Eulerian near-field dynamic shock wave simulation method, device and electronic equipment

Abstract

This application relates to a method, apparatus, and electronic device for simulating shock waves using Euler near-field dynamics. The method includes: determining the decoupling characteristics of material points and spatial points in the Euler coordinate system; based on the decoupling characteristics, reconstructing the kinematic relationship of state-type near-field dynamics within the Euler framework; establishing an Euler near-field dynamics model under the Euler description based on the kinematic relationship; and modifying the Euler near-field dynamics model using a target artificial viscous dissipation term to construct an artificial viscous dissipation model, which is then used to simulate Euler near-field dynamics shock waves. This solves the problems in related technologies, such as the numerical divergence under high-speed impact loads due to the Lagrangian framework assumption in near-field dynamics, and the tendency for non-physical numerical oscillations to occur on the wavefront when simulating strong discontinuities like shock waves using the Euler framework, thus affecting the accuracy and stability of the simulation.

Description

Technical Field

[0001] This application relates to the field of continuum mechanics, and in particular to an Euler near-field dynamics shock wave simulation method, device, and electronic equipment. Background Technology

[0002] Currently, classical continuum mechanics theory and corresponding numerical methods have achieved great success in numerous scientific problems and engineering applications after years of development. However, they encounter bottlenecks in dealing with various complex discontinuous phenomena caused by the failure of solid materials and structures. For example, difficulties remain regarding the scientific validity of models, computational accuracy, and efficiency in areas such as the evolution of micro-defects, the initiation and propagation of macroscopic cracks, and the interactions between cracks. Furthermore, classical continuum mechanics theory adopts the assumption of local contact and lacks length-scale parameters to describe long-range material interactions or nonlocal effects. This makes it insufficient when analyzing mechanical problems dominated by long-range forces and with significant nonlocal effects, such as failing to reflect the nonlocal effects in the fracture process zone at the crack tip.

[0003] In related technologies, peridynamics introduces nonlocal characteristic lengths and describes particle motion through integral equations. It treats materials as being composed of material points containing material property information, and describes damage and cracking through the interaction forces between material points and the breaking and accumulation of "bonds". It does not require pre-setting crack paths and includes bond-type peridynamic models and state-type peridynamic models. Bond-type peridynamic models are widely used in the simulation of deformation, damage and impact failure of quasi-brittle materials. State-type peridynamic models are divided into two categories: conventional state-type and unconventional state-type. Among them, unconventional state-type peridynamics can be easily connected with the physical quantities in the classical continuum mechanics constitutive model to achieve nonlocal reconstruction of the classical constitutive model.

[0004] However, in related technologies, since the material model assumed by near-field dynamics is a Lagrangian framework, numerical divergence is prone to occur under high-speed impact loads. When extreme physical processes are involved, distortion becomes the core bottleneck restricting the accuracy of the simulation. Although the Euler framework can avoid mesh distortion, it is easy to generate non-physical numerical oscillations on the wavefront when simulating strong discontinuities such as shock waves, which affects the accuracy and stability of the simulation and urgently needs to be improved. Summary of the Invention

[0005] This application provides an Euler near-field dynamics shock wave simulation method, apparatus, and electronic device to solve the problems in related technologies, such as the fact that the working assumption of near-field dynamics is that the material model is a Lagrangian framework, which makes it easy for numerical divergence to occur under high-speed impact loads, and the Euler framework is prone to non-physical numerical oscillations on the wavefront when simulating strong discontinuities such as shock waves, thus affecting the accuracy and stability of the simulation.

[0006] The first aspect of this application provides a method for simulating Euler near-field dynamics shock waves, comprising the following steps: determining the decoupling characteristics of a material point and a spatial point in the Euler coordinate system; based on the decoupling characteristics, reconstructing the kinematic relationship of the state-type near-field dynamics under the Euler framework; based on the kinematic relationship, establishing an Euler near-field dynamics model under the Euler description; and based on the Euler near-field dynamics model, modifying the Euler near-field dynamics model using a target artificial viscous dissipation term to construct an artificial viscous dissipation model, and using the artificial viscous dissipation model to simulate Euler near-field dynamics shock waves.

[0007] Through the aforementioned technical means, the embodiments of this application can reconstruct the kinematic relationship of state-type peridynamics under the Euler framework, based on the decoupling characteristics of material points and spatial points in the Euler coordinate system. An Euler peridynamic model under the Euler description is established, and the Euler peridynamic model is modified by introducing a target artificial viscous dissipation term to simulate Euler peridynamic shock waves. This establishes an Euler peridynamic calculation framework based on the correction of the artificial viscous dissipation term, which can capture shock waves with high precision. It can be widely applied to one-dimensional, two-dimensional, and three-dimensional elastic wave, plastic wave, and shock wave propagation problems, providing an accurate simulation tool for transient problems such as high-speed impacts.

[0008] Optionally, in one embodiment of this application, the step of correcting the Euler peri-field dynamics model using a preset artificial viscous dissipation term includes: determining the stretching ratio of each bond; obtaining the target artificial viscous dissipation term based on the stretching ratio of each bond, so as to correct the Euler peri-field dynamics model based on the target artificial viscous dissipation term.

[0009] Through the above-mentioned technical means, the embodiments of this application can calculate the target artificial viscous dissipation term based on the stretching ratio of each bond, and modify the Euler near-field dynamics model based on the target artificial viscous dissipation term, thereby stabilizing the zero-energy mode and other non-physical deformation modes, eliminating non-physical oscillations, accurately capturing shock waves, and establishing a high-precision Euler near-field dynamics model for shock wave capture.

[0010] Optionally, in one embodiment of this application, the expression for the target artificial viscous dissipation term is: , in, For the target artificial viscous dissipation term, For quasi-static dissipation terms, For dynamic dissipation terms, For volume wave velocity, This represents the velocity change within the neighborhood of a material point.

