Calculation method, calculation device, program, and calculation model

Abstract

To easily calculate the behavior of particles.SOLUTION: A particle behavior calculation method performed by a computer includes setting a spring constant assuming that a particle is an aggregate of a plurality of components, two adjacent components are coupled by two spring coupling elements, and the two spring coupling elements have the same spring constant, setting a friction coefficient between the particle and a member outside the particle, and calculating a behavior based on the spring constant and the friction coefficient.SELECTED DRAWING: Figure 5

Description

[Technical Field]

[0001] The present invention relates to a calculation method for calculating particle behavior. [Background technology]

[0002] One method for calculating (analyzing) the behavior of particles that make up a material is the BPM (Bonded Particle Model), which is a type of DEM (Discrete Element Method). For example, Patent Document 1 discloses a method for constructing a particle model based on the BPM theory. Furthermore, Patent Document 2 discloses a fracture analysis model made up of a particle model. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Patent No. 6789274 [Patent Document 2] Patent No. 6093717 Summary of the Invention [Problem to be solved by the invention]

[0004] Conventional BPM has a problem in that eight mutually dependent parameters, such as normal stiffness and shear stiffness, must be set to calculate particle behavior.

[0005] The present invention has been made in view of the above-mentioned problems, and one of its objects is to make it possible to easily calculate the behavior of particles. [Means for solving the problem]

[0006] According to a first aspect of the present invention, a method for calculating particle behavior performed by a computer includes: setting a spring constant assuming that the particle is a collection of multiple components, two adjacent components are connected by two spring connection elements, and the two spring connection elements have the same spring constant; setting a friction coefficient between the particle and a member external to the particle; and calculating behavior based on the spring constant and the friction coefficient. According to a second aspect of the present invention, a computing device for calculating particle behavior includes a processing unit that sets a spring constant assuming that the particle is a collection of multiple components, two adjacent components are connected by two spring connecting elements, the two spring connecting elements have the same spring constant, sets a friction coefficient between the particle and a member external to the particle, and calculates the behavior based on the spring constant and the friction coefficient. According to a third aspect of the present invention, a program for causing a computer to calculate the behavior of a particle includes: setting a spring constant assuming that the particle is a collection of multiple components, two adjacent components are connected by two spring connecting elements, and the two spring connecting elements have the same spring constant; setting a friction coefficient between the particle and a member external to the particle; and calculating the behavior based on the spring constant and the friction coefficient. According to a fourth aspect of the present invention, a computational model for calculating the behavior of a particle comprises: a first coupling model in which the particle is an aggregate of a plurality of components, the center of the first component is coupled to the center of the second component adjacent to the first component, the first coupling model having a first spring coupling element; and a second coupling model in which a coupling point in the first component spaced apart from the center is coupled to a coupling point in the second component spaced apart from the center, the second coupling model having a second spring coupling element, the first spring coupling element and the second spring coupling element having the same spring constant. [Effects of the Invention]

[0007] According to the present invention, the behavior of particles can be easily calculated. [Brief explanation of the drawings]

[0008] [Figure 1] FIG. 2 is a diagram showing an example of the configuration of a calculation model according to an embodiment. [Figure 2] FIG. 2 is a diagram showing an example of a calculation model in the embodiment. [Figure 3] FIG. 2 is an explanatory diagram showing a coupling state of a calculation model in the embodiment. [Figure 4] FIG. 2 is a diagram showing an example of a calculation model in the embodiment. [Figure 5] 1 is a flowchart showing an example of a processing flow in an embodiment. [Figure 6] FIG. 10 is a diagram showing an example of an experimental result in the embodiment. [Figure 7] FIG. 1 is a diagram showing an example of the configuration of a computing device according to an embodiment. [Figure 8] 1 is a flowchart showing an example of a processing flow in an embodiment. [Figure 9] FIG. 2 is an explanatory diagram showing a particle model in the embodiment. [Figure 10] FIG. 2 is an explanatory diagram showing a particle model in the embodiment. [Figure 11] FIG. 2 is an explanatory diagram showing a particle model in the embodiment. [Figure 12] FIG. 2 is an explanatory diagram showing a particle model in the embodiment. [Figure 13] FIG. [Figure 14] FIG. [Figure 15] FIG.

