plate, and an ice body model in which particles of a predetermined size are arranged vertically, horizontally, and vertically.

[0047] The rolling analysis unit 12 shown in Fig. 1 is a functional unit that performs rolling analysis by bringing a block model into contact with an ice body model and moving the block model relative to the ice body model. Rolling analysis is a process required to analyze changes that occur when the block model in contact with the ice body model is moved relative to the ice body model, particularly physical quantities related to friction, contact pressure, etc.

[0048] Specifically, the contact pressure generated between the block model and the ice body model, and the amount of relative movement between the block model and the ice body model are set using the block model and the ice body model generated by the model generation unit 11. The setting of this amount of movement is a restriction to maintain accuracy when performing a rolling analysis in which the block model is brought into contact with the ice body model and the block model is moved relative to the ice body model.

[0049] More specifically, by moving the block model while it is in contact with the ice body model, it is possible to obtain information such as stress, strain, and slippage for any contact surface element or control point of the block model that is in contact with the ice body model. For example, it is possible to determine the friction energy from the force and slippage of the calculation points set on the contact surface element and understand the distribution of friction performance (details will be explained later).

[0050] As described above, sipes are provided on the contact surface of the block model that comes into contact with the ice body model, and therefore the contact surface of the block model with the ice body model is composed of multiple contact surface elements divided by the sipes.

[0051] When the block model moves relative to the ice body model, the contact surface elements deform, which changes the contact force between the contact surface elements. The rolling analysis unit 12 analyzes physical quantities related to friction, contact pressure, etc., taking into account the contact force between the contact surface elements.

[0052] The rolling analysis unit 12 moves at least one of the block model and the ice body model in a predetermined direction (for example, vertically or in the opposite direction) to bring the block model and the ice body model closer together and into contact. In this case, it is assumed that the block model approaches (flatly pushes) the ice body model horizontally. This flat push is controlled by a load value or deflection amount. Next, the block model is moved relative to the ice body model in a direction intersecting the above-mentioned predetermined direction (for example, horizontally) by the above-mentioned set movement amount. The flat push and horizontal movement cause friction between the block model and the ice body model. Due to the frictional force generated between the block model and the ice body model, the constraint of the block model is released and the block model moves.

[0053] The thermal analysis unit 13 is a functional unit that derives the thermal energy generated in the block model and the ice body model based on the physical quantities of the analysis results in the rolling analysis unit 12.

[0054] Specifically, the thermal analysis unit 13 derives the frictional heat generated by the frictional force between the elements of the block model (i.e., contact surface elements) and the particles of the ice body model (i.e., particles in the particle method). In this embodiment, a friction model based on Coulomb friction, as shown below, is introduced between the elements of the block model and the particles of the ice body model. In addition, the frictional heat is calculated from the frictional force F and the sliding velocity v, and the calculated frictional heat is applied as heat generation to the elements of the block model and the particles of the ice body model, respectively.

[0055]

number

[0056] where μ is the coefficient of friction.

[0057] The thermal coupling analysis unit 14 is a functional unit that performs a thermal coupling analysis between the block model and the ice body model.

[0058] Specifically, the thermal coupling analysis unit 14 performs coupling by deriving the interaction force acting between the elements of the block model and the particles of the ice body model. More specifically, as shown in Fig. 4, calculations are performed by providing the interaction of the following equation between a particle in the particle method and the contact surface element of the block model that is closest to the particle. Note that virtual particles (hereinafter referred to as "virtual particles") are generated in the elements of the block model to perform the coupled analysis.

[0059]

number

[0060] where k is the thermal conductivity between the contact surface element and the particle, λ is a coefficient for matching the statistical variance increase in the Laplacian model of the MPS method with the analytical solution, T is the temperature, and j is the virtual particle generated in the contact surface element.

[0061] The phase change particle deriving unit 15 is a functional unit that derives particles that undergo a phase change due to heat given to each particle of the ice body model.

[0062] Specifically, the phase change particle deriving unit 15 sets the phase of the particles using the phase change model shown in Fig. 5. In the example shown in Fig. 5, as the energy increases, the temperature rises, and when the energy Eth and temperature Tth are reached, the phase changes from solid to liquid. This phase change particle deriving unit 15 is an example of a deriving unit.

[0063] The particle coupling analysis unit 16 is a functional unit that performs thermal coupling analysis of each particle of the ice body model.