[0011] Through the above-mentioned technical means, the embodiments of this application can introduce necessary numerical damping through the target artificial viscous dissipation term, effectively suppressing the numerical oscillation of the wavefront, obtaining a clear and steep shock wave profile that is highly consistent with the analytical solution, and avoiding the problem of calculation divergence under extreme conditions such as high-speed impact.

[0012] Optionally, in one embodiment of this application, the method further includes: analyzing the parameter sensitivity of the viscous force state; and adjusting the model parameters of the artificial viscous dissipation model for adapting to different velocity gradient scenarios based on the parameter sensitivity.

[0013] Through the above-mentioned technical means, the embodiments of this application can address the lack of a clear control mechanism for artificial viscous parameters, analyze the parameter sensitivity of viscous force states, adjust parameters to adapt to different velocity gradient scenarios, and improve the versatility and engineering adaptability under different materials and different impact intensities.

[0014] Optionally, in one embodiment of this application, the model parameters include a quasi-static dissipation coefficient and a dynamic dissipation coefficient.

[0015] Through the above-mentioned technical means, the embodiments of this application can complete the analysis of different influence mechanisms on the shock wave capture effect based on the artificial viscous parameters quasi-static dissipation coefficient and dynamic dissipation coefficient, providing guidance for parameter selection.

[0016] A second aspect of this application provides an Euler near-field dynamics shock wave simulation device, comprising: a determination module for determining the decoupling characteristics of a material point and a spatial point in an Euler coordinate system; a reconstruction module for reconstructing the kinematic relationship of state-mode near-field dynamics within the Euler framework based on the decoupling characteristics; and a simulation module for establishing an Euler near-field dynamics model under the Euler description based on the kinematic relationship, and modifying the Euler near-field dynamics model using a target artificial viscous dissipation term to construct an artificial viscous dissipation model, and using the artificial viscous dissipation model to simulate Euler near-field dynamics shock waves.

[0017] Through the aforementioned technical means, the embodiments of this application can reconstruct the kinematic relationship of state-type peridynamics under the Euler framework, based on the decoupling characteristics of material points and spatial points in the Euler coordinate system. An Euler peridynamic model under the Euler description is established, and the Euler peridynamic model is modified by introducing a target artificial viscous dissipation term to simulate Euler peridynamic shock waves. This establishes an Euler peridynamic calculation framework based on the correction of the artificial viscous dissipation term, which can capture shock waves with high precision. It can be widely applied to one-dimensional, two-dimensional, and three-dimensional elastic wave, plastic wave, and shock wave propagation problems, providing an accurate simulation tool for transient problems such as high-speed impacts.

[0018] Optionally, in one embodiment of this application, the simulation module includes: a stretching ratio determination unit for determining the stretching ratio of each bond; and a correction unit for obtaining the target artificial viscous dissipation term based on the stretching ratio of each bond, so as to correct the Euler near-field dynamics model based on the target artificial viscous dissipation term.

[0019] Through the above-mentioned technical means, the embodiments of this application can calculate the target artificial viscous dissipation term based on the stretching ratio of each bond, and modify the Euler near-field dynamics model based on the target artificial viscous dissipation term, thereby stabilizing the zero-energy mode and other non-physical deformation modes, eliminating non-physical oscillations, accurately capturing shock waves, and establishing a high-precision Euler near-field dynamics model for shock wave capture.

[0020] Optionally, in one embodiment of this application, the expression for the target artificial viscous dissipation term is: , in, For the target artificial viscous dissipation term, For quasi-static dissipation terms, For dynamic dissipation terms, For volume wave velocity, This represents the velocity change within the neighborhood of a material point.

[0021] Through the above-mentioned technical means, the embodiments of this application can introduce necessary numerical damping through the target artificial viscous dissipation term, effectively suppressing the numerical oscillation of the wavefront, obtaining a clear and steep shock wave profile that is highly consistent with the analytical solution, and avoiding the problem of calculation divergence under extreme conditions such as high-speed impact.

[0022] Optionally, in one embodiment of this application, it further includes: an analysis module for analyzing the parameter sensitivity of the viscous force state; and an adjustment module for adjusting the model parameters of the artificial viscous dissipation model for adapting to different velocity gradient scenarios based on the parameter sensitivity.

[0023] Through the above-mentioned technical means, the embodiments of this application can address the lack of a clear control mechanism for artificial viscous parameters, analyze the parameter sensitivity of viscous force states, adjust parameters to adapt to different velocity gradient scenarios, and improve the versatility and engineering adaptability under different materials and different impact intensities.

[0024] Optionally, in one embodiment of this application, the model parameters include a quasi-static dissipation coefficient and a dynamic dissipation coefficient.

[0025] Through the above-mentioned technical means, the embodiments of this application can complete the analysis of different influence mechanisms on the shock wave capture effect based on the artificial viscous parameters quasi-static dissipation coefficient and dynamic dissipation coefficient, providing guidance for parameter selection.

[0026] A third aspect of this application provides an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the Euler near-field dynamics shock wave simulation method as described in the above embodiments.

[0027] A fourth aspect of this application provides a non-volatile computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described Euler near-field dynamics shock wave simulation method.

[0028] A fifth aspect of this application provides a computer program product that stores a computer program that, when executed by a processor, implements the above-described Euler near-field dynamics shock wave simulation method.

[0029] This application's embodiments, taking into account the decoupling characteristics of material points and spatial points in the Euler coordinate system, reconstruct the kinematic relationship of state-type peri-field dynamics within the Euler framework, establish an Euler peri-field dynamics model under the Euler description, and introduce a target artificial viscous dissipation term to correct the Euler peri-field dynamics model for Euler peri-field dynamics shock wave simulation. This establishes a computational framework for Euler peri-field dynamics based on the correction of the artificial viscous dissipation term, enabling high-precision shock wave capture. It can be widely applied to one-dimensional, two-dimensional, and three-dimensional elastic wave, plastic wave, and shock wave propagation problems, providing an accurate simulation tool for transient problems such as high-speed impacts. This solves the problems in related technologies, such as the numerical divergence phenomenon easily occurring under high-speed impact loads due to the working assumption of a Lagrangian framework for the material model in peri-field dynamics, and the tendency for non-physical numerical oscillations to occur on the wavefront when simulating strong discontinuities such as shock waves using the Euler framework, thus affecting the accuracy and stability of the simulation.