[0009] Hereinafter, an example of an embodiment of the present invention will be described with reference to the drawings. The components described in this embodiment are merely examples and are not intended to limit the scope of the present invention.

[0010] <Calculation model> FIG. 1 is a diagram showing an example of the configuration of a computational model 1 according to an embodiment of the present invention. The calculation model 1 is an example of a calculation model in the present invention, and may be a model for calculating (analyzing) the behavior of particles when materials such as minerals or recycled products are crushed, transported, or mixed. The behavior may refer to, for example, at least elastic deformation and fracture among elastic deformation, yielding, plastic deformation and fracture, but is not limited to this. Hereinafter, the particles will be designated by the symbol "PTC" and will be referred to as particles PTC as appropriate.

[0011] The computational model 1 is composed of a particle PTC, which is an aggregate of multiple components, such as one component i and another component k, and the components i and k are coupled via a first coupling model 2(1) and a second coupling model 2(2). While FIG. 1 illustrates a simulated state in which the component i is coupled only to the component k, the component i may be coupled to multiple other adjacent components within the particle PTC, and the other components may be coupled to multiple other adjacent components. A particle is a mass or a divided part of a mass, and may be an aggregate of the component i, the component k, and multiple other components.

[0012] The first coupling model 2(1) is coupled to one center Ci of component i and another center Ck of component k. The first coupling model 2(1) comprises a first spring coupling element 3(1) and a first damper coupling element 4(1) arranged in parallel. The first spring coupling element 3(1) elastically expands and contracts, and the first damper coupling element 4(1) stabilizes the vibration of the first spring coupling element 3(1). The spring constant of the first spring coupling element 3(1) is K B and the damping coefficient of the first damper connecting element 4(1) is η B is.

[0013] The second coupling model 2(2) is coupled to one coupling point Pi, which is spaced apart from the center Ci, in the component i, and to another coupling point Pk, which is spaced apart from the center Ck, in the component k. The second coupling model 2(2) includes a second spring coupling element 3(2) and a second damper coupling element 4(2) arranged in parallel. The second spring coupling element 3(2) elastically expands and contracts, and the second damper coupling element 4(2) stabilizes the vibration of the second spring coupling element 3(2). In the calculation model 1 of this embodiment, the spring constant of the second spring coupling element 3(2) is the same as that of the first spring coupling element 3(1), K Band the damping coefficient of the second damper connection element 4(2) is the same as that of the first damper connection element 4(1), η B It is assumed that...

[0014] The connection between components i and k is only through the first connection model 2(1) and the second connection model 2(2). Furthermore, the connections at the center Ci, center Ck, connection point Pi, and connection point Pk are, for example, pin connections, and no contact force occurs between components i and k. The contact force is a force in a direction perpendicular to the normal line connecting the center Ci and the center Ck, or a force in a direction perpendicular to the normal line connecting the connection point Pi and the connection point Pk, and refers to a frictional force, torsional force, etc.

[0015] The distance between the center Ci of component i and the center Ck of component k changes elastically. When an external force is applied to a particle PTC from a state where no external force is applied, the distance between the center Ci and the center Ck elongates by λ CB The distance between the connection point Pi and the connection point Pk increases by λ PB It changes with.

[0016] In the calculation model 1, contact force and friction force occur between the particle PTC and a member 5 outside the particle PTC. The particle PTC and the member 5 are assumed to be bonded in the same manner as in conventional DEM.

[0017] FIG. 2 is a diagram showing an example of a computational model 1 in which a component i is bonded to four other components. However, the number of other components to which one component is bonded is not limited. When multiple components are closely packed, one component is bonded to 12 other components. In computational model 1, the bond distance r between the surface of component i and the surface of the other components in the normal direction is CB is, for example, the radius r of component i CE It is assumed to be approximately 0.5 times r CB It is unnatural to assume that r is smaller than 0. CB r CEThe reason for setting it to 1 or more times is that it is necessary to take into consideration that component i may combine with other components other than the other components adjacent to component i. For this reason, for example, it is assumed to be approximately 0.5 times the average value of 0 to 1 times. CB For example, r CE It may be 0.2 to 0.8 times, preferably 0.4 to 0.6 times.

