A simulation method of shaped charge jet based on AMRM-FEM-SPH

Abstract

The present invention provides a shaped charge jet simulation method based on AMRM-FEM-SPH, the process of which is as follows: (1) during the liner collapse stage, i.e., the process from explosive ignition to the end of detonation, the finite element mesh is re-divided using the AMRM method. After the detonation reaction is completely completed, the explosive unit is deleted from the model containing the explosive and the liner. After deleting the explosive unit, the AMRM method is continued to be used to simulate the jet forming process; (2) during the jet stretching and fracture stage of the liner, the FEM-SPH method is combined with the Johnson-Cook failure criterion to convert the failure unit into SPH particles. The present invention breakthrough combines adaptive grid technology with a multi-algorithm coupling mechanism to achieve high-precision simulation of the entire process of jet forming, stretching and fracture while maintaining calculation accuracy, significantly improving the accuracy of prediction of the dynamic behavior of metal jets.

Description

Technical Field

[0001] The present invention relates to the technical field of numerical simulation of jet forming, and in particular to a focused jet simulation method based on AMRM-FEM-SPH. Background Art

[0002] A shaped charge jet is an ultra-high-speed, directional stream of metal produced by the detonation of a shaped charge. When the liner is crushed by the blast wave, the liner material undergoes intense plastic deformation due to axisymmetric convergence, forming a continuous metal jet with a head velocity of 7 to 12 km / s. This jet possesses extremely high kinetic energy density, making it invaluable in applications such as oil perforation and blasting. However, during the jet's stretching process, it gradually breaks apart, forming several particles, which directly affects its stability and destructive effectiveness. Therefore, accurately predicting the entire jet process, from formation to stretching to fracture, is crucial for optimizing charge design and improving engineering reliability.

[0003] In the field of numerical simulation of shaped-charge jets, traditional methods are primarily based on a fluid mechanics framework. Among them, the arbitrary Lagrangian-Eulerian method, the structured arbitrary Lagrangian-Eulerian method, and the pure Euler method are widely used. These methods effectively simulate jet formation and penetration by dynamically adjusting the relative motion between the mesh and the material. Simulating jet fracture requires relying on failure strain criteria to delete failed elements, which violates energy conservation in the system. The resulting voids can also cause unphysical expansion of the surrounding material. In contrast, the finite element method-smoothed particle hydrodynamics (FEM-SPH) method offers a superior approach for fracture simulation by automatically converting elements into smoothed particles upon reaching critical failure. This design cleverly combines the high accuracy of the finite element method with the ability of the SPH method to handle large post-fracture deformation and discrete material motion. However, the FEM-SPH method faces a key challenge in simulating jet tensile fracture: regions of localized extreme stretching can form elements with extremely high aspect ratios. When these distortion units are converted into SPH particles, the number of particles that can be generated is often insufficient, resulting in premature breakup of the simulated jet.

[0004] The root cause of this premature fracture problem is that the highly distorted regions fail to provide sufficient elements to generate a sufficient number of SPH particles. Therefore, the key to improving the accuracy of the FEM-SPH method in distorted regions lies in effectively managing the mesh distribution in these regions. The Adaptive Mesh Rezoning Method (AMRM) provides a new approach to this problem. The core of AMRM is to dynamically optimize the spatial position of mesh nodes, rather than increasing or decreasing the number of elements or changing the mesh topology. By migrating nodes to the distorted region, it significantly improves the mesh quality in this region, thereby effectively improving local computational accuracy and numerical stability while maintaining the overall computational scale.

[0005] Based on an analysis of existing technologies, this paper proposes an innovative technical solution that combines the AMRM algorithm with the FEM-SPH method. The AMRM algorithm is used to simulate the jet forming process during the detonation wave collapse of the liner. After jet forming, the FEM-SPH method is used to simulate the stretching and fracture processes. This solution fully integrates the advantages of both methods, providing a more optimized technical path for jet fracture simulation. Summary of the Invention

[0006] In response to the technical problems existing in the above-mentioned background technology, the present invention proposes a focused jet simulation method based on AMRM-FEM-SPH. The method has a reasonable concept and breakthroughly combines adaptive grid technology with a multi-algorithm coupling mechanism. While maintaining the calculation accuracy, it can achieve high-precision simulation of the entire process of jet forming, stretching and fracture, and significantly improve the accuracy of the prediction of the dynamic behavior of metal jets.