[0030] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0031] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein: Figure 1 This is a flowchart of an Euler near-field dynamics shock wave simulation method provided according to an embodiment of this application; Figure 2 This is a schematic diagram of the scope under deformation mapping according to an embodiment of this application; Figure 3 This is a block diagram for calculating Euler near-field dynamics with dissipation term correction according to an embodiment of this application; Figure 4 This is a schematic diagram of a one-dimensional elastic rod impact model provided according to an embodiment of this application; Figure 5 This is a schematic diagram comparing the numerical and analytical solutions of Euler peridynamics based on dissipation term correction according to an embodiment of this application; Figure 6 This is an axial velocity distribution diagram provided according to one embodiment of this application; Figure 7 This is a schematic diagram of the free end velocity of a one-dimensional elastic rod according to an embodiment of this application; Figure 8 This is a schematic diagram of the corrected numerical solution and the near-field dynamic solution at 1650 m / s according to an embodiment of this application; Figure 9 This is a schematic diagram illustrating the influence of quasi-static dissipation coefficient and dynamic dissipation coefficient on the shock wave capture effect according to an embodiment of this application; Figure 10 This is a schematic diagram of the structure of an Euler near-field dynamics shock wave simulation device provided according to an embodiment of this application; Figure 11 This is a schematic diagram of the structure of an electronic device provided according to an embodiment of this application.

[0032] Figure label: 10-Euler near-field dynamics shock wave simulation device; 100-Determination module, 200-Reconstruction module, 300-Simulation module; 1101-Memory, 1102-Processor, 1103-Communication interface. Detailed Implementation

[0033] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0034] The Euler near-field dynamics shock wave simulation method, apparatus, and electronic device of this application are described below with reference to the accompanying drawings. In the related technologies mentioned in the background section, the working assumption of near-field dynamics is that the material model is based on a Lagrangian framework, which easily leads to numerical divergence under high-speed impact loads. When simulating strong discontinuities such as shock waves, the Euler framework is prone to generating non-physical numerical oscillations on the wavefront, thus affecting the accuracy and stability of the simulation. This application provides an Euler near-field dynamics shock wave simulation method. In this method, the kinematic relationship of state-type near-field dynamics under the Euler framework is reconstructed based on the decoupling characteristics of material points and spatial points in the Euler coordinate system. An Euler near-field dynamics model under the Euler description is established, and a target artificial viscous dissipation term is introduced to correct the Euler near-field dynamics model for Euler near-field dynamics shock wave simulation. This establishes an Euler near-field dynamics calculation framework based on the correction of the artificial viscous dissipation term, enabling high-precision capture of shock waves. It can be widely applied to one-dimensional, two-dimensional, and three-dimensional elastic waves, plastic waves, and shock wave propagation problems, providing an accurate simulation tool for transient problems such as high-speed impacts. This solves the problems in related technologies, such as the fact that the material model of near-field dynamics is assumed to be a Lagrangian framework, which makes it easy for numerical divergence to occur under high-speed impact loads, and the fact that the Euler framework is prone to non-physical numerical oscillations on the wavefront when simulating strong discontinuities such as shock waves, thus affecting the accuracy and stability of the simulation.

[0035] Classical continuum mechanics theory and corresponding numerical methods have achieved great success in numerous scientific problems and engineering applications after years of development. However, they have encountered bottlenecks in dealing with various complex discontinuous phenomena caused by the failure of solid materials and structures. For example, difficulties remain in the scientific validity of models, computational accuracy, and efficiency in areas such as the evolution of micro-defects, the initiation and propagation of macroscopic cracks, and the interactions between cracks. This is because continuous models based on partial differential equations and locality are difficult to describe spatial discontinuities. They face significant challenges in dealing with singularity problems in material properties and mechanical behavior, often requiring additional numerical techniques, such as additional functions in extended finite element methods that can describe discontinuous phenomena. Furthermore, classical continuum mechanics theory adopts the assumption of local contact and lacks length-scale parameters to describe long-range material interactions or nonlocal effects. This makes it insufficient in analyzing mechanical problems dominated by long-range forces and with significant nonlocal effects, such as failing to reflect the nonlocal effects in the fracture process zone at the crack tip.

[0036] Perifield dynamics is a nonlocal theory describing continuous media. It introduces nonlocal characteristic lengths and describes particle motion through integral equations, handling discontinuous phenomena and continuous processes within a unified continuous model. Perifield dynamics posits that materials are composed of numerous material points containing physical property information, with each point interacting with other points within a certain radius. The integral equations based on nonlocal theory avoid singularities caused by the absence of spatial derivatives at cracks or interfaces. Damage and cracking are described through the breaking and accumulation of "bonds," eliminating the need for pre-defined crack paths. Cracks are not constrained by continuity or meshes, naturally describing crack initiation and propagation. It can be used to analyze the mechanical behavior of solid structures failing under ultimate loads or long-term cyclic loads. Bond-type perifield dynamics models were the first proposed and have been widely used to simulate deformation, damage, and impact failure of quasi-brittle materials. However, the constitutive model of bond-type perifield dynamics is relatively simple and struggles to describe various nonlinear and complex mechanical behaviors of materials. Subsequently, state-type perifield dynamics models were proposed and further divided into conventional and unconventional state-type models. Among them, unconventional peri-field dynamics can be conveniently linked to the physical quantities in the classical continuum mechanics constitutive model, realizing the nonlocal reconstruction of the classical constitutive model.

