Any-shape rock-soil particle material accelerated simulation method based on level set

Abstract

The invention discloses a level set-based accelerated simulation method for rock-soil granular materials in any shape. Comprising the steps of establishing a level set particle model of any shape; obtaining particle data through the shape template; according to an extended multi-level Linked-cell method, constructing a potential contact pair list; calculating point-to-surface contact information on the vertex of the particle model; according to the normal contact force, tangential contact force and contact torque are calculated, and the particle motion state is updated; and outputting analog information. Compared with a traditional discrete element method, the high-performance level set discrete element algorithm for the particles in any shape can consider more extreme particle gradation distribution and complex particle shapes, has good calculation efficiency and can solve the problem of large-scale particle material simulation; and by establishing the shape template and the Verlet list, memory consumption and memory access delay are reduced, and the computing performance of the GPU can be fully utilized.

Description

Technical Field

[0001] The present invention relates to the field of computational mechanics of high-performance granular materials, and in particular to a level set-based accelerated simulation method for rock and soil granular materials of arbitrary shapes. Background Art

[0002] Particle systems are widely present in geotechnical engineering, and factors such as particle shape and gradation have a significant impact on the physical and mechanical properties of particle systems. Although discrete element methods and molecular dynamics methods have become important approaches for studying the behavior of particle systems in recent years, the round or spherical particles commonly used in traditional methods have limitations and cannot fully reflect the characteristics of particle systems with complex particle compositions.

[0003] To address the numerical simulation of complex-shaped particles using discrete element methods (DEM), algorithms for ellipsoidal and spherical particles have been developed. These methods still approximate the particle shape. While they can conveniently establish contact detection and calculation algorithms based on traditional DEM, they still cannot accurately reflect the true particle shape. In recent years, combined superquadratic surface methods and level set methods have also been developed to describe or approximate the true particle shape. The level set method uses a regular grid to discretize the particle space and stores a signed distance field at that grid to describe the irregular particle surface, enabling a more realistic representation of particles of arbitrary shape. However, these methods can lead to non-convex contact between particles, making traditional contact methods ineffective for contact detection and calculation, significantly increasing computational costs. Furthermore, these methods cannot address the high contact detection costs associated with poorly graded particles.

[0004] In traditional discrete element methods, the computational cost of contact detection limits the number of particles and the application of complex-shaped particles. To address this issue, various parallel computing programs have been developed. Taking advantage of the rapid development of graphics processing unit (GPU) technology in recent years, and taking into account the fact that GPU computing cores far outnumber central processing units (CPUs), computing threads have been allocated to each GPU core, significantly improving computational efficiency. However, the pre-contact information of particles, especially those with complex shapes, leads to high memory consumption. The poor data transmission performance and memory space size of GPU computing cores compared to CPUs have become a problem that restricts computational efficiency and even prevents the full utilization of GPU computing cores. Further optimization of computational algorithms is needed to improve this problem.

[0005] Based on the above problems, the present invention proposes an accelerated simulation method for arbitrary-shaped rock and soil granular materials based on level sets, which to a certain extent makes up for the shortcomings of the existing technology, can better describe the real particle shape, adapt to poor particle grading, and ensure good computational efficiency, providing a basis for further research on the macroscopic performance of the particle system. Summary of the Invention

[0006] The present invention aims to address the deficiencies of the prior art and propose an accelerated simulation method for arbitrarily shaped rock and soil granular materials based on level sets.

[0007] The object of the present invention is achieved through the following technical solution: a method for accelerating the simulation of arbitrarily shaped rock and soil granular materials based on level sets, comprising the following steps:

[0008] S1. Establish a level set particle model of arbitrary shape and obtain the corresponding level set function;

[0009] S2. Obtain the level set function value and its gradient value of the structured grid node through the level set function, and obtain the particle information according to the shape template;

[0010] S3, constructing a potential contact pair list, including constructing a particle-particle Verlet list and a particle-vertex Verlet list;

[0011] S4. performing point-to-surface narrow-area contact detection based on the vertices obtained from the particle model and calculating the normal contact force, including calculating the local contact normal based on the gradient value of the vertex, obtaining the overlap between the master and slave particles based on the local contact normal, and then calculating the normal contact force;

[0012] S5. Calculate the tangential contact force and contact torque based on the normal contact force and update the particle motion state, taking into account the viscous damping coefficient for reduction during the calculation. The updated particle motion state is updated using the Velocity-Verlet format according to the Newton-Euler equation;

[0013] S6. Output particle simulation information.