[0018] The left side of Fig. 3 shows a particle PTC with a packed structure, and the right side of Fig. 3 shows a calculation model 1 that models the particle PTC with a packed structure. The calculation model 1 on the right side of Fig. 3 includes components i, k, s, and t. The left side of FIG. 4 shows a particle PTC with a porous structure, and the right side of FIG. 4 shows a calculation model 1 that models the particle PTC with a porous structure. The calculation model 1 on the right side of FIG. 4 includes components i, k, s, and t. The structure of the particle PTC that forms calculation model 1 may be either a packed structure or a porous structure. Furthermore, the shapes of the components when forming calculation model 1 are not limited.

[0019] <Effects of the computational model> In the calculation model 1, one component i and another component k, etc. are connected by a first connection model 2(1) and a second connection model 2(2), and no contact force occurs between the one component i and another component k, etc. Therefore, by calculating the behavior of the simple calculation model 1, the behavior of the particle PTC can be easily calculated.

[0020] In addition, since the spring constant of the first spring coupling element 3(1) and the spring constant of the second spring coupling element 3(2) are the same, F CB and F PB The spring constant that determines the same K B (see equations (2) and (3)), which makes it easier to calculate the behavior based on equations (1) and (5).

[0021] Furthermore, in the calculation model 1, because the first bonded model 2(1) and the second bonded model 2(2) are each composed of a spring bond element and a damper bond element, no contact force occurs between one component i and other components k, etc. Therefore, the behavior of the particle PTC, which is an aggregate of components, can be easily calculated without considering the friction coefficient between one component i and other components k, etc. For example, when an external force is applied from an external member 5 to a particle PTC including one component i and other components k, etc., the elastic deformation behavior of the particles can be calculated by setting the friction coefficient between the particle PTC and the external member 5 and the spring constants of the first bonded model 2(1) and the second bonded model 2(2). Furthermore, by setting the maximum elongation, the fracture behavior of the particles can be calculated and a load-displacement curve can be plotted.

[0022] <Calculation method> Fig. 5 is a flowchart showing an example of processing for implementing the method for calculating particle behavior in this embodiment. The processing in the flowchart of Fig. 5 may be performed by, for example, a computer (for example, a processing unit of a calculation device described later), and may be implemented by reading and executing a program stored in a storage unit (not shown).

[0023] Hereinafter, each symbol S in the flowchart represents a step. It should be noted that the flowchart described below merely shows an example of the processing procedure in this embodiment, and other steps may be added or some steps may be deleted. In addition, some of the steps in the flowchart may be interchanged.

[0024] Although manual work may be involved, the setting of parameters (parameter values) may be performed by the processing unit. Setting of parameters may include, for example, the processing unit storing the parameter values ​​in the storage unit. Furthermore, the processing unit may calculate and set the parameter values, or the processing unit may set parameter values ​​input by a user based on experimental results or the like.

[0025] First, the processing unit sets the friction coefficient μ between the constituent element and the member 5 (S110). The friction coefficient μ may be determined in the same manner as in a general DEM. For example, the friction coefficient μ is determined based on the angle of repose, which is the inclination angle of the surface of the particle group when the friction coefficient determination particles are released from a container, and the outflow speed when the friction coefficient determination particles are discharged from the container.

[0026] Next, the processing unit calculates the spring constant K of the first spring coupling element 3(1) and the second spring coupling element 3(2). B (S120) The spring constant K B For example, as shown in FIG. 6, the elastic deformation curve of the load-displacement curve (the horizontal axis is the displacement λ, and the vertical axis is the load P) obtained by a compression test using an actual machine may be fitted with a line. For example, 10 compression tests are performed and the elastic deformation curve of the average value is fitted. The fitting may be performed by drawing a graph such as a quadratic function curve, an exponential function curve, a logarithmic function curve, or a straight line using the least squares method for the elastic deformation curve of the compression test. From these graphs, "K B = P / λ as K B The spring constant K can be calculated. B may be determined by tensile testing if possible.

