Large deformation SPH large-scale engineering simulation method, electronic device and storage medium

Abstract

The present application belongs to the technical field of numerical simulation and geotechnical engineering, and provides a large deformation SPH large-scale engineering simulation method, an electronic device and a storage medium, wherein the method comprises: discretizing the calculation domain of the SPH particle model and establishing a neighbor search relationship, and assigning material mechanical parameters by using a random field mapping method; performing half-step and full-step updating of the SPH particle by using a position-based Verlet method; performing correction by using the dissipation strategy of a low-dissipation Riemann solver, and then performing second half-step updating of density and position; calculating the velocity gradient and the strain rate tensor of the SPH particle, and performing stress updating of the SPH particle by using a Drucker-Prager model and a return mapping algorithm; and performing smoothing processing on the stress-updated SPH particle to obtain a simulation result. The present application has the beneficial effect of improving the efficiency and accuracy of the simulation of the large deformation process of granular materials.

Description

Technical Field

[0001] This invention relates to the fields of numerical simulation and geotechnical engineering technology, and in particular to a large deformation SPH large-scale engineering simulation method, electronic equipment and storage medium. Background Technology

[0002] Many disasters and engineering phenomena in Earth science and geotechnical engineering are closely related to the large deformation behavior of granular materials under external forces, such as landslides, debris flows, avalanches, and the instability of large earth-rock dams, slopes, and underground engineering structures. In-depth research on these granular flows and engineering deformation mechanisms is of great significance for revealing Earth's surface processes and ensuring the safety of major engineering projects. While traditional physical experiments have accumulated rich results in granular flow research, limitations in experimental scale and observation conditions make it difficult to comprehensively obtain key data such as velocity distribution, stress field, and strain field at the particle scale. This limits the revelation of microscopic mechanisms and the comprehensive analysis of large-scale engineering problems.

[0003] Numerical simulation technology provides an important approach for studying large deformation problems of granular materials. Among them, the Smooth Particle Hydrodynamics (SPH) method, as a meshless method based entirely on Lagrangian particles, is naturally suitable for simulating large deformation, fracture, and failure processes. Compared with mesh-based numerical methods such as the finite element method and the finite difference method, SPH avoids the problem of decreased computational accuracy caused by mesh distortion, making it more suitable for handling large-scale deformation and failure, especially in complex terrain and large-scale engineering simulations. However, existing SPH methods generally suffer from numerical instability and non-physical oscillations when applied to the simulation of large deformation of granular materials. To improve computational stability, traditional approaches often introduce artificial viscosity or artificial stress terms into the momentum equation to reduce pressure oscillations and tensile instability. However, these numerical dissipation terms often lead to excessive energy dissipation, resulting in deviations in physical flow properties, making it difficult to balance numerical stability and computational accuracy.

[0004] Furthermore, the mechanical properties of granular materials typically exhibit significant spatial heterogeneity and randomness; for example, strength and stiffness parameters show uncertainty in their spatial distribution. The impact of this material randomness is significant in disaster processes such as landslides and debris flows, as well as in the stability analysis of large earth-rock dams and the safety of engineering fill structures. However, most existing SPH studies assume a homogeneous spatial distribution of material parameters, failing to effectively characterize the random characteristics of granular materials, leading to discrepancies between simulation results and actual conditions. Summary of the Invention

[0005] Aimed at at least in solving one of the technical problems existing in the prior art, the present invention provides a large deformation SPH large-scale engineering simulation method, electronic device and storage medium, which improves the efficiency and accuracy of simulating the large deformation process of particulate materials.

[0006] One aspect of the present invention provides a large-deformation SPH (Special Perception) large-scale engineering simulation method, comprising: SPH particle models of soil and boundaries are established. The computational domain of the SPH particle model is discretized to obtain SPH particles, and neighbor search relationships are established. SPH particles are assigned mechanical parameters by random field mapping. Based on the material mechanics parameters of SPH particles, the position-based Verlet method is used for the first half-step update, followed by a full-step update of the SPH particle velocity field. The dissipation strategy of the low-dissipation Riemann solver is used to correct the SPH particle, which includes density dissipation term and momentum dissipation term. A second half-step update of the density and position of the corrected SPH particles is performed. The velocity gradient and strain rate tensor of SPH particles are calculated, and then the stress of SPH particles is updated using the Drucker-Prager model and the back-mapping algorithm. The SPH particles updated by stress were smoothed to obtain the simulation results.