[0014] Furthermore, the establishing of the level set particle model of arbitrary shape includes: generating a level set function based on a particle model of implicit surface function, a particle model of SDF function or a particle model of polyhedron.

[0015] Furthermore, obtaining the level set function value and gradient value of the structured grid node specifically includes:

[0016]

[0017] Where φ is the value of the level set function, is the interpolation basis function, p Nis the grid node, Ω is the space where the irregular particles are located, and v i represents the level set background grid, p is v i A little inside.

[0018] Furthermore, the obtaining of particle information according to the shape template specifically includes: obtaining basic quantities and particle data of mass, center of mass, moment of inertia according to the shape template, and calculating the basic quantities by the following formula:

[0019]

[0020] in, is the mass of the shape template, c is the center of mass, I is the moment of inertia, ρ is the material density, V c is the voxel volume, H(φ) is the smooth Heaviside function, and the subscripts x, y, and z represent the components on the x, y, and z axes, respectively;

[0021] The formula for obtaining the rigid particle information by scaling, rotating, and translating the shape template is as follows:

[0022]

[0023] in, is a spatial point in local coordinates, t is a translation vector, R is a rotation matrix, and S is a diagonal scaling matrix.

[0024] Furthermore, the potential contact pair list is constructed as follows: a particle-particle Verlet list is constructed according to an extended multi-level Linked-cell method, a wide-area search is performed according to the multi-level Linked-cell method, and bounding sphere detection is adopted, including intra-level search and inter-level search; the particle-particle Verlet list is updated after the maximum cumulative displacement of the bounding sphere at level i reaches half of the Verlet distance, and the formula is as follows:

[0025]

[0026] in, is the cumulative displacement of the i-th level enclosing sphere at time t; is the i-th level Verlet distance of the particle-particle Verlet list;

[0027] The vertex-particle Verlet list is constructed according to the extended multi-level linked-cell method, in which directed bounding box detection is adopted. The vertex-particle Verlet list is updated after the maximum relative displacement between the master particle i and the slave particle j reaches the Verlet distance. The formula is as follows:

[0028]

[0029] in, and are the velocity, angular velocity and radius of the surrounding sphere, respectively, where the superscript □=i,j represents the bead particle and the slave particle, respectively, l v is the Verlet distance.

[0030] Furthermore, the narrow-area contact detection and calculation of normal contact force include:

[0031] Based on the vertices obtained from the particle model, point-to-surface narrow-area contact detection is performed. The particle with the smaller volume is selected as the master particle, and the other particle is selected as the slave particle. The data of the master particle vertex invading the slave particle is obtained. The formula is as follows:

[0032]

[0033] Where δ is the overlap, is the local contact normal, is a local contact point, Surface nodes The position in the local coordinate system of the particle;

[0034] Calculating point-to-surface contact information on the vertices of the particle model, including:

[0035] The contact force and contact potential energy field formulas are as follows:

[0036]

[0037] W(x)=k n ω v ε(δ)

[0038] in, is the normal contact force, W(x) is the contact potential energy, k n is the normal contact stiffness, ω v is the coefficient to correct the influence of vertex distribution, ε(δ) is the directed distance potential energy field function;

[0039] Specifically, ω v Take it as:

[0040]

[0041] in, and is the area, external normal direction and angle of the i-th adjacent patch, N af and S p are the number of adjacent facets around the vertex and the surface area of ​​the particle;

[0042] Specifically, ε(δ) is taken as:

[0043]

[0044] Among them, β is the potential energy parameter.