[0027] Next, the processing unit calculates the maximum elongation λ of the first binding model 2(1) and the second binding model 2(2). max is set (S130). max may be determined by, for example, adjusting the value corresponding to the displacement λ at the time of fracture in a compression test. Fracture may refer to the phenomenon of crack generation or separation that occurs after elastic deformation, yielding, or plastic deformation. Fracture may be considered to be the state when the load is reduced to approximately 0 in the load-displacement curve from the compression test shown in Figure 6. λ max may be determined by tensile testing if possible.

[0028] Next, the processing unit calculates the behavior of the calculation model 1, such as deformation and destruction, based on the formulas (1) and (2) (S140). The processing unit may also plot a load-displacement curve based on the calculation results.

[0029] For calculation model 1, the parallel motion equation of component i for calculating the behavior is shown in equation (1).

number

[0030] Equation (1) is the equation of motion when component i is three-dimensionally connected to nb other components (including component k), and component i moves parallel at a velocity Vi in a state where the particle PTC is in contact with nc external members 5. In equation (1), mi is the mass of component i, and F CB is the vector of binding forces in the first binding model 2(1), and F PB is the vector of binding forces of the second binding model 2(2), and F C is the vector of the contact force with the external member 5, and G is an external force such as gravity.

[0031] F CB is expressed by equation (2), and F PB is expressed by equation (3), and η in equations (2) and (3) B is expressed by equation (4).

number

number

number

[0032] In equation (2), K B is the spring constant common to the first coupled model 2(1) and the second coupled model 2(2), and λ CB is the elongation of the first coupled model 2(1), and η B is the damping coefficient of the first coupled model 2(1), and uCB is the relative velocity between the center Ci of component i and the center of other components, and n CB is the direction vector of the first coupled model 2(1). In equation (3), K B is the spring constant common to the first coupled model 2(1) and the second coupled model 2(2), and λ PB is the elongation of the second bond model 2(2), and n PB,n is the normal vector of the second coupled model 2(2), and n PB,s is the tangential vector of the second coupled model 2(2), and η B is the damping coefficient of the second coupled model 2(2), and u PB is the relative velocity between the connection point Pi of component i and the connection point of another component, and n PB is the direction vector of the second coupled model 2(2). In equation (3), λ PB <0 indicates that the distance between the bond points has decreased. In equation (4), m is the mass of the component, which is mi for component i. According to equation (4), the damping coefficient η B is the spring constant K B The spring constant K is determined by B is the damping coefficient η B It is determined by.

[0033] F in equation (1) C is determined by the normal spring constant, normal damping coefficient, and friction coefficient. B and the damping coefficient is η B By setting the friction coefficient μ, F C The coefficient of friction μ is determined by the angle of repose, etc., as described above.

[0034] As mentioned above, the spring constant K B By F CB and F PB is determined, and F is calculated by the friction coefficient μ C That is, the spring constant K B By determining the friction coefficient μ, the behavior of the particle PTC can be calculated based on the equation of motion of Equation (1).

[0035] For calculation model 1, the rotational motion equation of component i for calculating the behavior is shown in equation (5).

number

[0036] Equation (5) is the equation of motion when the particle PTC is in contact with nc external members 5 and the component i rotates at a velocity ωi. In equation (5), Ii is the moment of inertia, np is the number of second coupling models 2(2), and T PB is F PB is the vector of torques acting on component i due to

[0037] T PB is expressed by equation (6). In equation (6), r CP is a vector from Ci to Pi, and the symbol "x" represents the cross product of two vectors.

number

[0038] Spring constant K B By F PB is determined, and F PB By T PB is determined, and T PB The formula (5) is determined by the spring constant K B By defining the above, the deformation behavior of the particle PTC can be calculated based on the equation of motion of Equation (5).