[0007] To solve the above technical problems, the present invention provides a shaped charge jet simulation method based on AMRM-FEM-SPH, the process of which is as follows:

[0008] (1) During the liner collapse phase, i.e., from ignition to detonation, the AMRM method is used to re-mesh the finite element. When the detonation reaction is complete, the explosive unit is deleted from the model containing the explosive and the liner. After deleting the explosive unit, the AMRM method is continued to simulate the jet formation process.

[0009] (2) During the jet stretching and fracture stage of the liner, the failure units are converted into SPH particles by combining the FEM-SPH method with the Johnson-Cook failure criterion.

[0010] The AMRM-FEM-SPH-based shaped charge jet simulation method, wherein the step (1) specifically includes the following steps:

[0011] (1.1) Initial parameter setting

[0012] Set the time interval and grid feature size for adaptive grid re-division;

[0013] (1.2) Mesh redistribution

[0014] At each interval, the inner angle of the finite element grid is To check the mesh distortion; the mesh inner angle Refers to the angle formed by two adjacent edges on the unit boundary at the vertex; when the internal angle of the grid If the grid exceeds the interval [45°, 135°], it is marked as a distorted grid, and then the grid is redistributed to ensure that the grid size is close to the grid characteristic size;

[0015] (1.3) Mesh remapping

[0016] Map the state variables such as stress, strain, pressure, velocity and temperature rise of the mesh before mesh redistribution to the new mesh;

[0017] First, extrapolate all variables of the old mesh from the Gaussian points to the element nodes:

[0018] ;

[0019] In the above formula, is the physical quantity of the old mesh node, The number of elements in the old mesh that share this node, For the old grid The shape function of the unit Gaussian point, For the old grid The physical quantity of a unit Gauss point;

[0020] Then, transfer all the variables of the old grid's nodes to the nodes of the new grid:

[0021] ;

[0022] In the above formula, is the physical quantity of the new mesh node, is the interpolation function;

[0023] Finally, map the nodal quantities of the new mesh to the Gaussian points of each element in the new mesh:

[0024] ;

[0025] In the above formula, is the physical quantity of the new grid Gaussian point, is the number of nodes in the cell where the new grid Gaussian point is located, For the new grid The shape function of the nodes, For the new grid The physical quantity of a node.

[0026] The AMRM-FEM-SPH-based shaped charge jet simulation method, wherein the specific process of step (2) is as follows:

[0027] First, it is necessary to output the results of the AMRM method used in step (1) to simulate the jet forming process; then, import the results into the FEM-SPH model for calculation; when the liner has not yet broken, the finite element method is used for calculation; when the strain of the liner material reaches the failure strain, the finite element calculation method is converted into SPH particles in smooth particle fluid dynamics; the Johnson-Cook failure criterion is used to define the failure strain :

[0028] ;

[0029] In the above formula, is the failure parameter, determined experimentally; is the stress triaxiality, is the strain rate, is the reference strain rate, is the temperature, is room temperature, Is the melting point.

[0030] The AMRM-FEM-SPH-based focused jet simulation method, wherein the results of the AMRM method simulating the jet forming process in step (3) include node coordinates, stress, strain, velocity and grid.