[0045] Furthermore, the calculation of the tangential contact force and the contact moment based on the normal contact force and the reduction considering the viscous damping coefficient includes:

[0046] The normal contact force, tangential contact force and contact moment are:

[0047]

[0048] Among them, k t is the tangential stiffness, μ is the friction coefficient, ε n , ε t are the normal and tangential viscous damping coefficients, δ t is the cumulative tangential displacement.

[0049] Furthermore, the updating of the particle motion state using the Velocity-Verlet format according to the Newton-Euler equation includes:

[0050]

[0051] Where m is the mass of the particle, v and ω are the velocity and angular velocity respectively, is the damping coefficient.

[0052] On the other hand, the present invention also provides an accelerated simulation device for arbitrary-shaped rock and soil granular materials based on level sets, comprising a memory and one or more processors, wherein the memory stores executable code, and when the processor executes the executable code, it implements the method for accelerated simulation of arbitrary-shaped rock and soil granular materials based on level sets.

[0053] On the other hand, the present invention also provides a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the aforementioned method for accelerated simulation of arbitrary-shaped rock and soil granular materials based on level sets.

[0054] The beneficial effects of the present invention are as follows: Compared with the existing technology, the present invention adopts the level set function to describe particles of arbitrary irregular shapes; utilizes advanced graphics processors to accelerate the level set discrete element neighbor search, proposes an extended double-layer Verlet list to store particle neighbor information, reduces GPU access latency, and greatly improves computational efficiency; establishes a particle storage template to greatly reduce memory consumption; achieves efficient and accurate simulation of particles of arbitrary shapes within the framework of discrete medium mechanics, and obtains the dynamic response of particle aggregates under external forces; introduces an energy conservation contact model to ensure the energy conservation characteristics of the overall particle system, while solving the problem of unstable contact of sharp gravel-shaped particles, and finally outputs simulation information as needed, including measurement circles, force chain diagrams, particle positions, velocities, and contact information. The present invention effectively characterizes and simulates the complex dynamic processes of irregular particles.

[0055] At present, the level set discrete element simulation method is limited to CPU calculation, with a small calculation scale and a long simulation time. The present invention solves the simple assumption of particle shape in traditional discrete elements when solving the mechanical behavior of particles, and solves the problem of low computational efficiency of discrete element methods, and provides a set of universal level set particle generation templates. Through the GPU parallel level set discrete element method and the extended multi-level linked-cell method, a high-performance level set discrete element algorithm for particles of arbitrary shape is proposed. Compared with the traditional discrete element method, it can consider more extreme particle gradation distribution and particle shape, and has good computational efficiency; and through the shape template and double-layer Verlet list, the memory consumption and memory access delay of the calculation process are reduced, which is conducive to fully utilizing the computing performance of the GPU. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 This is a flow chart of an accelerated simulation method for arbitrary-shaped rock and soil granular materials based on level sets according to the present invention;

[0057] Figure 2 Schematic diagram of the particle model based on implicit surface equation;

[0058] Figure 3 Schematic diagram of particle model based on SDF function;

[0059] Figure 4 Schematic diagram of the polyhedron-based particle model;

[0060] Figure 5 Schematic diagram of contact detection;

[0061] Figure 6 The stacking structure of complex-shaped particles and their energy evolution;

[0062] Figure 7 It is a large-scale particle accumulation structure;

[0063] Figure 8 Simulation of deposition for extreme particle size ratios;

[0064] Figure 9 Schematic diagram of an accelerated simulation device for rock and soil granular materials of arbitrary shapes based on level sets provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0065] The specific embodiments of the present invention are further described in detail below with reference to the accompanying drawings.

[0066] To facilitate a better understanding of the objectives, technical solutions, and advantages of the present invention, the present invention is further described below with reference to the accompanying drawings and specific embodiments. Those skilled in the art will readily appreciate the other advantages and benefits of the present invention from the contents disclosed herein. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a more thorough and comprehensive disclosure of the present invention.