[0007] According to the large deformation SPH large-scale engineering simulation method, which includes establishing an SPH particle model of soil and boundary, discretizing the computational domain of the SPH particle model to obtain SPH particles, and establishing neighbor search relationships, it also includes: A SPH particle model for soil and boundary is established. The computational domain of the SPH particle model is discretized to obtain discretized SPH particles, which include soil particles and boundary particles. For the discretized SPH particles, a neighbor list is constructed according to a preset search radius, where the neighbor list is used to characterize the interaction relationship between adjacent particles; Calculate the kernel function and gradient for each SPH particle based on the neighbor list.

[0008] According to the large deformation SPH large-scale engineering simulation method, the SPH particles are assigned material mechanical parameters using a random field mapping method, including: SPH particles are assigned material mechanical parameters, including density, elastic modulus, Poisson's ratio, friction angle, and cohesion. The friction angle and cohesion are assigned values ​​using a random field generation method, including generating an independent standard normal sample matrix ζ using Latin hypercube sampling and utilizing the correlation coefficient matrix between parameters. The Cholesky decomposition introduces the correlation between parameters, resulting in a correlation standard normal random sample matrix. The standard normal random sample matrix The lower triangular matrix obtained by decomposing the autocorrelation matrix of the parameters Multiply to generate a standard Gaussian random field and the standard Gaussian random field Taking the logarithm yields the log-normal random field Normal random field The generated friction angle and cohesion are mapped onto SPH particles, where and For different locations, For the mean parameter of the random field, Let be the standard deviation parameter of the random field.

[0009] According to the large-deformation SPH large-scale engineering simulation method, based on the material mechanics parameters of the SPH particles, a position-based Verlet method is used for the first half-step update, followed by a full-step update of the SPH particle velocity field, including: Based on the material mechanical parameters of SPH particles, determine the density change rate and velocity of SPH particles in the previous time step. The density of SPH particles is corrected half-step using the discrete form of the continuity equation, and the density and position of SPH particles are predicted half-step:

[0010] in, The density of SPH particles, The position of the SPH particles. For time step, For time steps, The velocity of the SPH particles; Based on the density and position of the SPH particles updated half-step, the momentum conservation equation is applied to traverse each real particle. Neighborhood particles To calculate particles Acceleration:

[0011] in, For particles speed For particles quality For particles Stress Tensor For particles Stress tensor For particles density For particles density For kernel function For gravitational acceleration, particles For soil particles, particles For boundary particles; According to particles The acceleration is updated in full step using no-slip boundary conditions for the SPH particle velocity field: .

[0012] According to the large deformation SPH large-scale engineering simulation method, the dissipation strategy of the SPH particles is modified using a low-dissipation Riemann solver, including: The dissipation strategy is expressed as follows:

[0013] in, For the speed of sound, For particles gradient, For density dissipation, For momentum dissipation, For dissipation terms, The stress is in the left-hand state. The stress is in the right-hand state. The average density of the left and right states. The velocity in the left state, The velocity is the velocity in the right state, where the velocity is the velocity in the left state. Located in the particle Right state Located in the particle , For limiter, for:

[0014] The limiter is used to prevent dissipation when the fluid is subjected to an expansion wave, i.e. , These are parameters used to control numerical dissipation.

[0015] According to the large-deformation SPH large-scale engineering simulation method, the second half-step update of the density and position of the corrected SPH particles includes: Calculate the particle using the mass conservation equation. Density change rate:

[0016] By applying no-slip boundary conditions, the density change rate of SPH particles is used to update the neighborhood containing particles. particles When the density change rate is... for particles speed Calculate using the following formula:

[0017] in, The overall velocity at the boundary; According to particles Density change rate and speed A second half-step update will be performed: .

[0018] According to the large deformation SPH large-scale engineering simulation method, the SPH particle velocity gradient and strain rate tensor are calculated, and then the Drucker-Prager model and return mapping algorithm are used to update the stress of the SPH particles, including: Based on the position and velocity of the SPH particles after the second half-step update, calculate the particle... velocity gradient, particle The discrete representation of the velocity gradient is:

[0019] According to particles Discrete representation of the velocity gradient, determining the strain rate tensor of the SPH particle. and rotation tensor for:

[0020] in, transpose of a tensor Based on strain rate tensor and rotation tensor The Drucker-Prager algorithm and return mapping algorithm are used for volume stress correction and deviatoric stress correction. The stress rate tensor is calculated using the Drucker-Prager constitutive relation:

[0021] in, It is the stress rate tensor; Shear modulus; For the partial strain rate tensor; Bulk modulus; It is a plastic multiplier; It is the expansion / contraction factor; This is the second deviatoric stress invariant; It is the deviatoric stress tensor; If satisfied The formula for correcting body stress using the return mapping algorithm is as follows:

[0022] in, To return the mapped stress tensor; To return the stress tensor before mapping; This is the first stress invariant; It is the Drucker-Prager constant; Unit tensor; When satisfied When the deviatoric stress is updated using the return mapping algorithm, the formula is:

[0023] in, To return the pre-mapped biased stress tensor.