[0031] By adopting the above technical solution, the present invention has the following beneficial effects:

[0032] The AMRM-FEM-SPH-based focused jet simulation method of the present invention is well conceived and breakthrough in combining the AMRM method (i.e., adaptive grid re-division method) with the FEM-SPH method (i.e., finite element-smoothed particle fluid dynamics method) coupling mechanism. It can better simulate the jet forming, stretching and fracture processes, while maintaining the calculation accuracy, and achieve high-precision simulation of the entire jet forming, stretching and fracture process, significantly improving the accuracy of the prediction of the dynamic behavior of metal jets. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the specific embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0034] Figure 1 Flowchart of the AMRM-FEM-SPH-based shaped charge jet simulation method of the present invention;

[0035] Figure 2 Schematic diagram of simulating focused jet stretching based on the AMRM-FEM-SPH focused jet simulation method of the present invention. DETAILED DESCRIPTION

[0036] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts are within the scope of protection of the present invention.

[0037] The present invention will be further explained below with reference to specific embodiments.

[0038] like Figure 1 As shown, this embodiment provides a shaped charge jet simulation method based on AMRM-FEM-SPH, which includes the following steps:

[0039] (1) Liner crushing stage

[0040] From ignition to detonation, a violent chemical reaction occurs within the explosive, sending a detonation wave propagating at extremely high speeds. The intense pressure generated by the detonation wave acts on the liner, causing it to rapidly collapse toward its axis, thus forming a shaped charge jet. In this complex and dynamic process, the AMRM method (adaptive mesh reshaping method) is used to re-mesh the finite element model. This method avoids the problem of low mesh density at high strains and accurately simulates the shaped charge jet's collapse. Once the detonation reaction is complete, the explosive's energy is completely released, and its driving effect on the jet becomes extremely weak. To improve computational efficiency, the explosive unit is removed from the model containing the explosive and liner. After removing the explosive unit, the AMRM method is used to simulate the jet's formation.

[0041] The core concept of the AMRM algorithm lies in solving finite element simulations of large material deformation processes through adaptive repartitioning. It first solves the dynamic equations using an explicit time integration method, gradually updating the physical quantities to simulate large material deformation processes. At regular intervals, mesh redistribution is triggered by detecting element distortion. Subsequently, a remapping process remaps state variables from the old mesh to the new mesh, ensuring continuity of physical quantities and allowing simulation to continue. This adaptive mesh redistribution and mapping mechanism effectively addresses mesh distortion in large deformation problems, improving simulation accuracy and efficiency.

[0042] (1.1) Initial parameter setting

[0043] Sets the time interval between adaptive remeshing and the mesh feature size.

[0044] (1.2) Mesh redistribution

[0045] At each interval, the inner angle of the finite element grid is To check the mesh distortion. Refers to the angle formed by two adjacent edges on the unit boundary at the vertex. If the grid is too small, the unit will be compressed into a sharp shape, which may lead to singular Jacobian matrix and numerical instability. If the value is too large, the unit will be stretched into a flat shape, which will cause the shape function gradient calculation to be distorted and reduce the integration accuracy. Beyond the [45°, 135°] interval, it is marked as a distorted mesh, and then the mesh is redistributed to ensure that the mesh size is close to the mesh characteristic size, which helps to improve the accuracy and stability of the simulation.

[0046] (1.3) Mesh remapping

[0047] The state variables such as stress, strain, pressure, velocity and temperature rise of the mesh before mesh redistribution are mapped to the new mesh.

[0048] First, extrapolate all variables of the old mesh from the Gaussian points to the element nodes:

[0049] ;

[0050] Where: is the physical quantity of the old mesh node, The number of elements in the old mesh that share this node, For the old grid The shape function of the unit Gaussian point, For the old grid The physical quantity of a unit Gauss point.

[0051] Then, transfer all the variables of the old grid nodes to the nodes of the new grid:

[0052] ;

[0053] Where: is the physical quantity of the new mesh node, is the interpolation function.

[0054] Finally, map the nodal quantities of the new mesh to the Gaussian points of each element in the new mesh:

[0055] ;

[0056] Where: is the physical quantity of the new grid Gaussian point, is the number of nodes in the cell where the new grid Gaussian point is located, For the new grid The shape function of the nodes, For the new grid The physical quantity of a node.

[0057] (2) Jet stretching and fracture process

[0058] When the bottom of the liner converges toward the axis, the shaped charge jet has completed its transition from initial collapse to full formation. During the jet's stretching process, factors such as velocity gradient and temperature can cause localized necking, ultimately leading to breakage. To address this complex material failure process, an adaptive FEM-SPH transformation method was employed.