[0067] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art of the present invention. The terms used in this specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0068] It should be noted that if the embodiments of the present invention involve directional indications (such as up, down, left, right, front, back, etc.), the directional indications are only used to explain the relative position relationship, movement status, etc. between the various components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indications will also change accordingly.

[0069] In addition, if there are descriptions involving "first", "second", etc. in the embodiments of the present invention, the descriptions of "first", "second", etc. are only for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of such features. Secondly, the technical solutions between the various embodiments can be combined with each other, but this must be based on the fact that ordinary technicians in this field can implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0070] Reference Figure 1 , Figure 1 The figure is a flow chart of an embodiment of a method for accelerating the simulation of arbitrarily shaped rock and soil granular materials based on level sets. In one embodiment, the method for accelerating the simulation of arbitrarily shaped rock and soil granular materials based on level sets includes:

[0071] S01, establish a level set particle model of arbitrary shape.

[0072] S02, obtaining particle data through a shape template.

[0073] S03: Construct a potential contact pair list based on the extended multi-level linked-cell method.

[0074] S04: Calculate point-to-surface contact information on the vertices of the particle model.

[0075] S05: Calculate the tangential contact force and contact torque based on the normal contact force and update the particle motion state.

[0076] S06, output simulation information, enter the next calculation process or end the calculation.

[0077] The establishment of the level set particle model of arbitrary shape can be based on one of a variety of different particle models, including:

[0078] S011, the particle model based on the implicit surface equation generates the level set function, such as Figure 2 As shown, the formula is as follows:

[0079]

[0080] in, is a grid node, is the level set function value at the grid node, To describe the particle surface with at least C 1 Continuous scalar function.

[0081] Specifically, the particle model based on the implicit surface equation can be:

[0082]

[0083] Among them, r x 、r y and r z are the semi-major axis length, ε x , ε y and ε z is the shape parameter.

[0084] S012, the particle model based on the SDF function generates the level set function, such as Figure 3 As shown, the formula is as follows:

[0085]

[0086] in, is a grid node, is the level set function value at the grid node, To describe the distance from a point in a geometric shape to its surface, 0 Continuous function.

[0087] S013, polyhedron-based particle model, e.g. Figure 4 As shown, without loss of generality, the level set function is generated based on the shortest distance from a point to its surface, edge, or vertex.

[0088] The obtaining of particle data by using a shape template further includes:

[0089] S021, according to the generated level set function, obtain the level set function value of the structured grid node, and obtain the level set function and its gradient value of the spatial point. The formula of the level set function and its gradient value of the spatial point is as follows:

[0090]

[0091] Where φ is the value of the level set function, is the interpolation basis function, p N is the grid node, Ω is the space where the irregular particles are located, and v i represents the level set background grid, p is v i A little inside.

[0092] Specifically, It can be taken as a linear shape function.

[0093] The obtaining of particle data by using a shape template further includes:

[0094] S022: Obtain zero level set point data based on the level set function value, and obtain basic quantities and particle data of mass, center of mass, moment of inertia, etc. based on the shape template. The basic quantity formula is as follows:

[0095]

[0096] in, is the mass of the shape template, c is the center of mass, I is the moment of inertia, ρ is the material density, V c is the voxel volume, H(φ) is the smooth Heaviside function, and the subscripts x, y, and z represent the components on the x, y, and z axes, respectively.

[0097] The formula for obtaining the rigid particle information by scaling, rotating, and translating the shape template is as follows:

[0098]

[0099] in, is a spatial point in local coordinates, t is a translation vector, R is a rotation matrix, and S is a diagonal scaling matrix.

[0100] Specifically, the zero level set point data can be obtained by the Newton-Raphson method, and the formula is as follows:

[0101] x(r,θ,ψ)=r(sinθcosψ,sinθsinψ,cosθ) T

[0102]

[0103] where r, θ, and ψ are the spherical coordinates of point x, and i is the number of iterations.