[0037] To date, almost all work on near-field dynamics assumes that the material model is Lagrangian, meaning that bond forces depend not only on the current (deformed) configuration of the object but also on a reference (undeformed) configuration. However, under high-speed impact loads, the Lagrangian framework has significant limitations. The neighborhood of a material point moves with material deformation, easily leading to numerical divergence under large deformation conditions. This distortion problem becomes a core bottleneck restricting simulation accuracy, especially when dealing with extreme physical processes such as metal micro-jeting, shock wave propagation, and material phase transitions. The Eulerian framework, on the other hand, describes material motion through a fixed mesh, avoiding the Lagrangian distortion problem. It achieves conserved transport of mass, momentum, and energy through computation, making it more suitable for transient processes such as shock wave propagation and micro-jet formation. In problems involving multiphase interfaces, such as metal delamination and micro-jet fragmentation, the Lagrangian method requires complex interface reconstruction algorithms, while the Eulerian framework naturally describes interface evolution through mass transport equations.

[0038] Shock wave propagation is a crucial physics problem to consider in numerical simulations of high-speed impacts and explosions. Peri-field dynamics offers significant advantages due to its inherent ability to simulate transient discontinuities. While the Euler framework avoids mesh distortion, it can easily generate non-physical numerical oscillations on the wavefront when simulating strongly discontinuous problems such as shock waves, affecting the accuracy and stability of the simulation. Therefore, there is an urgent need to construct an Euler peri-field dynamics material model that relies solely on deformation configuration and introduces a nonlocal dissipation correction mechanism to handle high-speed impact problems.

[0039] Specifically, Figure 1This is a schematic flowchart of an Euler near-field dynamic shock wave simulation method provided in an embodiment of this application.

[0040] like Figure 1 As shown, the Euler near-field dynamic shock wave simulation method includes the following steps: In step S101, the decoupling characteristics of material points and spatial points in the Euler coordinate system are determined.

[0041] It is understood that the material points in the embodiments of this application may contain material property information. In near-field dynamics, the material is composed of a large number of material points containing material property information, and there is an interaction force between each material point and the material points within a certain range around it. In actual implementation, the embodiments of this application can determine the decoupling characteristics between material points and spatial points in the Euler coordinate system.

[0042] For example, the static behavior under strong impact can be described by the Mie-Grüneisen equation of state, which has been successfully applied to the simulation study of impact loading phenomena. Fracture occurs when the internal pressure of the material is lower than the fracture pressure. In the embodiments of this application, damage can be considered, and tensile stress is used for truncated fracture, with the pressure obtained from the equation of state being corrected.

[0043] The embodiments of this application can determine the decoupling characteristics of material points and spatial points in the Euler coordinate system. By describing the material motion through a fixed mesh in the Euler coordinate system, the Lagrange distortion problem is avoided, providing a basic support for constructing a near-field dynamic model that relies solely on the deformation configuration, and effectively solving the numerical divergence bottleneck of the Lagrange frame under high-speed impact loads.

[0044] In step S102, based on the decoupling characteristics, the kinematic relationship of the reconstructed state-type peridynamics under the Euler framework is reconstructed.

[0045] It is understood that the kinematic relationships in the embodiments of this application may include the first law expression and the second law expression at any material point in the thermodynamic formula of near-field dynamics.

[0046] In actual implementation, the embodiments of this application can be applied to any material point in the thermodynamic formula of near-field dynamics. The first law of the law is expressed as follows: (1) in It is the internal energy density (internal energy per unit volume under the reference configuration). From other material points within the object The heat transfer rate, It is the source rate. Known as absorbed power density, it is the equivalent quantity of classical stress power in peridynamics. The second law of peridynamics is expressed as: (2) in It is entropy density. It refers to absolute temperature. The first and second laws can be combined to impose constraints on near-field dynamics material models.

[0047] Using the free energy defined by the following formula: (3) The force state can be decomposed into an equilibrium part and a dissipative part: (4) Only the dissipative component contains rate dependence. The following identity holds: (5) Nonlocal mass density The calculations are based on the proximity of material points in the deformed configuration rather than the reference configuration. This model uses this nonlocal mass density to calculate pressure and then converts it to a force state.

[10] .set up This represents the scope of a deformable configuration. If the distance between points in the deformable configuration is greater than [a certain value], then [the scope is defined as follows]. If they do not interact, then they will not interact, such as Figure 2 As shown.

[0048] To simplify the symbols, use Represents a general key vector: (6) set up It is defined in A nonnegative, continuously differentiable function on [a, b]. Further assumptions: (7) in ,and: (8) Specifically, we set: (9) choose This definition is based on the fact that its second derivative is positive.

[0049] set up The reference density of the material. Nonlocal density is defined as follows: (10) The bond length after deformation It is given by the following formula: (11) and: (12) It is calculated from the bond length after deformation. (13) The integrand in equation (10) is only related to the inverted configuration. Location distance is Points within the range The value is not zero. Unlike the Lagrange material model, this may include values ​​in the reference configuration that are not zero. Longer keys.

[0050] For any nonlocal mass density Relative volume is defined in the following way. and compression : (14) Let the pressure, internal energy density, and absolute temperature of the fluid under the reference configuration be represented by... and This is represented by the statement. Assume the material has a free energy function. , so that: (15) The first expression in equation (14), combined with the chain rule, can be derived as follows: (16) To calculate the Freser derivative First, we observe that for an incremental change , (17) in The unit vector representing the bond direction after deformation is defined as: (18) From the above, we can conclude that:

[0051] (19) Based on the above formula, the Fréchet derivative of the nonlocal mass density can be obtained as follows: (20) Equation (16) can be transformed into: ,(twenty one) in It is a scalar force state caused by Eulerian-like fluid interactions. Note that the bond force is parallel to the direction of the deformed bond, which means that this peridynamic material model is a conventional peridynamic model. This means that the requirement for angular momentum balance is automatically satisfied without further restrictions. Since in the second equation of equation (21), the bond force and The relationship is linear, as defined in equation (9). The convexity will affect the deformation. If If the second derivative is positive, then the repulsive force between material points that are close to each other is often stronger than that between material points that are far apart. This helps to maintain equal spacing between nodes in numerical simulations and improves stability.