[0064] Specifically, the particle coupling analysis unit 16 performs structural coupling between solid phase particles (hereinafter referred to as Peridynamics particles) and liquid phase particles (hereinafter referred to as MPS particles) as particles of the ice body model.More specifically, to couple the MPS particles and the Peridynamics particles, a calculation method is used that takes into account the pressure gradient term of the Navier-Stokes equations in the MPS method, where the pressure gradient based on the particle number density is used as the interaction force, and coupling is performed by calculating the interaction force using the following equation.

[0065]

number

[0066]

number

[0067] where p is pressure, d m is the number of dimensions, n 0 is the reference particle number density, and w is a weighting function. However, the pressure in the above equation is not the actual pressure, but a pressure for coupling, and is calculated using the following equation using a virtual sound speed c.

[0068]

number

[0069] The thermal coupling between the block model and ice model described above has the relationship shown in Figure 6. Specifically, the block model is analyzed using IGA, the solid-phase ice model is analyzed using the Peridynamics method, and the liquid-phase ice model is analyzed using the MPS method. Note that when analyzing an ice model, if ice deformation or cracks are taken into consideration, the Peridynamics method is used as described above. However, if ice deformation or cracks are not taken into consideration, the ice may be modeled using rigid particles. The thermal coupling between the block model and the ice model made of solid-phase particles is achieved by frictional heat generated by friction between the block model elements and the solid-phase particles. The thermal coupling between the solid-phase particles and the liquid-phase particles in the ice model is achieved using a phase change model. The thermal coupling between the block model elements and the ice model made of liquid-phase particles is achieved by the interaction force between virtual particles generated in the block model elements and the liquid-phase particles.

[0070] The structural interaction analysis unit 17 is a functional unit that performs a structural interaction analysis between the block model and the ice body model.

[0071] Specifically, the structural interaction analysis unit 17 couples the contact surface elements, which are the element surfaces of the block model, and the particles in the particle method by introducing an interaction force that takes into account the pressure gradient term in the MPS method. The interaction force is calculated using the following equation.

[0072]

number

[0073] Here, W is a virtual particle generated in the contact surface element of the block model that is closest to the particle (see Figure 4).

[0074] Therefore, the structural coupling between the block model and the ice model has the relationship shown in Figure 7. Specifically, the block model is analyzed using IGA, the solid-phase ice model is analyzed using the Peridynamics method, and the liquid-phase ice model is analyzed using the MPS method. The structural coupling between the block model and the ice model made up of solid-phase particles is achieved by an interaction force that takes into account the pressure gradient between the liquid-phase particles and the virtual particles generated on the contact surface elements that are the element surfaces of the block model. The structural coupling between the solid-phase particles and the liquid-phase particles in the ice model is achieved by an interaction force that takes into account the pressure gradient based on the particle number density. The structural coupling between the block model and the ice model made up of liquid-phase particles is achieved by an interaction force that takes into account the pressure gradient between the liquid-phase particles and the virtual particles generated on the contact surface elements that are the element surfaces of the block model.

[0075] The particle coupled analysis unit 16 and the structure coupled analysis unit 17 are an example of the coupling unit in the present disclosure.

[0076] The above-described behavior analysis device 10 can be realized by a computer system including a control unit configured by a general-purpose computer.

[0077] FIG. 8 shows an example of a schematic configuration of a computer 40 that can function as the behavior analysis device 10.

[0078] 8, a computer 40 functioning as the behavior analysis device 10 includes a computer main unit 40A. The computer main unit 40A includes a CPU 40B, which is an example of a processor, 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 to a bus 40G, enabling mutual exchange of data and commands. 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.

[0079] The auxiliary storage device 40E stores an analysis program 40EP for causing the computer main body 40A to function as the behavior analysis device 10 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 processing. As a result, the computer main body 40A that has executed the analysis program 40EP operates as the behavior analysis device 10 of the present disclosure.

[0080] The auxiliary storage device 40E stores various values used in the behavior analysis process in the behavior analysis device 10 as setting values 40ED. The analysis program 40EP may be provided from a recording medium such as a CD-ROM or by downloading from an external device via the communication unit 40K.

[0081] Next, the behavior analysis process in the behavior analysis device 10 realized by the computer 40 will be described.

[0082] 9 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.

[0083] First, in step S100, the CPU 40B models a block of an elastic body made of rubber material using a spline function, and generates a block model.

[0084] In step S102, the CPU 40B models the ice body and generates an ice body model.