[0104] The constructing of the potential contact pair list according to the extended multi-level Linked-cell method further includes:

[0105] S031: Construct a particle-particle Verlet list according to the multi-level Linked-cell method.

[0106] Specifically, a wide-area search is performed based on the multi-level linked-cell method, using bounding sphere detection, including intra-level search and inter-level search. The cell size of the i-th level is given by the following formula:

[0107]

[0108] in, and are the maximum and minimum radii of the i-th level enclosing sphere, Λ is the Verlet factor, ranging from 0.1 to 0.3, is the i-th level Verlet distance.

[0109] Furthermore, the particle-particle Verlet list is updated after the maximum cumulative displacement of the i-th level enclosing sphere reaches half of the Verlet distance, and the formula is as follows:

[0110]

[0111] in, is the cumulative displacement of the i-th level enclosing sphere at time t.

[0112] The constructing of the potential contact pair list according to the extended multi-level Linked-cell method further includes:

[0113] S032: Construct a vertex-particle Verlet list according to the extended multi-level Linked-cell method.

[0114] Specifically, the search is performed based on the extended multi-level Linked-cell method, using directed bounding box detection. The Verlet distance of the i-th level is given by the following formula:

[0115]

[0116] in, is the minimum equivalent radius of the particle, and λ is the Verlet factor, which ranges from 0.3 to 0.5.

[0117] Furthermore, the vertex-particle Verlet list is updated after the maximum relative displacement between the master particle i and the slave particle j reaches the Verlet distance, and the formula is as follows:

[0118]

[0119] in, and are the velocity, angular velocity and radius of the surrounding sphere respectively.

[0120] The calculating of point-to-surface contact information on the vertices of the particle model further includes:

[0121] S041, performing point-to-surface narrow-area contact detection based on the vertices obtained from the particle model, selecting the smaller particle as the master particle and the other particle as the slave particle, obtaining data on the master particle vertex intruding into the slave particle, such as Figure 5 As shown, the formula is as follows:

[0122]

[0123] Where δ is the overlap, is the local contact normal, is a local contact point, Surface nodes The position in the local coordinate system of the particle.

[0124] The calculating of point-to-surface contact information on the vertices of the particle model further includes:

[0125] S042, the contact force and contact potential energy field formulas are as follows:

[0126]

[0127] W(x)=k n ω v ε(δ)

[0128] in, is the normal contact force, W(x) is the contact potential energy, k n is the normal contact stiffness, ω vis the coefficient to correct the influence of vertex distribution, and ε(δ) is the directed distance potential energy field function.

[0129] Specifically, ω v Can be taken as:

[0130]

[0131] in, and is the area, external normal direction and angle of the i-th adjacent patch, N af and S p are the number of adjacent faces around the vertex and the surface area of ​​the particle respectively.

[0132] Specifically, ε(δ) can be taken as:

[0133]

[0134] Among them, β is the potential energy parameter.

[0135] The method of calculating the tangential contact force and the contact torque according to the normal contact force and updating the particle motion state further includes:

[0136] S051: Calculate the tangential contact force and contact moment based on the normal contact force, and reduce them by taking the viscous damping coefficient into account.

[0137] Specifically, the normal contact force, tangential contact force and contact moment can be taken as:

[0138]

[0139] Among them, k t is the tangential stiffness, μ is the friction coefficient, ε n , ε t are the normal and tangential viscous damping coefficients, δ t is the cumulative tangential displacement.

[0140] The method of calculating the tangential contact force and the contact torque according to the normal contact force and updating the particle motion state further includes:

[0141] S052: Update the particle motion state using the Velocity-Verlet format according to the Newton-Euler equation. The formula is as follows:

[0142]

[0143] Where m is the mass of the particle, v and ω are the velocity and angular velocity respectively, is the damping coefficient.

[0144] Outputting simulation information, entering the next calculation process or ending the calculation also includes:

[0145] S061, judging whether the calculation process is completed according to the user settings.

[0146] S062, output calculation results, including particle position, velocity, acceleration, and rotation angle.