[0039] The fracture behavior of the particle PTC is expressed as the elongation λ of the distance between the center Ci of one component i and the center Ck of another component k based on equations (1) and (2). CB , and the distance between the connection point Pi of one component i and the connection point Pk of another component k, λ PB Define λ CB exceeds the maximum elongation λmax of the actual particle PTC, or λ PB When exceeds λmax, it is assumed that damage such as cracks will occur. CBexceeds λmax, and λ PB It may be assumed that when λ exceeds λmax, destruction such as cracking occurs. The same λmax is used to determine whether destruction has occurred. CB and λ PB is used as a comparison target.

[0040] After calculating the deformation and fracture behavior of the PTC particles as described above, a load-displacement curve is created based on the calculation results and output (for example, displayed or transmitted). The load-displacement curve is plotted, for example, by dividing the displacement λ on the horizontal axis of the graph by λ. CB or λ PB and the load P on the vertical axis of the graph corresponds to the F on the right side of equation (1). C The load-displacement curve may be created by a computer, or may be created manually by a user.

[0041] <Effects of calculation method> The calculation method of the present invention is based on the friction coefficient μ and the spring constant K B By setting the coefficient of friction μ and the spring constant K, it is possible to calculate at least the elastic deformation among the elastic deformation, yield, plastic deformation, and fracture, and to draw the load-displacement curve. B Elastic deformation can be analyzed simply by setting the parameters.

[0042] In addition, the calculation method of the present invention is also applicable to the case where the spring constant of the first spring coupling element 3(1) and the spring constant of the second spring coupling element 3(2) are the same K B Therefore, the parameters can be set as follows: F CB and F PB The spring constant that determines the same K B (see equations (2) and (3)), which makes it easier to calculate the behavior based on equations (1) and (5).

[0043] In addition, the calculation method of the present invention uses the friction coefficient μ and the spring constant K BWhen λ and λmax are set as parameters, the deformation and fracture behavior of particulate PTC can be easily calculated based on only these three parameters. This makes it easy to understand the behavior of minerals when an external force is applied to them.

[0044] In conventional BPM (Potyondy), it is necessary to set eight parameters to calculate behavior: the normal stiffness of the component, the shear stiffness of the component, the friction coefficient between the components, the normal stiffness of the bond, the shear stiffness of the bond, the tensile strength, the shear strength, and the bond radius. In contrast, the calculation method of the present invention requires fewer parameters to be set compared to conventional BPM, and allows for efficient parameter setting for calculating deformation and fracture behavior.

[0045] In addition, the calculation method of the present invention uses the friction coefficient μ and spring constant K as parameters. B Since λ and λmax can be set as being independent of each other and not dependent on each other, it is not necessary to consider other parameters in order to determine one parameter, and parameters can be set efficiently.

[0046] In conventional BPM, the eight parameters to be set are mutually dependent, making the process for determining the parameters complicated. In contrast, in the calculation method of the present invention, the three parameters to be set are mutually independent, making it possible to set the parameters more easily and uniquely than in conventional BPM.

[0047] In addition, the calculation method of the present invention is also applicable to the first damper connection element 4(1) and the second damper connection element 4(2) with the same damping coefficient η B Here, by determining the spring constant to be one, the damping coefficient is determined to be one (see equation (4)). Therefore, F included in the right-hand side terms of equations (1) and (5) CB and F PB The damping coefficient that determines B (see equations (2) and (3)), which facilitates the calculation of the behavior based on equations (1) and (5).

[0048] <Computing device> Next, a calculation device that performs the above-mentioned behavior calculation will be described. The calculation device may be called a behavior calculation device or a behavior analysis device.

[0049] FIG. 7 is a diagram showing an example of the configuration of the computing device 10 in this embodiment. The calculation device 10 includes, for example, a behavior calculation unit 14, a load-displacement curve creation unit 15, and a behavior image generation unit 16. These may be, for example, functional units (functional blocks) of the processing unit (or control unit) of the computing device 10, and may be configured to have processing circuits such as a CPU (Central Processing Unit), a GPU (Graphics Processing Unit), a DSP (Digital Signal Processor), an ASIC (Application Specific Integrated Circuit), an FPGA (Field Programmable Gate Array), etc.