[0024] According to the large deformation SPH large-scale engineering simulation method described above, the smoothing process for stress-updated SPH particles includes: The Drucker-Prager constitutive relation is constrained by adding a stress diffusion term:

[0025] For particles Among them, the diffusion term The calculation formula is:

[0026] in, This is the adjustment coefficient; For smooth length; For diffusion operators; For particles With particles The position vector.

[0027] Another aspect of the present invention provides an electronic device, including a processor and a memory; The memory is used to store programs; The processor executes the program to implement the method as described above.

[0028] This invention also discloses a computer program product or computer program, which includes computer instructions stored in a computer-readable storage medium. A processor of a computer device can read the computer instructions from the computer-readable storage medium and execute the computer instructions, causing the computer device to perform the methods described above.

[0029] The beneficial effects of this invention are as follows: By precisely controlling numerical dissipation through a low-dissipation Riemannian solver and correcting stress oscillations by incorporating a stress diffusion term, while simultaneously introducing a random field to characterize the spatial heterogeneity and randomness of the material, the stability and realism of the simulation are significantly improved while ensuring computational accuracy. This invention can more realistically reproduce the complex deformation process of granular materials in large-scale engineering projects, and is suitable for simulating and analyzing major engineering problems such as landslides, debris flows, earth-rock dams, and slopes. It improves the efficiency and accuracy of simulating large deformation processes of granular materials, providing a reliable basis for disaster risk assessment, engineering instability prediction, and geotechnical structure design. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the large-scale engineering simulation process of SPH with large deformation according to an embodiment of the present invention.

[0031] Figure 2 This is a schematic diagram of particle discreteness according to an embodiment of the present invention.

[0032] Figure 3 This is an approximate particle diagram in the SPH of this invention embodiment.

[0033] Figure 4 This is an embodiment of the invention along the particle and particles A schematic diagram of the Riemann problem construction of interaction lines.

[0034] Figure 5 This is a schematic diagram of the return mapping algorithm according to an embodiment of the present invention.

[0035] Figure 6 This is a two-dimensional particle flow model according to an embodiment of the present invention.

[0036] Figure 7 This is a comparison chart of the numerical model and experimental results of L=0.2m in an embodiment of the present invention.

[0037] Figure 8 This is a comparison chart of the numerical model and experimental results of L=0.1m in an embodiment of the present invention.

[0038] Figure 9 This is a simulation diagram of the angle of repose test according to an embodiment of the present invention.

[0039] Figure 10 This is a three-dimensional particle flow comparison diagram of the method and experimental empirical equation results of the embodiments of the present invention.

[0040] Figure 11 This refers to the interaction between the particle flow and the rigid structure, as determined by the method and experimental empirical equations in this embodiment of the invention.

[0041] Figure 12These are diagrams showing the evolution of particle flow at different times based on the method and experimental empirical equation results of this invention, where (a) represents the evolution of particle flow at time T1, and (b) represents the evolution of particle flow at time T2.

[0042] Figure 13 This is a comparison chart of the impact force results obtained by the method of this invention embodiment and the experimental empirical equation. Detailed Implementation

[0043] The embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings. Throughout the description, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions. In the following description, suffixes such as "module," "part," or "unit" used to denote elements are used only for the purpose of illustrative purposes and have no specific meaning in themselves. Therefore, "module," "part," or "unit" can be used interchangeably. Terms such as "first," "second," etc., are used only to distinguish technical features and should not be construed as indicating or implying relative importance, or implicitly indicating the number of indicated technical features, or implicitly indicating the sequential relationship of the indicated technical features. In the following description, the consecutive reference numerals for method steps are for ease of review and understanding. Adjusting the implementation order of steps, in conjunction with the overall technical solution of the present invention and the logical relationship between the various steps, will not affect the technical effect achieved by the technical solution of the present invention. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0044] refer to Figure 1 This is a flowchart illustrating the large deformation SPH large-scale engineering simulation method, which includes, but is not limited to, steps S100~S700: S100: Establish an SPH particle model for the soil and boundary, discretize the computational domain of the SPH particle model to obtain SPH particles, and establish neighbor search relationships.