[0085] The first continuum, the block model, is formed to include contact surface elements divided by sipes to enable analysis by IGA, while the second continuum, the ice body model, is formed by a collection of multiple particles of a predetermined size to enable analysis by particle method.

[0086] Specifically, the block model generation process shown in step S100 and the ice body model generation process shown in step S102 are processed in parallel. Note that the processes of steps S100 and S102 are not limited to parallel processing, as long as a block model and an ice body model can be obtained. Therefore, for example, steps S100 and S102 may be processed sequentially. Also, at least one of the block model and the ice body model may be generated in advance, and the generated data may be acquired instead of the model generation process.

[0087] In step S104, the CPU 40B brings the block model into contact with the ice body model and performs a rolling analysis of the block model being moved relative to the ice body model. The rolling analysis analyzes changes, particularly physical quantities related to friction, when the block model in contact with the ice body model is moved relative to the ice body model.

[0088] The contact force between the contact surface elements of the block model is also used in analyzing physical quantities related to friction. The CPU 40B sets an integration point on one of the contact surface elements and calculates the contact force between the contact surface elements at the set integration point by numerical integration. Since the contact surface element that is in contact at the integration point is the other contact surface element that is closest to the integration point (hereinafter referred to as the "neighboring point of the contact surface element with respect to the integration point"), the CPU 40B calculates the neighboring point of the contact surface element with respect to the integration point when calculating the contact force.

[0089] The neighboring points of the contact surface elements for the integration points are obtained by solving the following nonlinear equation:

[0090]

number

[0091] where d is the particle coordinate vector and x(r 1 ,r 2 ) is an arbitrary point on the contact surface element, and r 1 ,r 2 are parametric coordinates.

[0092] The CPU 40B calculates a restoring force when the contact surface elements are separated or overlapped due to the calculated contact force between the contact surface elements. g is calculated by the following formula:

[0093]

number

[0094] Here, K is the coefficient of the restoring force, and Δt is the time increment. N1 and N2 are the shape functions of the contact surface elements, and r1 and r2 are the parametric coordinates of the integration points of the contact surface elements. Also, x and X are the coordinates of the control point at the current time and the coordinates of the control point at the reference time, respectively, and S is the area of the contact surface. g g is a variable introduced to maintain a gap between the surfaces if there is one at the reference time. The forces f1 and f2 at the control points of the contact surface elements are calculated using the following equations:

[0095]

number

[0096] The CPU 40B calculates the following equation of motion from the calculated restoring force: The equation of motion is expressed by the following equation.

[0097]

number

[0098] where m is mass, a is acceleration, F int is the internal force, F ext is the external force, F tied is the restoring force.

[0099] After that, the CPU 40B determines whether the calculation is complete. If it determines that the calculation is not complete, the CPU 40B updates the time and recalculates the restoring force. That is, the CPU 40B analyzes physical quantities related to friction while moving the block model relative to the ice body model.

[0100] In the next step S106, the CPU 40B derives the thermal energy generated by contact between the block model and the ice body model based on the physical quantities obtained from the rolling analysis result of step S104. That is, the CPU 40B calculates the frictional heat generated by the frictional force between the elements of the block model and the particles of the ice body model from the frictional force F and the sliding velocity v, and applies the calculated frictional heat as heat generation to the elements of the block model and the particles of the ice body model, respectively.

[0101] In step S108, the CPU 40B performs a coupled analysis of heat between the block model and the ice body model, that is, coupling is performed by deriving the interaction force acting between the elements of the block model and the particles of the ice body model.

[0102] In step S110, the CPU 40B derives the melting state of the ice body model taking latent heat into consideration, that is, derives particles that undergo phase changes due to heat given to each particle of the ice body model. The phase changes of the particles are set using a phase change model (see FIG. 5).

[0103] In step S112, a coupled analysis is performed on the heat of each of the particles of the ice body model, which are the fluid (melted water) and the structure (ice body). That is, the structural coupling between the Peridynamics particles and the MPS particles as the particles of the ice body model is performed by calculating the interaction force, specifically, the interaction force is calculated using the pressure gradient based on the particle number density.

[0104] In step S114, the CPU 40B performs a coupled analysis of the structures of the block model and the ice body model. That is, coupling is performed by introducing an interaction force that takes into account the pressure gradient term in the MPS method between the contact surface elements, which are the element surfaces of the block model, and the particles in the particle method. This completes the behavior analysis process shown in Figure 9.