[0147] In the description provided herein, numerous specific details are described. However, it is understood that embodiments of the present invention may be practiced without these specific details. In some instances, well-known methods, structures, and techniques are not shown in detail so as not to obscure the understanding of this description.

[0148] The following introduces several examples of simulation using the algorithm provided by the present invention, which are completed under Ubuntu 22.04 (CPU@8 cores, GeForce RTX 3070).

[0149] Example 1: Simulation of complex-shaped particle accumulation.

[0150] This test is used to examine the contact stability of particles with complex shapes. Three particle models based on implicit surface function, SDF function and polyhedron are used to generate seven particles with complex shapes, such as Figure 6 As shown in the figure. The particle equivalent radius is set to 0.1m, and there are 6300 level set particles in total. The initial positions and orientations are randomly generated. The normal and tangential contact stiffness between particles are set to 1×10 6 N / m, and the contact stiffness between the particles and the wall is set to 10 times the contact stiffness between the particles. The stacking boxes are 5m×5m×10m square boxes, which are allowed to freely fall, collide, and stack under the action of gravity. It can be seen that during the stacking process, the system's energy is conserved, and a stable stacking structure is formed. This demonstrates that the proposed method can perform stable calculations for concave and complex-shaped particles.

[0151] Example 2: Large-scale particle accumulation.

[0152] This test is used to examine the performance of contact calculations for a large number of particles. We used essentially the same steps and methods as in Example 1, but increased the length and height of the box to 15m and 28m, the particle equivalent radius to 0.1m, and the number of level set particles to several values ​​between 100,000 and 540,000. The box width was adjusted based on the number of particles, and the remaining parameters were the same as in Example 1, e.g. Figure 7 It can be observed that a stable stacking structure can be obtained in each case, and the relationship between simulation time and the number of particles increases substantially linearly, indicating that the method provided by the present invention has relatively good computational performance and can well adapt to various scales required for computation.

[0153] Example 3: Sedimentation simulation for extreme particle size ratios.

[0154] This test is used to examine the performance and stability of particle contact calculation under poor gradation distribution. The same steps and methods as in Examples 1 and 2 are used. The number of level set particles is set to 200,000, and a coarse particle with an equivalent radius of 1m is fixed in a square box. The same particle model is used as for the fine particle and the corresponding contact stiffness is set, as shown in the following figure. Figure 8 It can be observed that the deposition process can be calculated stably and the overall calculation time is only 20 minutes.

[0155] Corresponding to the aforementioned embodiment of a method for accelerated simulation of arbitrarily shaped rock and soil granular materials based on level sets, the present invention also provides an embodiment of a device for accelerated simulation of arbitrarily shaped rock and soil granular materials based on level sets.

[0156] See also Figure 9 An embodiment of the present invention provides an accelerated simulation device for arbitrary-shaped rock and soil granular materials based on level sets, comprising a memory and one or more processors, wherein the memory stores executable code, and when the processor executes the executable code, it is used to implement an accelerated simulation method for arbitrary-shaped rock and soil granular materials based on level sets in the above-mentioned embodiment.

[0157] The embodiment of the accelerated simulation device for rock and soil granular materials of arbitrary shapes based on level sets provided by the present invention can be applied to any device with data processing capabilities, and the device with data processing capabilities can be a device or apparatus such as a computer. The device embodiment can be implemented through software, or through hardware or a combination of software and hardware. Taking software implementation as an example, as a device in a logical sense, it is formed by the processor of any device with data processing capabilities in which it is located reading the corresponding computer program instructions in the non-volatile memory into the memory for execution. From the hardware level, if Figure 9 As shown in the figure, it is a hardware structure diagram of any device with data processing capability where the accelerated simulation device of arbitrary-shaped rock and soil granular materials based on level set provided by the present invention is located. Figure 9 In addition to the processor, memory, network interface, and non-volatile memory shown, any device with data processing capabilities in which the apparatus in the embodiment is located may also include other hardware, generally based on the actual functions of the device with data processing capabilities, which will not be described in detail.