[0052] As can be seen from the above, for any key, when hour, In other words, if the pressure is positive, then the bond force is pressure. Furthermore, according to equation (8), if the deformed bond length exceeds... Then the bond force disappears. Therefore, when calculating the integral in equation (10), The deformation length within the neighborhood is less than or equal to Only the bonds need to be calculated in the integral. In this sense, although all formal systems are Lagrangian in form, this material model is essentially Euler in nature.

[0053] By each material point By integrating the energy balance equation over time, we can obtain the internal energy density. The pressure defined by equation (15) and temperature It is through the form of , The calculations were obtained from the material model, where It is the nonlocal mass density defined in equation (10).

[0054] The static behavior under strong impact can be described by the Mie–Grüneisen equation of state, which has been successfully applied to the simulation study of impact loading phenomena. Shock wave velocity. and particle velocity The relationship between them is: ,(twenty two) Where S is a constant, This is the speed of sound within the material. Therefore, the Mie–Grüneisen equation of state can be expressed in the following form: ,(twenty three) in It is the Grüneisen parameter. , It refers to relative volume. and These are the internal energy densities of the deformed configuration and the initial configuration, respectively.

[0055] Fracture occurs when the internal pressure of the material is lower than the fracture pressure. This application employs a damage-considering method of tensile stress during fracture, and the pressure derived from the equation of state is corrected as follows: ,(twenty four) in It is the fracture pressure, which is negative because liquid metal can withstand limited tensile stress without cavitation.

[0056] The embodiments of this application can reconstruct the kinematic relationship of the state-mode near-field dynamics under the Euler framework based on the decoupling characteristics of material points and spatial points in the Euler coordinate system, so as to model steady-state shock waves and achieve accurate capture of shock waves.

[0057] In step S103, based on kinematic relationships, an Euler peri-field dynamics model described by Euler is established. Based on the Euler peri-field dynamics model, the Euler peri-field dynamics model is modified using the target artificial viscous dissipation term to construct an artificial viscous dissipation model, which is then used to simulate Euler peri-field dynamics shock waves.

[0058] It is understood that the Euler near-field dynamics model in the embodiments of this application can be understood as a continuous medium mechanics model based on the Euler framework and in the form of nonlocal integrals, used to describe the motion and interaction of material points; the target artificial viscous dissipation term can be used to suppress non-physical oscillation phenomena caused by strong discontinuities during the impact process.

[0059] In actual implementation, to suppress non-physical oscillations caused by strong discontinuities during the impact process, this embodiment of the application can introduce an artificial viscosity term during the modeling process. The rate-related term in equation (10) Its main purpose is to dissipate energy in order to model steady-state shock waves and achieve accurate capture of shock waves. Without these terms, shock waves with constant profiles, thicknesses, and velocities would not satisfy the Rankine-Hugoniot relation.

[0060] This application embodiment can address dissipation items. An artificial viscosity parameter with a quadratic term is introduced, derived from the quasi-static dissipation term. and dynamic dissipation terms Composed of two parts. Quasi-static dissipation coefficient Controlling dissipation intensity, By controlling the weights of dynamic effects, we can describe the energy dissipation caused by dynamic shock waves and high-frequency oscillations.

[0061] The embodiments of this application can establish an Euler near-field dynamics calculation framework based on artificial viscous dissipation terms, which effectively suppresses non-physical numerical oscillations of the Euler framework, accurately simulates transient problems such as high-speed impacts, and improves engineering applicability.

[0062] Optionally, in one embodiment of this application, the Euler near-field dynamics model is modified using a preset artificial viscous dissipation term, including: determining the stretching ratio of each bond; obtaining a target artificial viscous dissipation term based on the stretching ratio of each bond, so as to modify the Euler near-field dynamics model based on the target artificial viscous dissipation term.

[0063] It is understood that the bond stretching ratio in the embodiments of this application can be a parameter that characterizes the degree of bond deformation, such as the ratio of the current length of the interaction bond between material points to a reference length.

[0064] In practical implementation, the embodiments of this application can calculate the linear term of the dynamic dissipation term based on the stretching ratio of each bond. This linear term stabilizes the zero-energy mode and other non-physical deformation modes. By adding an artificial viscous dissipation term to the Euler near-field dynamics framework, a high-precision Euler near-field dynamics model for shock wave capture is established. The calculation block diagram is shown below. Figure 3 As shown.

[0065] like Figure 3 As shown, the embodiments of this application can perform mesh discretization on the computational domain, import discrete data from the input mesh file, set initial conditions and boundary conditions, define the initial state and constraints of the simulation, generate a neighborhood list, and establish the neighborhood relationships of each node.

[0066] The forces acting on nodes are calculated based on neighborhood relationships and divided into two branches: equilibrium force state and dissipative force state. The node velocity, node displacement, and node internal energy are calculated, the node state is updated, and the neighborhood list is updated according to the displacement changes to adapt to the deformed configuration.

[0067] Determine if the termination condition has been met. If not, execute the iteration time step, return to the calculation node force, and enter the next loop; if the condition has been met, the simulation ends.

[0068] The embodiments of this application can calculate the target artificial viscous dissipation term based on the stretching ratio of each bond, and then modify the Euler near-field dynamics model based on the target artificial viscous dissipation term, thereby stabilizing the zero-energy mode and other non-physical deformation modes, eliminating non-physical oscillations, accurately capturing shock waves, and establishing a high-precision Euler near-field dynamics model for shock wave capture.

[0069] Optionally, in one embodiment of this application, the expression for the target artificial viscous dissipation term is: , in, For the target artificial viscous dissipation term, For quasi-static dissipation terms, For dynamic dissipation terms, For volume wave velocity, This represents the velocity change within the neighborhood of a material point.