[0050] The calculation device 10 also includes, for example, a friction coefficient storage unit 11, a spring constant storage unit 12, and a maximum elongation storage unit 13. These may be configured to include a memory such as a RAM (Random Access Memory), for example.

[0051] Although not shown in the drawings, the computing device 10 may perform the following processing in accordance with a program stored in a memory such as a ROM (Read Only Memory).

[0052] The computing device 10 may include an output unit that outputs various types of information (for example, display or sound output). The output unit may be, for example, a display device included in the computing device 10, or a communication unit (including a communication processor, etc.) that provides various types of data, including display data, to a display device connected to the computing device 10 via a communication line.

[0053] The computing device 10 may also include an input unit for inputting various types of information. The input unit may be, for example, an input device (e.g., a touch panel integrated with a display device, a keyboard, a pointing device, etc.) operated by a user of the computing device 10, or a communication unit (including a communication processor) that receives various types of data from an information processing device connected to the computing device 10 via a communication line.

[0054] Furthermore, the calculation device 10 realizes the calculation method by a computer based on the calculation model 1, but it is not necessary to draw the calculation model 1 by a computer in order to realize the calculation method. However, the calculation model 1 may be drawn by a computer in order to confirm the underlying calculation model.

[0055] 8 is a flowchart showing an example of the flow of behavior analysis processing executed by the computing device 10. In the processing of this flowchart, other steps may be added or some steps may be deleted. Also, some of the steps in the flowchart may be interchanged.

[0056] The processing unit of the calculation device 10 stores the determined friction coefficient μ in the friction coefficient storage unit 11 (S210). The friction coefficient μ may be determined based on the angle of repose, etc., as in S110 of FIG. 5. The processing unit of the calculation device 10 also stores the determined spring constant K B is stored in the spring constant storage unit 12 (S220). B may be determined based on an actual machine test, similar to S120 in Fig. 5. Furthermore, the processing unit of the calculation device 10 stores the determined maximum elongation λmax in the maximum elongation storage unit 13 (S230). λmax may be determined based on an actual machine test, similar to S130 in Fig. 5.

[0057] Next, the behavior calculation unit 14 performs the calculations of the formulas (1) and (5) (S240). Specifically, the stored friction coefficient μ and spring constant K B Based on F CB , F PB , FC and T PB Calculate F CB , F PB , F C Calculate the left side of equation (1) based on T PB Calculate the left side of equation (5) based on

[0058] Next, the load-displacement curve creation unit 15 creates a load-displacement curve based on the calculation result of the behavior calculation unit 14, and outputs (for example, displays or transmits) it (S250). The load-displacement curve is plotted, for example, by dividing the displacement λ on the horizontal axis of the graph by λ CB or λ PB and the load P on the vertical axis of the graph corresponds to the F on the right side of equation (1). C This is done by matching the above.

[0059] Next, the behavior image generating unit 16 generates and outputs (for example, displays or transmits) an image showing a change in the shape of the particle model PTCM due to the compressive load as an image relating to the behavior of the particle (S260). The image can be generated based on, for example, equations (1) and (5). Specific images will be described later.

[0060] The information such as the image output as described above may be an example of information relating to particle behavior. Other information may be used as long as it is related to the behavior of the particles to be calculated.

[0061] The above processing may be realized by a calculation system (behavior calculation system, behavior analysis system) including two or more devices. In this case, for example, some of the behavior calculation unit 14, the load-displacement curve creation unit 15, and the behavior image generation unit 16 may be provided in the first device, and the others may be provided in the second device, or they may be provided in different devices (first device, second device, third device). The same may be true for the friction coefficient storage unit 11, the spring constant storage unit 12, and the maximum extension storage unit 13.

[0062] <Effects of computing devices, etc.> The calculation device 10 (which may be a calculation system) of the present invention enables the calculation method of particle behavior of the present invention to be realized by a computer. The program of the present invention is stored in a storage unit of the calculation device or the like. These allow the calculation method of the present invention to be processed more efficiently. For example, the behavior image generation unit 16 draws the change in the shape of the particle model PTCM, so that the behavior of the particle model PTCM can be visually confirmed.