[0045] In some embodiments, by establishing an SPH particle model of soil and boundary, the computational domain of the SPH particle model is discretized to obtain discretized SPH particles, wherein the SPH particles include soil particles and boundary particles; a neighbor list is constructed for the discretized SPH particles according to a preset search radius, wherein the neighbor list is used to characterize the interaction relationship between adjacent particles; the kernel function and gradient of each SPH particle are calculated according to the neighbor list.

[0046] In some embodiments, reference Figure 2 Schematic diagram of particle discreteness and Figure 3 An approximate particle diagram in SPH. Figure 2A SPH particle model of soil and boundary is established, and the computational domain is discretized to divide the continuous soil and boundary into discrete particles, generating soil particles and boundary particles. Figure 3 exist Figure 2 Based on this, the kernel function and its gradient are calculated for each particle, providing support for the subsequent solution of the SPH motion equations and the updating of mechanical quantities.

[0047] S200 assigns mechanical parameters to SPH particles using a random field mapping method.

[0048] In some embodiments, SPH particles are assigned material mechanical parameters, including density, elastic modulus, Poisson's ratio, friction angle, and cohesion. The friction angle and cohesion are assigned values ​​using a random field generation method, including generating an independent standard normal sample matrix ζ using Latin hypercube sampling and utilizing the correlation coefficient matrix between parameters. The Cholesky decomposition introduces the correlation between parameters, resulting in a correlation standard normal random sample matrix. The standard normal random sample matrix The lower triangular matrix obtained by decomposing the autocorrelation matrix of the parameters Multiply to generate a standard Gaussian random field and the standard Gaussian random field Taking the logarithm yields the log-normal random field Normal random field The generated friction angle and cohesion are mapped onto SPH particles, where and For different locations, For the mean parameter of the random field, Let be the standard deviation parameter of the random field.

[0049] It is understandable that, through the method of this embodiment, the number of discrete random variables is exactly equal to the number of discrete SPH particles, which has an intuitive physical meaning. Finally, these are mapped onto each SPH particle, so that each particle obtains a corresponding randomized friction angle and cohesion, thereby reflecting the heterogeneity and randomness of the material in space.

[0050] S300 uses the position-based Verlet method to perform the first half-step update based on the material mechanics parameters of SPH particles, and then performs a full-step update of the SPH particle velocity field.

[0051] In some embodiments, the density change rate and velocity of the SPH particles at the previous time step are determined based on the material mechanical parameters of the SPH particles.

[0052] The density of SPH particles is corrected half-step using the discrete form of the continuity equation, and the density and position of SPH particles are predicted half-step:

[0053] in, The density of SPH particles, The position of the SPH particles. For time step, For time steps, The velocity of the SPH particles.

[0054] In some embodiments, the particle density and position are advanced by half a time step using the density change rate and velocity information obtained from the previous time step. Specifically, the density is corrected half a step using the discrete form of the continuity equation, and the position is predicted half a step based on the particle velocity, thus providing an intermediate state for subsequent momentum and stress updates.

[0055] Based on the density and position of the SPH particles updated half-step, the momentum conservation equation is applied to traverse each real particle. Neighborhood particles To calculate particles Acceleration:

[0056] in, For particles speed For particles quality For particles Stress tensor For particles Stress tensor For particles density For particles density For kernel function For gravitational acceleration, particles For soil particles, particles For boundary particles; According to particles The acceleration is updated in full step using no-slip boundary conditions for the SPH particle velocity field:

[0057] Understandably, to ensure that boundary particles accurately reflect external constraints while maintaining numerical stability and physical consistency of the velocity field near the boundary, when updating particle acceleration near the boundary using the above formula, if the particles... If it is a boundary particle, then assume the particle Stress tensor equals particle The stress tensor. After updating the accelerations of all particles, update the particle velocities to the full time step using the following formula.

[0058] S400 modifies the dissipation strategy of the SPH particle using a low-dissipation Riemann solver, which includes density dissipation and momentum dissipation terms.

[0059] In some embodiments, the dissipation strategy is expressed as:

[0060] in, For the speed of sound, For particles gradient, For density dissipation, For momentum dissipation, For dissipation terms, The stress is in the left-hand state. The stress is in the right-hand state. The average density of the left and right states. The velocity in the left state, The velocity is the velocity in the right state, where the velocity is the velocity in the left state. Located in the particle Right state Located in the particle , For limiter, for:

[0061] The limiter is used to prevent dissipation when the fluid is subjected to an expansion wave, i.e. , For parameters used to control numerical dissipation, preferably, wherein Set as , Represents the dimension of the model space.