[0158] The implementation process of the functions and effects of each unit in the above-mentioned device is specifically described in the implementation process of the corresponding steps in the above-mentioned method, and will not be repeated here.

[0159] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to the partial description of the method embodiments. The device embodiments described above are merely illustrative, wherein the units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the present invention. A person of ordinary skill in the art can understand and implement the present invention without inventive work.

[0160] An embodiment of the present invention further provides a computer-readable storage medium having a program stored thereon. When the program is executed by a processor, the method for accelerating the simulation of arbitrary-shaped rock and soil granular materials based on level sets in the above embodiment is implemented.

[0161] The computer-readable storage medium may be an internal storage unit of any device with data processing capabilities described in any of the aforementioned embodiments, such as a hard disk or memory. The computer-readable storage medium may also be an external storage device of any device with data processing capabilities, such as a plug-in hard disk, a smart media card (SMC), an SD card, a flash card, etc. equipped on the device. Furthermore, the computer-readable storage medium may also include both an internal storage unit and an external storage device of any device with data processing capabilities. The computer-readable storage medium is used to store the computer program and other programs and data required by any device with data processing capabilities, and may also be used to temporarily store data that has been output or is to be output.

[0162] The present invention also provides a computer program product, comprising a computer program, which, when executed by a processor, implements the method for accelerated simulation of arbitrary-shaped rock and soil granular materials based on level sets.

[0163] Those skilled in the art will readily appreciate other embodiments of the present application after considering the specification and practicing the contents disclosed herein. This application is intended to cover any variations, uses, or adaptations of the present application that follow the general principles of the present application and include common knowledge or customary techniques in the art not disclosed herein. The description and examples are to be considered merely as exemplary, and the true scope and spirit of the present application are indicated by the claims.

[0164] It should be understood that the above general description and the detailed description that follows are exemplary and explanatory only and do not limit the present application. The present application is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes may be made without departing from the scope of the present application. The scope of the present application is limited only by the appended claims.

Claims

1. A method for accelerating the simulation of arbitrarily shaped rock and soil granular materials based on level sets, characterized in that: The steps include: S1. Establish a level set particle model of arbitrary shape and obtain the corresponding level set function; S2. Obtain the level set function value and its gradient value of the structured grid node through the level set function, and obtain the particle information according to the shape template; S3, constructing a potential contact pair list, including constructing a particle-particle Verlet list and a particle-vertex Verlet list; S4. performing point-to-surface narrow-area contact detection based on the vertices obtained from the particle model and calculating the normal contact force, including calculating the local contact normal based on the gradient value of the vertex, obtaining the overlap between the master and slave particles based on the local contact normal, and then calculating the normal contact force; S5. Calculate the tangential contact force and contact torque based on the normal contact force and update the particle motion state, taking into account the viscous damping coefficient for reduction during the calculation. The updated particle motion state is updated using the Velocity-Verlet format according to the Newton-Euler equation; S6. Output particle simulation information.

2. The method for accelerated simulation of arbitrary-shaped rock and soil granular materials based on level sets according to claim 1, characterized in that: The establishment of the level set particle model of arbitrary shape includes: generating a level set function based on a particle model of implicit surface function, a particle model of SDF function or a particle model of polyhedron.

3. The method for accelerating the simulation of arbitrary-shaped rock and soil granular materials based on level sets according to claim 1, characterized in that: The step of obtaining the level set function value and gradient value of the structured grid node specifically includes: Where φ is the value of the level set function, is the interpolation basis function, p N is the grid node, Ω is the space where the irregular particles are located, and v i represents the level set background grid, p is v i A little inside.