[0070] In actual implementation, the embodiments of this application can dissipate terms An artificial viscosity parameter with a quadratic term is introduced, derived from the quasi-static dissipation term. and dynamic dissipation terms Composed of two parts. Quasi-static dissipation coefficient Controlling dissipation intensity, The dynamic effect weights are controlled to describe the energy dissipation caused by dynamic shock waves and high-frequency oscillations. The dissipation term in the material model is given by the following equation: (25) in and It is a dimensionless constant, volume wave velocity. It can be obtained from the following formula: (26) It is a material point The velocity change within the neighborhood of can be defined as: (27) The dissipation term is discretized as follows, and the discretized dissipation term is similar to artificial viscosity. Equation (25) can be discretized as follows: (28) The effective velocity variation within a family defined in equation (27) is approximately: (29) Equation (28) contains This term is an improvement on the secondary artificial viscosity, which is widely used in modern fluid mechanics code. It includes... Unlike typical linear artificial viscosity, the linear term is calculated based on the elongation of each bond rather than the volumetric strain rate. This linear term stabilizes the zero-energy mode and other non-physical deformation modes. By incorporating an artificial viscous dissipation term into the Euler peri-field dynamics framework, a high-precision Euler peri-field dynamics model for shock wave capture is established.

[0071] The embodiments of this application introduce necessary numerical damping through the target artificial viscous dissipation term, which effectively suppresses the numerical oscillation of the wavefront and obtains a clear and steep shock wave profile that is highly consistent with the analytical solution, thus avoiding the problem of calculation divergence under extreme conditions such as high-speed impact.

[0072] Optionally, in one embodiment of this application, the method further includes: analyzing the parameter sensitivity of the viscous force state; and adjusting the model parameters of the artificial viscous dissipation model to adapt to different velocity gradient scenarios based on the parameter sensitivity.

[0073] It is understood that the parameter sensitivity in the embodiments of this application can be understood as the degree of influence of model parameters on the simulation results of shock waves (such as waveform smoothness and oscillation amplitude). Quantifying this sensitivity can guide the adaptive optimization of parameters.

[0074] To verify the feasibility and reliability of the dissipative model, a one-dimensional elastic rod impact model will be used as a case study to investigate the propagation and capture of shock waves. Many experimental setups, such as plate impact tests, are essentially one-dimensional in both the loading and measurement directions. Therefore, to simplify computational complexity and facilitate the capture of shock wave characteristics, a one-dimensional model is more suitable for verification.

[0075] like Figure 4 As shown, the lengths of both the incident rod and the transmission rod are 50. The model was discretized using the meshless particle method, with a discrete grid size of 0.01. scope Size is 0.031 The number of nodes is 10000. The materials of the two rods are assumed to be ideal elastic materials, and other material parameters are set according to Al6061, as shown in Table 1. The initial velocity of the incident rod is set to 300. The initial velocity of the transmission rod is 0. The model is subject to roller constraints in the transverse direction, allowing deformation only along the axial direction. Table 1 shows the material parameters of the one-dimensional elastic rod.

[0076] Table 1

[0077] Since the material is assumed to be an ideal elastic material, only elastic waves are generated within the rod. The analytical solution to this problem can be calculated based on the Rankine–Hugoniot jump condition. In this embodiment, reflection can occur at the free end before (3...) ) and after reflection from the free end (7 Sampled at two different times. Figure 5 (a) It can be seen that 3 The numerical solution of Euler peridynamics based on the dissipation term correction is very close to the analytical solution calculated theoretically. In 7 At that time, after reflection from the free end, the magnitude of the velocity generated inside the rod is related to time 3. It remains the same and matches the analytical solution very well. Figure 5 (b)). Among them, Figure 5 (a) 3 provided according to one embodiment of this application A schematic diagram comparing the numerical and analytical solutions of Euler peridynamics based on dissipation term corrections at each time step; Figure 5 (b) 7 provided according to one embodiment of this application A schematic diagram comparing the numerical and analytical solutions of Euler peridynamics based on dissipation term corrections.

[0078] The dissipation term is added to eliminate non-physical oscillations and accurately capture shock waves. The shock wave capture effect of this method is verified below. The embodiments of this application can simulate 3... and 7 Numerical solutions of Euler peri-field dynamics at two time points without any corrections are given and compared with the corrected numerical solutions. For example... Figure 6 and Figure 7 As shown, the axial velocity distribution within the rod and the tip velocity in the Euler near-field dynamics exhibit severe oscillations. After adding a dissipation term for correction, the non-physical oscillations are eliminated, and the shock wavefront becomes steeper. Among these, Figure 6 (a) 3 provided according to one embodiment of this application Axial velocity distribution diagram at any given time; Figure 6 (b) 7 provided according to one embodiment of this application Axial velocity distribution at any given time.

[0079] High-speed impact is a problem that needs to be solved in Euler near-field dynamics. To test the capabilities of the dissipative model under higher speed conditions, we set the initial velocity of the incident rod to 1650. The discrete grid size is 0.1. scope Size is 0.31 The number of nodes is 1000. Other conditions are the same as in the model in 3.4.1. Figure 7 In the meantime, the numerical solution of Euler's peri-field dynamics shows better performance than 300... More intense amplitude oscillations and local extreme value jumps occurred, and high-frequency errors were not effectively suppressed; the velocity curve after the dissipation term correction was smooth overall, and the fluctuations in the key region were significantly suppressed, alleviating numerical instability. Figure 8In (b), the reflected wave in the Euler near-field dynamics solution is excited at the boundary, and its direction is opposite to that of the incident wave, resulting in a half-wave loss phenomenon. This leads to significant numerical fluctuations at both ends after waveform superposition. Furthermore, the reflected wave at the boundary is not properly absorbed, causing numerical interference to the velocities at both ends. By adding a dissipation term, instability caused by local energy accumulation is avoided, making the results more consistent with actual shock wave propagation and evolution. Simultaneously, due to the half-wave loss phenomenon, the wavefront of the reflected wave has a smaller slope than the incident wave. Figure 8 (a) The corrected numerical solution and the near-field dynamic solution at 1650 m / s provided according to an embodiment of this application 3 A diagram illustrating the time; Figure 8 (b) Corrected numerical solution and peri-field dynamic solution at 1650 m / s according to an embodiment of this application 7 A diagram illustrating the time.