[0062] It should be noted that, in order to correct the non-physical oscillations and tensile instability that may occur in the SPH method during large deformation simulations, appropriate numerical dissipation needs to be introduced. This embodiment of the invention employs a dissipation strategy based on a low-dissipation Riemann solver, in the particle... Pointing to particles Construct a Riemann problem between particles along the unit vector direction, such as Figure 4 The following is along the particle and particles A schematic diagram of the Riemann problem construction for interaction lines, in which the initial left state... Right state Located in the particle and particles Above, the discontinuous surface is located at the midpoint between the two particles.

[0063] It is understood that the embodiments of the present invention provide the jump or average value of the velocity, pressure and other states at the interface by solving the Riemann problem. The numerical dissipation can be implicitly introduced by replacing the average particle variable in the control equation with the Riemann solution, and finally the density dissipation term and momentum dissipation term can be obtained.

[0064] S500 performs a second half-step update on the density and position of the corrected SPH particles.

[0065] In some embodiments, particle mass conservation equations are used to calculate... Density change rate:

[0066] By applying no-slip boundary conditions, the density change rate of SPH particles is used to update the neighborhood containing particles. particles When the density change rate is... for particles speed Calculate using the following formula:

[0067] in, The overall boundary velocity is preferably set to 0.

[0068] According to particles Density change rate and speed A second half-step update will be performed:

[0069] S600 calculates the velocity gradient and strain rate tensor of SPH particles, and then uses the Drucker-Prager model and the return mapping algorithm to update the stress of SPH particles.

[0070] In some embodiments, the particle is calculated based on the position and velocity of the SPH particles after the second half-step update. velocity gradient, particle The discrete representation of the velocity gradient is:

[0071] According to particles Discrete representation of the velocity gradient, determining the strain rate tensor of the SPH particle. and rotation tensor for:

[0072] in, transpose of a tensor Based on strain rate tensor and rotation tensor The Drucker-Prager algorithm and return mapping algorithm are used for volume stress correction and deviatoric stress correction. The stress rate tensor is calculated using the Drucker-Prager constitutive relation:

[0073] in, It is the stress rate tensor; Shear modulus; For the partial strain rate tensor; Bulk modulus; It is a plastic multiplier; It is the expansion / contraction factor; This is the second deviatoric stress invariant; It is the deviatoric stress tensor.

[0074] It should be noted that the stress tensor can be updated based on the stress rate tensor obtained above. For the Drucker–Prager model, the stress state cannot exceed the yield surface. However, in actual numerical calculations, due to the discretization effect of time step integration, the stress state may exceed the yield surface after updating.

[0075] like Figure 5 As shown, the return mapping algorithm performs volume stress correction and deviatoric stress correction. It needs to check whether the stress state exceeds the yield surface at each time step. If it does, an additional correction operation must be applied to project the stress state back into the yield surface.

[0076] If satisfied The formula for correcting body stress using the return mapping algorithm is as follows:

[0077] in, To return the mapped stress tensor; To return the stress tensor before mapping; This is the first stress invariant; It is the Drucker-Prager constant; Unit tensor; When satisfied When the deviatoric stress is updated using the return mapping algorithm, the formula is:

[0078] in, To return the pre-mapped biased stress tensor.

[0079] S700 is used to smooth the stress-updated SPH particles to obtain the simulation results.

[0080] The Drucker-Prager constitutive relation is constrained by adding a stress diffusion term:

[0081] For particles Among them, the diffusion term The calculation formula is:

[0082] in, This is the adjustment coefficient; For smooth length; For diffusion operators; For particles With particles The position vector.

[0083] Understandably, most existing geotechnical engineering applications of SPH (Stress Propagation) focus primarily on kinematic predictions, which can be well correlated with experimental results. However, under conditions of large deformation, stress fluctuations can occur, affecting the accuracy of the SPH method. This invention employs a stress diffusion term to obtain a smooth stress profile, which is directly added to the constitutive equations.

[0084] In some embodiments, by repeating steps S200 to S700 until a preset simulation time is reached, the numerical results of this invention can be processed and output, including particle velocity distribution, density and stress changes, and flow range at each time point. The obtained output results can be further used for the analysis and visualization of large deformation behavior of granular materials, and can provide a reliable basis for risk assessment and engineering safety analysis of disasters such as landslides and debris flows.