[0105] The coupled block model and ice 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 ice body model may be included in each of the above steps or a specific step.

[0106] The processing processes of steps S100 and S102 shown in Fig. 9 are an example of the function of the model generation unit 11 shown in Fig. 1, and the processing process of step S104 is an example of the function of the rolling analysis unit 12. Furthermore, the processing process of step S106 is an example of the function of the thermal analysis unit 13, the processing process of step S108 is an example of the function of the thermal coupled analysis unit 14, and the processing process of step S110 is an example of the function of the phase change particle derivation unit 15. Furthermore, the processing process of step S112 is an example of the function of the particle coupled analysis unit 16, and the processing process of step S114 is an example of the function of the structure coupled analysis unit 17.

[0107] Fig. 10 is a diagram showing an example of the block model and ice body model when moving on an ice body model that models an icy road surface, whose behavior was analyzed by the behavior analysis device 10. As shown in Fig. 10, the temperature of the icy road surface rises due to frictional heat between the blocks and the icy road surface, causing the ice to melt, and it is possible to see the state of water between the blocks and the icy road surface and water entering the sipes.

[0108] FIG. 11 shows an example of the results of compression and shear analysis of blocks. The horizontal axis of FIG. 11 represents time, and the vertical axis represents the contact force between sipes. Graph 20A in FIG. 11 shows the contact force between sipes calculated from a block model generated using FEM. Graph 20B in FIG. 11 shows the contact force between sipes calculated from a block model generated using IGA. Note that the actual contact force between sipes shows values closer to those shown in Graph 20B than those shown in Graph 20A. This is thought to be because, unlike IGA, which uses a spline function to create a curved surface, the block model using FEM forcibly approximates the originally curved surface with a straight line, resulting in a larger contact force between sipes than the evaluation by IGA.

[0109] Figure 12 shows an example of the coefficient of friction on ice predicted by coupling a block model generated using IGA with an ice model using particle methods, following the behavior analysis process shown in Figure 9. The horizontal axis of Figure 12 represents time, and the vertical axis represents friction coefficient. Graph 20C in Figure 12 also shows the change in friction coefficient over time. The coefficient of friction on ice predicted by the behavior analysis process shown in Figure 9 tends to be closer to the actual coefficient of friction on ice than the coefficient of friction on ice predicted by coupling a block model generated using FEM with an ice model using particle methods. This is because the difference in the evaluation of the contact force between the sipes between IGA and FEM, as explained above, is reflected in the prediction of the coefficient of friction on ice.

[0110] When a liquid such as water enters a groove such as a sipe in a block, the continuous inflow of the liquid can cause the groove to fill with the liquid, resulting in a saturated state. On the other hand, when the block and ice body are moved relative to each other, particles in the ice body that the block comes into contact with may pass through the groove, such as a sipe. Therefore, it is preferable to set particle inflow and outflow boundaries in the block model. The particle inflow boundary is a boundary region that simulates the inflow of particles into the block model by providing an area in a part of the space, such as a groove, where particles are generated. The particle outflow boundary is a boundary region that simulates the outflow of particles from a part of the space, such as a groove, where particles are eliminated. By setting particle inflow and outflow boundaries, the behavior of the block model and the ice body model can be analyzed in two dimensions.

[0111] The behavior analysis device 10 of the present disclosure may output the physical quantities, such as the interaction force derived between the first continuum model and the second continuum model, such as the friction force and sliding velocity, in correspondence with a predetermined index value of friction performance. Furthermore, since the derived thermal energy is primarily a function of friction, the derived thermal energy may be associated with a predetermined index value of friction performance. This makes it possible to evaluate the friction performance of the block.

[0112] As described above, the behavior analysis device 10 of the present disclosure makes it possible to clarify the mechanism by which water appears in patterns and block friction on ice, to consider how grooves and sipes can improve the water drainage effect, and to clarify friction phenomena.

[0113] Furthermore, the disclosed form of the behavior analysis device 10 is an example, and the form of the behavior analysis device 10 is not limited to the scope described in the embodiment. Various changes or improvements can be made to the embodiment without departing from the gist of the present disclosure, and forms of the behavior analysis device 10 with such changes or improvements are also included in the technical scope of the disclosure.