[0080] For example, embodiments of this application can be used to analyze quasi-static dissipation coefficients. and dynamic dissipation coefficient Different control mechanisms for shock wave capture effects were investigated, and the two coefficients were quantitatively analyzed. The parameter sensitivity of the viscous force state was analyzed; based on the parameter sensitivity, the model parameters of the artificial viscous dissipation model adapted to different velocity gradient scenarios were adjusted.

[0081] The embodiments of this application can address the lack of a clear control mechanism for artificial viscous parameters by analyzing the parameter sensitivity of viscous force states and adjusting parameters to adapt to different velocity gradient scenarios, thereby improving the versatility and engineering adaptability under different materials and impact intensities.

[0082] Optionally, in one embodiment of this application, the model parameters include a quasi-static dissipation coefficient and a dynamic dissipation coefficient.

[0083] It is understood that, in the embodiments of this application, the quasi-static dissipation coefficient can control the dissipation intensity, and the dynamic dissipation coefficient can control the dynamic effect weight, and can be used to describe the energy dissipation caused by dynamic shock waves and high-frequency oscillations.

[0084] In actual implementation, the embodiments of this application can analyze the quasi-static dissipation coefficients separately. and dynamic dissipation coefficient Different control mechanisms for shock wave capture effect. Adjusting the smoothness of the overall deformation region and suppressing overall numerical noise, such as... Figure 9 As shown in (a), when hour, The overall impact is relatively small. For example... Figure 9 As shown in (b), Oscillation suppression in the dominant dynamic shock zone, when At that time, with Increased intensity enhances the suppression of high-frequency oscillations, but excessive dissipation can smooth out the steep leading edge of the shock wave; as... Reducing the frequency can preserve more high-frequency details, but may lead to non-physical oscillations. Therefore, and The combination exhibits an optimal balance between accuracy and stability, preserving more details of the material's dynamic response. Among these, Figure 9 (a) Provided according to one embodiment of this application A schematic diagram illustrating the impact on shock wave capture performance; Figure 9 (b) Provided according to one embodiment of this application A schematic diagram illustrating the impact on the shock wave capture effect.

[0085] The embodiments of this application can analyze the different influence mechanisms on the shock wave capture effect based on the artificial viscous parameters quasi-static dissipation coefficient and dynamic dissipation coefficient, providing guidance for parameter selection.

[0086] The Euler near-field dynamics shock wave simulation method proposed in this application reconstructs the kinematic relationship of state-type near-field dynamics within the Euler framework, taking into account the decoupling characteristics of material points and spatial points in the Euler coordinate system. It establishes an Euler near-field dynamics model under the Euler description and introduces a target artificial viscous dissipation term to correct the Euler near-field dynamics model for Euler near-field dynamics shock wave simulation. This establishes a computational framework for Euler near-field dynamics based on the correction of the artificial viscous dissipation term, enabling high-precision capture of shock waves. It can be widely applied to one-dimensional, two-dimensional, and three-dimensional elastic wave, plastic wave, and shock wave propagation problems, providing an accurate simulation tool for transient problems such as high-speed impacts. This solves the problems in related technologies where the working assumption of near-field dynamics using a Lagrangian framework for the material model leads to numerical divergence under high-speed impact loads, and where the Euler framework easily generates non-physical numerical oscillations on the wavefront when simulating strong discontinuities such as shock waves, thus affecting the accuracy and stability of the simulation.

[0087] Next, referring to the accompanying drawings, we describe the Euler near-field dynamics shock wave simulation device proposed according to an embodiment of this application.

[0088] Figure 10 This is a schematic diagram of the structure of the Euler near-field dynamic shock wave simulation device according to an embodiment of this application.

[0089] like Figure 10 As shown, the Euler near-field dynamic shock wave simulation device 10 includes: a determination module 100, a reconstruction module 200, and a simulation module 300.

[0090] Among them, the determination module 100 is used to determine the decoupling characteristics between material points and spatial points in the Euler coordinate system.

[0091] Reconstruction module 200 is used to reconstruct the kinematic relationship of the state-mode peridynamics within the Euler framework based on decoupling characteristics.

[0092] The simulation module 300 is used to establish an Euler peri-field dynamics model under the Euler description based on kinematic relationships, and to modify the Euler peri-field dynamics model based on the Euler peri-field dynamics model and using the target artificial viscous dissipation term to construct an artificial viscous dissipation model, so as to simulate Euler peri-field dynamics shock waves using the artificial viscous dissipation model.

[0093] Optionally, in one embodiment of this application, the simulation module 300 includes: a stretching ratio determination unit and a correction unit.

[0094] The stretching ratio determination unit is used to determine the stretching ratio of each bond.

[0095] A correction unit is used to obtain the target artificial viscous dissipation term based on the stretching ratio of each bond, so as to correct the Euler peri-field dynamics model based on the target artificial viscous dissipation term.

[0096] Optionally, in one embodiment of this application, the expression for the target artificial viscous dissipation term is: , in, For the target artificial viscous dissipation term, For quasi-static dissipation terms, For dynamic dissipation terms, For volume wave velocity, This represents the velocity change within the neighborhood of a material point.

[0097] Optionally, in one embodiment of this application, the Euler near-field dynamic shock wave simulation device 10 further includes an analysis module and an adjustment module.

[0098] The analysis module is used to analyze the parameter sensitivity of viscous force states.

[0099] The adjustment module is used to adjust the model parameters of the artificial viscous dissipation model to adapt to different velocity gradient scenarios based on parameter sensitivity.

[0100] Optionally, in one embodiment of this application, the model parameters include a quasi-static dissipation coefficient and a dynamic dissipation coefficient.

[0101] It should be noted that the foregoing explanation of the embodiment of the Euler near-field dynamics shock wave simulation method also applies to the Euler near-field dynamics shock wave simulation device of this embodiment, and will not be repeated here.