[0085] The effectiveness and accuracy of the model proposed in the embodiments of the present invention are verified through the following benchmark experiments.

[0086] Example 1: Two-dimensional granular flow like Figure 6 The two-dimensional granular flow model shown has an initial column length and height of L and H, respectively. Two sets of numerical experiments were conducted, with the model height being 0.1 m in both cases and the model widths being 0.1 m and 0.2 m, respectively. The particle material parameters are shown in Table 1. The initial particle spacing was set to 2 mm.

[0087] Table 1. Parameter values ​​for two-dimensional particle flow

[0088] The particle column was released freely under its own weight, and its dynamic evolution during the collapse was recorded and compared with experimental results. Figure 7 Comparison of numerical model and experimental results for L=0.2m and Figure 8 A comparison of the numerical model and experimental results for L=0.1m is shown in the figure. Figure 7 and Figure 8 The velocity distribution of the particle column at different time points obtained from SPH simulations for models with L=0.2m and L=0.1m are shown. Furthermore, the particle profiles observed in the experiment (solid red lines) are presented to demonstrate the performance of the algorithm proposed in this embodiment. The particle flow begins at the front of the column and gradually moves forward until it stops at the toe of the sediment. The collapse mechanism is shear failure, and a shear band interface can be observed below which particles remain stationary while other particles move outward. For the L=0.2m model, the upper region remains undisturbed after failure, thus maintaining its height. However, for the L=0.1m model, the column completely collapses, and its height gradually decreases. Throughout the entire failure process of the particle column, the simulation results are very similar to the profiles observed in the experiment, demonstrating the accuracy of the method in this embodiment.

[0089] Example 2: Three-dimensional granular flow like Figure 9 The diagram showing the simulation process of the angle of repose test is illustrated by setting the height to... , radius is The cylindrical particle column was released instantaneously under its own weight, and the flow distance was measured after it finally stabilized. The initial particle spacing was 5 mm. The initial height of the soil column was changed. And keep the radius The design and development of different height-to-radius ratios were carried out. Numerical experiments were conducted under different conditions to obtain the flow distance under different circumstances, and the results were compared with experimental results to verify the correctness of the three-dimensional model. The results are as follows: Figure 10 The diagram shows a comparison of three-dimensional particle flows. It can be seen that the relationship between flow distance and height-to-radius ratio is consistent with experimental data, and the proposed algorithm can predict the flow distance of three-dimensional particle flows.

[0090] Example 3: Interaction between granular flow and rigid structures like Figure 11 The interaction between the particle flow and the rigid structure is illustrated in the series of physical experiments conducted on the particle flow using dry fine sand on an inclined chute. Initially, the gravel is contained in a box located at the top of the chute. After release, the material flows under gravity and then impacts a rigid barrier. A measuring instrument is mounted on the rigid barrier to measure the impact force generated by the particle flow. Additional space is provided behind the rigid barrier to allow the particle flow to overflow. The same three-dimensional model is established in this embodiment, with the particle spacing set to 0.01 m. The evolution of the particle flow at different times is shown below. Figure 12 The diagrams show the evolution of particle flow at different times, where (a) represents the particle flow evolution at time T1, and (b) represents the particle flow evolution at time T2, where T2>T1, for comparison with experimental results. Figure 11 The particle flow profile in the experiment is marked with a red line. Similar to the experiment, in the SPH simulation, particulate matter flows downwards after release. The sand particles then impact a rigid barrier and accumulate in front of it. As the accumulated sand particles gradually reach the top of the barrier, they overflow the barrier.

[0091] The measured impact force of the rigid barrier is as follows Figure 12 As shown, the trend of the SPH model in this embodiment of the invention is consistent with the experimental curve. The initial impact force is zero until the particle flow collides with the barrier. Afterward, the impact force gradually increases and then reaches a peak, corresponding to the stage where material accumulates near the barrier. Subsequently, the impact force decreases to some extent due to overflow. Compared with the previous numerical curves SPH-1, SPH-2, and CFD, the peak and residual impact forces of the SPH method in this embodiment of the invention match the experimental data very well.

[0092] This invention also provides an electronic device, which includes a processor and a memory; The memory stores the program; The processor executes a program to perform the aforementioned large deformation SPH large-scale engineering simulation method; the electronic device has the function of carrying and running the software system for large deformation SPH large-scale engineering simulation provided in the embodiments of the present invention, such as a personal computer, minicomputer, mainframe, workstation, network or distributed computing environment, standalone or integrated computer platform, or communicating with charged particle tools or other imaging devices, etc.