[0063] <Comparison of compression test simulation and actual compression test> Fig. 9 is a front view of a particle model PTCM for performing a compression test simulation on the calculation model 1 by the calculation device 10, and Fig. 10 is a plan view of the particle model PTCM. Fig. 11 is a front view of a particle replica PTCR for performing an actual compression test as a comparison test, and Fig. 12 is a plan view of the particle replica PTCR. The particle model PTCM in Figs. 9 and 10 is, for example, a particle model PTCM drawn by the behavior image generation unit 16 of the calculation device 10.

[0064] The particle model PTCM and particle replica PTCR have approximately the same contour shape, with a cylindrical central portion in the vertical direction and curved upper and lower surfaces. The particle model PTCM has a random structure composed of an assembly of multiple components, and each component is connected to 12 other components by a first binding model 2(1) and a second binding model 2(2).

[0065] The compression test simulation was performed using a calculation device 10. The conditions for the compression test simulation were density ρ of each component = 2240 kg / m 3 , the radius of each component r CE =0.4×10 -3 m, number of components n = 1200, external force such as gravity G = 9.80665 m / s 2 , the friction coefficient between the particle model PTCM and the external components μ = 0.1, the spring constant K B =1.0×10 6 N / m, maximum elongation λmax=1.36×10 -3 mm. ρ, rCE , n and G are predetermined values, and μ, K B and λmax are values ​​set as parameters.

[0066] Figure 13 is a graph comparing the load-displacement curve of the compression test simulation with the load-displacement curve of the actual compression test. In Figure 13, the thick line is the load-displacement curve of the compression test simulation, and the thin line is the load-displacement curve of the actual compression test. For the actual compression test, the load-displacement curves of 10 tests are plotted.

[0067] In the elastic deformation portion of the load-displacement curve, the load-displacement curve of the compression test simulation and the load-displacement curve of the actual compression test are approximately the same, and the slopes are also approximately the same. Furthermore, the displacement at the time of failure, when the load drops instantaneously, is approximately the same in the load-displacement curve of the compression test simulation and the load-displacement curve of the actual compression test. This shows that the compression test simulation based on calculation model 1 can simulate or reproduce the actual compression test.

[0068] Figure 14 shows an image of a particle model PTCM placed vertically on a compression table model 20M and compressed from above by a compression jig model 21M. The image may be generated by the behavior image generation unit 16 for each mode of change. Figure 15 shows a photograph of a particle replica PTCR placed vertically on a compression table 20R using a real compression tester and compressed from above by a compression jig 21R. In Figures 14 and 15, Δ is the compression distance in the vertical direction. The compression jig model 21M and compression jig 21R correspond to the external member 5 (shown in Figure 2).

[0069] For both the particle model PTCM and particle replica PTCR, cracks occurred at Δ = 0.15 mm and fragments occurred at Δ = 1.5 mm. Also, although not shown, when the particle model PTCM and particle replica PTCR were placed horizontally, both the particle model PTCM and particle replica PTCR cracked at Δ = 0.15 mm and fragments occurred at Δ = 1.5 mm. Furthermore, although not shown, when the particle model PTCM and particle replica PTCR were arranged in two rows, with the lower row horizontal and the upper row vertical, both the particle model PTCM and particle replica PTCR cracked at Δ = 0.30 mm. Therefore, the changes in the external shape of the compression test simulation and the actual compression test match. From this perspective, it can be seen that the compression test simulation based on computational model 1 can simulate or reproduce the actual compression test.

[0070] <Modification> Although the embodiments of the present invention have been described above with reference to the drawings, the present invention is not limited to those shown in the drawings.

[0071] For example, the calculation model of the present invention may include a plurality of particles, each of which is an aggregate of a plurality of constituent elements. In the calculation method of the present invention, the internal stress or elastic energy of the particles may be calculated based on the calculation model 1. Furthermore, the thermal stress generated when a material is heated may be calculated based on the calculation model 1.

[0072] Furthermore, the calculation model of the present invention does not need to include a Dunbar coupling element. In this case, by simplifying equations (2), (3), and (6) and simplifying equations (1) and (5) for calculating the behavior of the particle PTC, it becomes possible to more easily calculate the behavior of the particle PTC.