[0114] In the above embodiment, as an example, the behavior analysis process shown in FIG. 9 is implemented by software. However, the same process as the flowchart of the behavior analysis process may be executed by hardware. In this case, the processing speed is increased compared to when the behavior analysis process is implemented by software. Furthermore, the processing flow in the behavior analysis process is an example, and unnecessary processes may be deleted, new processes may be added, or the processing order may be changed within the scope of the present invention.

[0115] In the embodiment, CPU 40B has been used as an example of a general-purpose processor, but in the embodiment, the term "processor" refers to a processor in a broad sense, and includes not only general-purpose processors such as CPU 40B, but also dedicated processors (e.g., GPU: Graphics Processing Unit, ASIC: Application Specific Integrated Circuit, FPGA: Field Programmable Gate Array, programmable logic device, etc.).

[0116] 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.

[0117] 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.

[0118] The following are additional notes related to this embodiment.

[0119] (Appendix 1) a generator that generates a first continuum model in which a shape is modeled using a spline function, and a second continuum model that is contactable with at least a portion of the first continuum model and is formed by an assembly of a plurality of particles of a predetermined size each of which exhibits a solid phase; a rolling analysis 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 calculation based on an applied condition related to friction between the first continuum model and the second continuum model; a derivation unit that derives thermal energy generated between the first continuum model and the second continuum model based on a result of the rolling calculation, and derives phase change particles that change from a solid phase to a liquid phase in the second continuum model by the derived thermal energy; a coupling unit that converts the phase of the phase change particles of the second continuum model into a liquid phase, couples the second continuum model based on an interaction force between particles of the second continuum model, and couples the first continuum model and the second continuum model based on an interaction force between a plurality of particles of the coupled second continuum model and the first continuum model; A continuum behavior analysis device equipped with the

[0120] (Appendix 2) the first continuum model is a model that can be analyzed using IGA, The second continuum model is a model that can be analyzed using a particle method. 2. The apparatus for analyzing the behavior of a continuum according to claim 1.

[0121] (Appendix 3) the first continuum model is a curved surface model representing an elastic body, The second continuum model is a fluid model that undergoes a phase change due to the addition of thermal energy. 3. The apparatus for analyzing the behavior of a continuum according to claim 2.

[0122] (Appendix 4) the curved surface model is a tire model showing a part of a tire, The fluid model is an ice road surface model that represents an ice road surface. 4. The apparatus for analyzing behavior of a continuum according to claim 3.

[0123] (Appendix 5) at least one groove is provided on a contact surface of the first continuum model with the second continuum model; The rolling contact analysis unit performs a rolling contact calculation in consideration of contact forces between the contact surface elements constituting the contact surface of the first continuum model divided by the grooves and other contact surface elements at integration points provided on the contact surface elements. The behavior analysis device for a continuum according to any one of Supplementary notes 1 to 4.

[0124] (Appendix 6) generating a first continuum model whose shape is modeled using a spline function, and a second continuum model formed by an assembly of a plurality of particles of a predetermined size that are in contact with at least a portion of the first continuum model and each of which represents a solid phase; bringing a part of the first continuum model into contact with the second continuum model, and moving the first continuum model and the second continuum model relatively in a predetermined direction by a predetermined movement amount; and performing a rolling calculation based on a given condition related to friction between the first continuum model and the second continuum model; deriving thermal energy generated between the first continuum model and the second continuum model based on a result of the rolling calculation; and deriving phase change particles that change from a solid phase to a liquid phase in the second continuum model by the derived thermal energy; A computer executes a process of converting the phase of the phase change particles of the second continuum model into a liquid phase, coupling the second continuum model based on an interaction force between particles of the second continuum model, and coupling the first continuum model and the second continuum model based on an interaction force between a plurality of particles of the coupled second continuum model and the first continuum model. Methods for analyzing the behavior of continuums.

[0125] (Appendix 7) On the computer, generating a first continuum model whose shape is modeled using a spline function, and a second continuum model formed by an assembly of a plurality of particles of a predetermined size that are in contact with at least a portion of the first continuum model and each of which represents a solid phase; bringing a part of the first continuum model into contact with the second continuum model, and moving the first continuum model and the second continuum model relatively in a predetermined direction by a predetermined movement amount; and performing a rolling calculation based on a given condition related to friction between the first continuum model and the second continuum model; deriving thermal energy generated between the first continuum model and the second continuum model based on a result of the rolling calculation; and deriving phase change particles that change from a solid phase to a liquid phase in the second continuum model by the derived thermal energy; A program for executing a process of converting the phase of the phase change particles of the second continuum model into a liquid phase, coupling the second continuum model based on an interaction force between particles of the second continuum model, and coupling the first continuum model and the second continuum model based on an interaction force between a plurality of particles of the coupled second continuum model and the first continuum model. [Explanation of symbols]