[0093] This invention also provides a computer-readable storage medium storing a program that is executed by a processor to implement the large deformation SPH large-scale engineering simulation method as described above.

[0094] In some alternative embodiments, the functions / operations mentioned in the block diagrams may not occur in the order shown in the operation diagrams. For example, depending on the functions / operations involved, two consecutively shown blocks may actually be executed substantially simultaneously, or the blocks may sometimes be executed in reverse order. Furthermore, the embodiments presented and described in the flowcharts of this invention are provided by way of example to provide a more comprehensive understanding of the technology. The disclosed methods are not limited to the operations and logic flows presented in the embodiments of this invention. Alternative embodiments are contemplated, in which the order of various operations is changed and sub-operations described as part of a larger operation are executed independently.

[0095] This invention also discloses a computer program product or computer program, which includes computer instructions stored in a computer-readable storage medium. A processor of a computer device can read the computer instructions from the computer-readable storage medium and execute the computer instructions, causing the computer device to perform the aforementioned large-scale deformation SPH large-scale engineering simulation method.

[0096] Furthermore, although the invention has been described in the context of functional modules, it should be understood that, unless otherwise stated, one or more of the described functions and / or features may be integrated into a single physical device and / or software module, or one or more functions and / or features may be implemented in a separate physical device or software module. It is also understood that a detailed discussion of the actual implementation of each module is unnecessary for understanding the invention. Rather, considering the properties, functions, and internal relationships of the various functional modules in the apparatus disclosed in the embodiments of the invention, the actual implementation of the module will be understood within the scope of conventional skill of an engineer. Therefore, those skilled in the art can implement the invention as set forth in the claims using ordinary techniques without excessive experimentation. It is also understood that the specific concepts disclosed are merely illustrative and are not intended to limit the scope of the invention, which is determined by the full scope of the appended claims and their equivalents.

[0097] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, essentially, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0098] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can include, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0099] More specific examples of computer-readable media (a non-exhaustive list) include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0100] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0101] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0102] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

[0103] The above is a detailed description of the preferred embodiments of the present invention, but the present invention is not limited to the embodiments described. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention, and these equivalent modifications or substitutions are all included within the scope defined by the claims of this application.

Claims

1. A large-scale engineering simulation method for large deformation SPH, characterized in that, include: SPH particle models of soil and boundaries are established. The computational domain of the SPH particle model is discretized to obtain SPH particles, and neighbor search relationships are established. SPH particles are assigned mechanical parameters by random field mapping. Based on the material mechanics parameters of SPH particles, the position-based Verlet method is used for the first half-step update, followed by a full-step update of the SPH particle velocity field. The dissipation strategy of the low-dissipation Riemann solver is used to correct the SPH particle, which includes density dissipation term and momentum dissipation term. A second half-step update of the density and position of the corrected SPH particles is performed. The velocity gradient and strain rate tensor of SPH particles are calculated, and then the stress of SPH particles is updated using the Drucker-Prager model and the back-mapping algorithm. The SPH particles updated by stress were smoothed to obtain the simulation results.

2. The large deformation SPH large-scale engineering simulation method according to claim 1, characterized in that, The process of establishing an SPH particle model for soil and boundaries, discretizing the computational domain of the SPH particle model to obtain SPH particles, and establishing neighbor search relationships also includes: A SPH particle model for soil and boundary is established. The computational domain of the SPH particle model is discretized to obtain discretized SPH particles, which include soil particles and boundary particles. For the discretized SPH particles, a neighbor list is constructed according to a preset search radius, where the neighbor list is used to characterize the interaction relationship between adjacent particles; Calculate the kernel function and gradient for each SPH particle based on the neighbor list.

3. The large deformation SPH large-scale engineering simulation method according to claim 1, characterized in that, The method of assigning mechanical parameters to SPH particles using random field mapping includes: SPH particles are assigned material mechanical parameters, including density, elastic modulus, Poisson's ratio, friction angle, and cohesion. The friction angle and cohesion are assigned values ​​using a random field generation method, including generating an independent standard normal sample matrix ζ using Latin hypercube sampling and utilizing the correlation coefficient matrix between parameters. The Cholesky decomposition introduces the correlation between parameters, resulting in a correlation standard normal random sample matrix. The standard normal random sample matrix The lower triangular matrix obtained by decomposing the autocorrelation matrix of the parameters Multiply to generate a standard Gaussian random field and the standard Gaussian random field Taking the logarithm yields the log-normal random field Normal random field The generated friction angle and cohesion are mapped onto SPH particles, where and For different locations, For the mean parameter of the random field, Let be the standard deviation parameter of the random field.