[0102] The Euler peri-field dynamics shock wave simulation device proposed in this application reconstructs the kinematic relationship of state-type peri-field dynamics within the Euler framework, taking into account the decoupling characteristics of material points and spatial points in the Euler coordinate system. It establishes an Euler peri-field dynamics model under the Euler description and introduces a target artificial viscous dissipation term to correct the Euler peri-field dynamics model for Euler peri-field dynamics shock wave simulation. This establishes a computational framework for Euler peri-field dynamics based on the correction of the artificial viscous dissipation term, enabling high-precision shock wave capture. It can be widely applied to one-dimensional, two-dimensional, and three-dimensional elastic wave, plastic wave, and shock wave propagation problems, providing an accurate simulation tool for transient problems such as high-speed impacts. This solves the problems in related technologies where the working assumption of the material model in peri-field dynamics is a Lagrangian framework, which easily leads to numerical divergence under high-speed impact loads. Furthermore, the Euler framework is prone to non-physical numerical oscillations on the wavefront when simulating strong discontinuities such as shock waves, thus affecting the accuracy and stability of the simulation.

[0103] Figure 11 A schematic diagram of the structure of an electronic device provided in an embodiment of this application. The electronic device may include: The memory 1101, the processor 1102, and the computer program stored on the memory 1101 and executable on the processor 1102.

[0104] When processor 1102 executes the program, it implements the Euler near-field dynamics shock wave simulation method provided in the above embodiments.

[0105] Furthermore, electronic devices also include: Communication interface 1103 is used for communication between memory 1101 and processor 1102.

[0106] The memory 1101 is used to store computer programs that can run on the processor 1102.

[0107] The memory 1101 may include high-speed RAM memory, and may also include non-volatile memory, such as at least one disk storage.

[0108] If the memory 1101, processor 1102, and communication interface 1103 are implemented independently, then the communication interface 1103, memory 1101, and processor 1102 can be interconnected via a bus to complete communication between them. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. The bus can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 11 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0109] Optionally, in a specific implementation, if the memory 1101, processor 1102, and communication interface 1103 are integrated on a single chip, then the memory 1101, processor 1102, and communication interface 1103 can communicate with each other through an internal interface.

[0110] The processor 1102 may be a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of this application.

[0111] This application also provides a non-volatile computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described Euler near-field dynamics shock wave simulation method.

[0112] This application also provides a computer program product storing a computer program that, when executed by a processor, implements the above-described Euler near-field dynamics shock wave simulation method.

[0113] In the description of this specification, the 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 this application. 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. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0114] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0115] Any process or method described in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

[0116] 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 contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), 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). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0117] It should be understood that the various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, the N steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. If implemented in hardware, as in another embodiment, it can be implemented using any one or more 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.

[0118] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0119] Furthermore, the functional units in the various embodiments of this application can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0120] The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of this application.

Claims

1. A method for simulating near-field dynamic shock waves using Euler principles, characterized in that... Includes the following steps: Determine the decoupling characteristics between material points and spatial points in the Euler coordinate system; Based on the aforementioned decoupling characteristics, the kinematic relationship of the reconstructed state-type peridynamics within the Euler framework is reconstructed. Based on the aforementioned kinematic relationship, an Euler peri-field dynamics model under the Euler description is established. Based on the Euler peri-field dynamics model, the Euler peri-field dynamics model is modified using a target artificial viscous dissipation term to construct an artificial viscous dissipation model, which is then used to simulate Euler peri-field dynamics shock waves.

2. The method according to claim 1, characterized in that, The step of modifying the Euler near-field dynamics model using a preset artificial viscous dissipation term includes: Determine the stretching ratio of each bond; The target artificial viscous dissipation term is obtained based on the stretching ratio of each bond, and the Euler near-field dynamics model is corrected based on the target artificial viscous dissipation term.

3. The method according to claim 1 or 2, characterized in that, The expression for the target artificial viscous dissipation term is: ， in, For the target artificial viscous dissipation term, For quasi-static dissipation terms, For dynamic dissipation terms, For volume wave velocity, This represents the velocity change within the neighborhood of a material point.

4. The method according to claim 1, characterized in that, Also includes: Analyze the parameter sensitivity of viscous force states; The model parameters of the artificial viscous dissipation model are adjusted according to the parameter sensitivity to adapt to different velocity gradient scenarios.

5. The method according to claim 4, characterized in that, The model parameters include quasi-static dissipation coefficient and dynamic dissipation coefficient.

6. A device for simulating Euler near-field dynamics shock waves, characterized in that, include: The determination module is used to determine the decoupling characteristics between material points and spatial points in the Euler coordinate system; The reconstruction module is used to reconstruct the kinematic relationship of the state-type peridynamics within the Euler framework based on the decoupling characteristics. The simulation module is used to establish an Euler near-field dynamics model under the description of Euler based on the kinematic relationship, and to modify the Euler near-field dynamics model based on the Euler near-field dynamics model and using the target artificial viscous dissipation term to construct an artificial viscous dissipation model, so as to simulate Euler near-field dynamics shock waves using the artificial viscous dissipation model.

7. The apparatus according to claim 6, characterized in that, The simulation module includes: The stretching ratio determination unit is used to determine the stretching ratio of each bond; The correction unit is used to obtain the target artificial viscous dissipation term based on the stretching ratio of each bond, so as to correct the Euler near-field dynamics model based on the target artificial viscous dissipation term.

8. An electronic device, characterized in that, include: A memory, a processor, and a computer program stored in the memory and capable of running on the processor, wherein the processor executes the program to implement the Euler near-field dynamic shock wave simulation method as described in any one of claims 1-5.

9. A non-volatile computer-readable storage medium having a computer program stored thereon, characterized in that, The program is executed by the processor to implement the Euler near-field dynamic shock wave simulation method as described in any one of claims 1-5.

10. A computer program product, comprising a computer program, characterized in that, The computer program is executed to implement the Euler near-field dynamic shock wave simulation method as described in any one of claims 1-5.

Images