[0073] Furthermore, in the calculation model of the present invention, the spring constants of the first spring coupling element 3(1) and the second spring coupling element 3(2) do not need to be the same. If the spring constants are not the same, the behavior of the particle PTC can be calculated by setting five parameters: the friction coefficient, the spring constant of the first spring coupling element 3(1), the spring constant of the second spring coupling element 3(2), the maximum elongation of the first coupling model 2(1), and the maximum elongation of the second coupling model 2(2). For example, if these five parameters are set and no contact force occurs between the components, the deformation behavior of the particle PTC can be calculated using equations similar to equations (1) and (5), assuming that the spring constants of the first spring coupling element 3(1) and the second spring coupling element 3(2) are different. Therefore, even when these five parameters are set, the behavior of the particle PTC can be calculated more easily than with conventional BPM, which requires setting eight parameters. [Explanation of symbols]

[0074] 1: Computational model 2(1): First binding model, 2(2): Second binding model 3(1): First spring coupling element, 3(2): Second spring coupling element 4(1): First damper connecting element, 4(2): Second damper connecting element 5: External components 10: Computing device 11: Friction coefficient storage unit, 12: Spring constant storage unit, 13: Maximum elongation storage unit, 14: Behavior calculation unit, 15: Load displacement curve creation unit, 16: Behavior image generation unit 20M: Compression table model, 20R: Compression table, 21M: Compression jig model, 21R: Compression jig PTC: particle, PTCM: particle model, PTCR: particle replica

Claims

1. A method for calculating particle behavior by a computer, comprising: The particle is an aggregate of a plurality of components, two adjacent components are connected by two spring connection elements, and the two spring connection elements have the same spring constant, and the spring constant is set; Setting a coefficient of friction between the particle and a member external to the particle; calculating the behavior based on the spring constant and the coefficient of friction; Calculation methods including:

2. setting the maximum extension such that the two spring coupling elements have the same maximum extension; The behavior is calculated based on the spring constant, the coefficient of friction, and the maximum elongation. The calculation method of claim 1 .

3. The spring constant, the friction coefficient, and the maximum elongation are parameters independent of each other. The calculation method according to claim 2.

4. In the calculation of the behavior, a damping coefficient of the damper connection element is used, the damping coefficient being calculated using the spring constants on the assumption that a damper connection element is provided corresponding to each of the two spring connection elements having the same spring constant. The calculation method according to any one of claims 1 to 3.

5. A computing device for calculating particle behavior, comprising: the particle is an aggregate of a plurality of components, two adjacent components are connected by two spring connection elements, the spring constants are set assuming that the two spring connection elements have the same spring constant, a friction coefficient is set between the particle and a member outside the particle, and the behavior is calculated based on the spring constant and the friction coefficient; computing device.

6. an output unit that outputs information about the behavior; 6. The computing device of claim 5.

7. the output unit has a display unit that displays an image related to the behavior.

7. The computing device of claim 6.

8. A program for causing a computer to calculate particle behavior, The particle is an aggregate of a plurality of components, two adjacent components are connected by two spring connection elements, and the two spring connection elements have the same spring constant, and the spring constant is set; Setting a coefficient of friction between the particle and a member external to the particle; calculating the behavior based on the spring constant and the coefficient of friction; Programs including.

9. A computational model for calculating particle behavior, comprising: The particle is an aggregate of a plurality of constituent elements, a first coupling model in which a center of a first component is coupled to a center of a second component adjacent to the first component and the first coupling model has a first spring coupling element; a second coupling model in which a coupling point in the first component that is spaced from the center and a coupling point in the second component that is spaced from the center are coupled, the second coupling model having a second spring coupling element; Equipped with The first spring coupling element and the second spring coupling element have the same spring constant. Computational model.

10. No contact force occurs between the first component and the second component. The computational model of claim 9.

11. the first coupling model has a first damper coupling element; the second coupling model has a second damper coupling element; A computational model according to claim 9 or 10.

12. the damping coefficients of the first damper coupling element and the second damper coupling element are the same; The computational model of claim 11.

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