4. The large deformation SPH large-scale engineering simulation method according to claim 2, characterized in that, The process involves performing a first half-step update based on the material mechanics parameters of the SPH particles using the position-based Verlet method, followed by a full-step update of the SPH particle velocity field, including: Based on the material mechanical parameters of SPH particles, determine the density change rate and velocity of SPH particles in the previous time step. The density of SPH particles is corrected half-step using the discrete form of the continuity equation, and the density and position of SPH particles are predicted half-step: in, The density of SPH particles, The position of the SPH particles. For time step, For time steps, The velocity of the SPH particles; Based on the density and position of the SPH particles updated half-step, the momentum conservation equation is applied to traverse each real particle. Neighborhood particles To calculate particles Acceleration: in, For particles speed For particles quality For particles Stress tensor For particles Stress tensor For particles density For particles density For kernel function For gravitational acceleration, particles For soil particles, particles For boundary particles; According to particles The acceleration is updated in full step using no-slip boundary conditions for the SPH particle velocity field: .

5. The large deformation SPH large-scale engineering simulation method according to claim 4, characterized in that, The modification of the SPH particle using a low-dissipation Riemann solver dissipation strategy includes: The dissipation strategy is expressed as follows: in, For the speed of sound, For particles gradient, For density dissipation, For momentum dissipation, For dissipation terms, The stress is in the left-hand state. The stress is in the right-hand state. The average density of the left and right states. The velocity in the left state, The velocity is the velocity in the right state, where the velocity is the velocity in the left state. Located in the particle Right state Located in the particle , For limiter, for: The limiter is used to prevent dissipation when the fluid is subjected to an expansion wave, i.e. , These are parameters used to control numerical dissipation.

6. The large deformation SPH large-scale engineering simulation method according to claim 5, characterized in that, The second half-step update of the density and position of the corrected SPH particles includes: Calculate the particle using the mass conservation equation. Density change rate: By applying no-slip boundary conditions, the density change rate of SPH particles is used to update the neighborhood containing particles. particles When the density change rate is... for particles speed Calculate using the following formula: in, The overall velocity at the boundary; According to particles density change rate and particles speed A second half-step update will be performed: 。 7. The large deformation SPH large-scale engineering simulation method according to claim 6, characterized in that, The calculation of the SPH particle velocity gradient and strain rate tensor, followed by stress update of the SPH particles using the Drucker-Prager model and the return mapping algorithm, includes: Based on the position and velocity of the SPH particles after the second half-step update, calculate the particle... velocity gradient, particle The discrete representation of the velocity gradient is: According to particles Discrete representation of the velocity gradient, determining the strain rate tensor of the SPH particle. and rotation tensor for: in, transpose of a tensor Based on strain rate tensor and rotation tensor The Drucker-Prager algorithm and return mapping algorithm are used for volume stress correction and deviatoric stress correction. The stress rate tensor is calculated using the Drucker-Prager constitutive relation: in, It is the stress rate tensor; Shear modulus; For the partial strain rate tensor; Bulk modulus; It is a plastic multiplier; It is the expansion / contraction factor; This is the second deviatoric stress invariant; It is the deviatoric stress tensor; If satisfied The formula for correcting body stress using the return mapping algorithm is as follows: in, To return the mapped stress tensor; To return the stress tensor before mapping; This is the first stress invariant; It is the Drucker-Prager constant; Unit tensor; When satisfied When the deviatoric stress is updated using the return mapping algorithm, the formula is: in, To return the pre-mapped biased stress tensor.

8. The large deformation SPH large-scale engineering simulation method according to claim 7, characterized in that, The smoothing process for stress-updated SPH particles includes: The Drucker-Prager constitutive relation is constrained by adding a stress diffusion term: For particles Among them, the diffusion term The calculation formula is: in, This is the adjustment coefficient; For smooth length; For diffusion operators; For particles With particles The position vector.

9. An electronic device, characterized in that, Including the processor and memory; The memory is used to store programs; The processor executes the program to implement the large deformation SPH large-scale engineering simulation method as described in any one of claims 1-8.

10. A computer-readable storage medium, characterized in that, The storage medium stores a program that is executed by a processor to implement the large deformation SPH large-scale engineering simulation method as described in any one of claims 1-8.

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