4. The method for accelerating the simulation of arbitrary-shaped rock and soil granular materials based on level sets according to claim 1, characterized in that: The step of obtaining particle information according to the shape template specifically includes obtaining basic quantities and particle data of mass, center of mass, moment of inertia, etc. according to the shape template. The formula for calculating the basic quantities is as follows: in, is the mass of the shape template, c is the center of mass, I is the moment of inertia, ρ is the material density, V c is the voxel volume, H(φ) is the smooth Heaviside function, and the subscripts x, y, and z represent the components on the x, y, and z axes, respectively; The formula for obtaining the rigid particle information by scaling, rotating, and translating the shape template is as follows: in, is a spatial point in local coordinates, t is a translation vector, R is a rotation matrix, and S is a diagonal scaling matrix.

5. The method for accelerating simulation of arbitrary-shaped rock and soil granular materials based on level sets according to claim 1, characterized in that: The potential contact pair list is constructed as follows: a particle-particle Verlet list is constructed according to an extended multi-level Linked-cell method; a wide-area search is performed according to the multi-level Linked-cell method, wherein bounding sphere detection is adopted, including intra-level search and inter-level search; the particle-particle Verlet list is updated after the maximum cumulative displacement of the i-level bounding sphere reaches half of the Verlet distance, and the formula is as follows: in, is the cumulative displacement of the i-th level enclosing sphere at time t; is the i-th level Verlet distance of the particle-particle Verlet list; The vertex-particle Verlet list is constructed according to the extended multi-level linked-cell method, in which directed bounding box detection is adopted. The vertex-particle Verlet list is updated after the maximum relative displacement between the master particle i and the slave particle j reaches the Verlet distance. The formula is as follows: in, and are the velocity, angular velocity and radius of the surrounding sphere, respectively, where the superscript □=i,j represents the bead particle and the slave particle, respectively, l v is the Verlet distance.

6. The method for accelerating simulation of arbitrary-shaped rock and soil granular materials based on level sets according to claim 1, characterized in that: The narrow-area contact detection and calculation of normal contact force include: Based on the vertices obtained from the particle model, point-to-surface narrow-area contact detection is performed. The particle with the smaller volume is selected as the master particle, and the other particle is selected as the slave particle. The data of the master particle vertex invading the slave particle is obtained. The formula is as follows: Where δ is the overlap, is the local contact normal, is a local contact point, Surface nodes The position in the local coordinate system of the particle; Calculating point-to-surface contact information on the vertices of the particle model, including: The contact force and contact potential energy field formulas are as follows: in, is the normal contact force, W(x) is the contact potential energy, k n is the normal contact stiffness, ω v is the coefficient to correct the influence of vertex distribution, ε(δ) is the directed distance potential energy field function; Specifically, ω v Take it as: in, and is the area, external normal direction and angle of the i-th adjacent patch, N af and S p are the number of adjacent facets around the vertex and the surface area of ​​the particle; Specifically, ε(δ) is taken as: Among them, β is the potential energy parameter.

7. The method for accelerating simulation of arbitrary-shaped rock and soil granular materials based on level sets according to claim 1, characterized in that: The calculation of the tangential contact force and contact moment based on the normal contact force and the reduction considering the viscous damping coefficient include: The normal contact force, tangential contact force and contact moment are: Among them, k t is the tangential stiffness, μ is the friction coefficient, ε n , ε t are the normal and tangential viscous damping coefficients, δ t is the cumulative tangential displacement.

8. The method for accelerated simulation of arbitrary-shaped rock and soil granular materials based on level sets according to claim 7, characterized in that: The updating of the particle motion state using the Velocity-Verlet format according to the Newton-Euler equation includes: Where m is the mass of the particle, v and ω are the velocity and angular velocity respectively, is the damping coefficient.

9. A level set-based accelerated simulation device for arbitrarily shaped rock and soil granular materials, comprising a memory and one or more processors, wherein the memory stores executable code, characterized in that: When the processor executes the executable code, the method for accelerating simulation of rock and soil granular materials of arbitrary shapes based on level sets according to any one of claims 1 to 8 is implemented.

10. A computer-readable storage medium having a program stored thereon, characterized in that: When the program is executed by a processor, the method for accelerating simulation of rock and soil granular materials of arbitrary shapes based on level sets according to any one of claims 1 to 8 is implemented.

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