[0059] When implementing the FEM-SPH adaptive conversion method, first, it is necessary to output the results of the AMRM method in step (1) to simulate the jet forming process, including node coordinates, stress, strain, velocity and mesh results; next, these results are imported into the FEM-SPH model for calculation; when the liner has not yet broken, the finite element method is used for calculation, and when the strain of the liner material reaches the failure strain, the finite element calculation method is converted into SPH particles in smooth particle fluid dynamics; the Johnson-Cook failure criterion is usually used to define the failure strain. :

[0060] ;

[0061] Where: is a failure parameter that can be determined experimentally. is the stress triaxiality, is the strain rate, is the reference strain rate, is the temperature, is room temperature, Is the melting point.

[0062] This invention breakthrough combines adaptive grid technology with a multi-algorithm coupling mechanism, achieving high-precision simulation of the entire process of jet forming, stretching and fracture while maintaining calculation accuracy, significantly improving the accuracy of prediction of the dynamic behavior of metal jets.

[0063] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A shaped charge jet simulation method based on AMRM-FEM-SPH, characterized in that: The process of the shaped jet simulation method is as follows: (1) During the liner collapse stage, i.e., from the ignition of the explosive to the end of the detonation, the AMRM method is used to re-divide the finite element mesh. When the detonation reaction is completely over, the explosive unit is deleted from the model containing the explosive and the liner. After deleting the explosive unit, the AMRM method is continued to simulate the jet forming process. The specific steps include: (1.1) Initial parameter setting Set the time interval and grid feature size for adaptive grid re-division; (1.2) Mesh redistribution At each interval, the inner angle of the finite element grid is To check the mesh distortion; the mesh inner angle Refers to the angle formed by two adjacent edges on the unit boundary at the vertex; when the internal angle of the grid If the grid exceeds the interval [45°, 135°], it is marked as a distorted grid, and then the grid is redistributed to ensure that the grid size is close to the grid characteristic size; (1.3) Mesh remapping Map the state variables such as stress, strain, pressure, velocity and temperature rise of the mesh before mesh redistribution to the new mesh; First, extrapolate all variables of the old mesh from the Gaussian points to the element nodes: ； In the above formula, is the physical quantity of the old mesh node, The number of elements in the old mesh that share this node, For the old grid The shape function of the unit Gaussian point, For the old grid The physical quantity of a unit Gauss point; Then, transfer all the variables of the old grid's nodes to the nodes of the new grid: ； In the above formula, is the physical quantity of the new mesh node, is the interpolation function; Finally, map the nodal quantities of the new mesh to the Gaussian points of each element in the new mesh: ； In the above formula, is the physical quantity of the new grid Gaussian point, is the number of nodes in the cell where the new grid Gaussian point is located, For the new grid The shape function of the nodes, For the new grid Physical quantity of each node; (2) During the jet stretching and fracture stage of the liner, the failure units are converted into SPH particles by combining the FEM-SPH method with the Johnson-Cook failure criterion.

2. The AMRM-FEM-SPH-based shaped charge jet simulation method according to claim 1, characterized in that: The specific process of step (2) is as follows: First, it is necessary to output the results of the AMRM method used in step (1) to simulate the jet forming process; then, the results are imported into the FEM-SPH model for calculation; when the liner has not yet broken, the finite element method is used for calculation; when the strain of the liner material reaches the failure strain, the finite element calculation method is converted into SPH particles in smooth particle fluid dynamics; The Johnson-Cook failure criterion is used to define the failure strain : ； In the above formula, ~ is the failure parameter, determined experimentally; is the stress triaxiality, is the strain rate, is the reference strain rate, is the temperature, is room temperature, Is the melting point.

3. The AMRM-FEM-SPH-based shaped charge jet simulation method according to claim 2, characterized in that: The results of the AMRM method simulating the jet forming process include node coordinates, stress, strain, velocity and grid.

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