[0126] 10 Behavior analysis device 11 Model Generation Unit 12 Rolling Analysis Department 13 Thermal Analysis Department 14 Thermal coupling analysis department 15 Phase change particle extraction section 16 Particle interaction analysis department 17 Structural interaction analysis department 20A, 20B, 20C graphs 60 tires 40 Computer 40E Auxiliary Storage Device 40EP Analysis Program 40H Input section 40J Display section 40K Communications Department

Claims

1. a generating unit that generates a first continuum model in which a shape is modeled using a spline function, and a second continuum model that is contactable with at least a portion of the first continuum model and is formed by an assembly of a plurality of particles of a predetermined size, each of which exhibits a solid phase; a rolling analysis 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 calculation based on an applied condition related to friction between the first continuum model and the second continuum model; a derivation unit that derives thermal energy generated between the first continuum model and the second continuum model based on a result of the rolling calculation, and derives phase change particles that change from a solid phase to a liquid phase in the second continuum model by the derived thermal energy; a coupling unit that converts the phase of the phase change particles of the second continuum model into a liquid phase, couples the second continuum model based on an interaction force between particles of the second continuum model, and couples the first continuum model and the second continuum model based on an interaction force between a plurality of particles of the coupled second continuum model and the first continuum model; A continuum behavior analysis device equipped with the

2. the first continuum model is a model that can be analyzed using IGA, The second continuum model is a model that can be analyzed using a particle method. The behavior analysis device for a continuum according to claim 1 .

3. the first continuum model is a curved surface model representing an elastic body, The second continuum model is a fluid model that undergoes a phase change due to the addition of thermal energy. The behavior analysis device for a continuum according to claim 2 .

4. the curved surface model is a tire model showing a part of a tire, The fluid model is an ice road surface model that represents an ice road surface. The behavior analysis device for a continuum according to claim 3 .

5. at least one groove is provided on a contact surface of the first continuum model with the second continuum model; The rolling analysis unit performs a rolling calculation in consideration of contact forces between the contact surface elements constituting the contact surface of the first continuum model divided by the grooves and other contact surface elements at integration points provided on the contact surface elements. The behavior analysis device for a continuum according to any one of claims 1 to 4.

6. generating a first continuum model whose shape is modeled using a spline function, and a second continuum model formed by a collection of a plurality of particles of a predetermined size that are in contact with at least a portion of the first continuum model and each of which represents a solid phase; bringing a portion of the first continuum model into contact with the second continuum model, and moving the first continuum model and the second continuum model relatively in a predetermined direction by a predetermined movement amount; and performing a rolling calculation based on a given condition related to friction between the first continuum model and the second continuum model; deriving thermal energy generated between the first continuum model and the second continuum model based on a result of the rolling calculation; and deriving phase change particles that change from a solid phase to a liquid phase in the second continuum model by the derived thermal energy; A computer executes a process of converting the phase of the phase change particles of the second continuum model into a liquid phase, coupling the second continuum model based on an interaction force between particles of the second continuum model, and coupling the first continuum model and the second continuum model based on an interaction force between the first continuum model and a plurality of particles of the coupled second continuum model. Methods for analyzing the behavior of continuums.

7. On the computer, generating a first continuum model whose shape is modeled using a spline function, and a second continuum model formed by a collection of a plurality of particles of a predetermined size that are in contact with at least a portion of the first continuum model and each of which represents a solid phase; bringing a portion of the first continuum model into contact with the second continuum model, and moving the first continuum model and the second continuum model relatively in a predetermined direction by a predetermined movement amount; and performing a rolling calculation based on a given condition related to friction between the first continuum model and the second continuum model; deriving thermal energy generated between the first continuum model and the second continuum model based on a result of the rolling calculation; and deriving phase change particles that change from a solid phase to a liquid phase in the second continuum model by the derived thermal energy; A program for executing a process of converting the phase of the phase change particles of the second continuum model into a liquid phase, coupling the second continuum model based on an interaction force between particles of the second continuum model, and coupling the first continuum model and the second continuum model based on an interaction force between multiple particles of the coupled second continuum model and the first continuum model.

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