A meshless-based simulation method for shaped charge jet forming in an axisymmetric coordinate system

Abstract

This invention discloses a simulation method for shaped charge jet formation in a meshless axisymmetric coordinate system, belonging to the field of computational mechanics and numerical simulation technology. The method includes the following steps: geometric modeling and finite element mesh generation in an axisymmetric coordinate system; constructing mass and volume weights for material points; constructing shape functions for each material point, applying boundary conditions, and obtaining the initial stress of each material point; calculating the deformation gradient of each material point and updating the stress of each material point; discretizing the stress of each material point onto each node using the shape functions to obtain the nodal forces of each node, calculating the acceleration of the nodes and updating the nodal velocities; updating the coordinates, neighborhood, shape functions, and derivatives of the material points, and updating the node positions; outputting the physical information and dynamic data for each time step to complete the shaped charge jet formation simulation. This invention reduces the original three-dimensional problem to two dimensions, significantly reducing the number of degrees of freedom, improving computational efficiency, and increasing the accuracy of stress-strain prediction near the axis.

Description

Technical Field

[0001] This invention belongs to the field of computational mechanics and numerical simulation technology, specifically relating to a simulation method for shaped jet formation in a meshless axisymmetric coordinate system. Background Technology

[0002] Shaped charge warheads are a typical type of munition that relies on the geometric shaped charge effect to achieve penetration and damage. Their basic structure typically consists of a high-energy explosive main charge, a shaped charge liner, initiation and detonation propagation / waveform shaping components, and a casing. During operation, the explosive detonates, creating a detonation wave that, under the influence of the charge structure, axially converges and loads the shaped charge liner, driving it to undergo high-speed collapse and reverse convergence, thus forming a high-speed metal jet with a significant velocity gradient that penetrates the target armor. The shaped charge jet formation process involves multi-physics coupling problems such as the strong nonlinear loading of detonation products, large deformation of the shaped charge liner, and high-speed plastic flow. Currently, engineering design urgently needs corresponding numerical simulation methods to achieve predictable and repeatable control of the jet formation stability and penetration capability.

[0003] Existing simulation methods for shaped charge jet forming typically employ the Euler method, the pure Lagrangian explicit finite element method, the arbitrary Lagrangian-Euler method (ALE), and the smoothed particle dynamics (SPH) method. However, due to the massive plastic deformation, plastic heat generation, and thermo-mechanical coupling experienced by the metal liner during shaped charge jet forming, these methods all have corresponding shortcomings. For example, the pure Lagrangian finite element method is prone to mesh entanglement when dealing with large deformations, making it difficult to predict the extremely large plastic deformation involved in jet forming; while the Euler method and ALE method can describe the large deformation process of jet forming, they struggle to track the historical variables of the metal liner, thus failing to accurately describe the plastic deformation and heat generation process of the liner; the SPH method suffers from tensile stress instability, making it difficult to handle the jet forming process. The current novel optimal transport meshless method combines the advantages of the Lagrange finite element method and the meshless method. It can handle large deformation, large plastic flow and the plastic heat generation process in jet forming. However, when dealing with three-dimensional problems, it still has the disadvantages of large computational load and insufficient computational efficiency, making it difficult to apply in practical engineering design. Summary of the Invention

[0004] The purpose of this invention is to provide a simulation method for shaped jet formation based on a meshless axisymmetric coordinate system, so as to solve the problems of mesh distortion, erosion mass loss, and interface diffusion in existing traditional shaped jet formation calculation methods.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: This invention relates to a simulation method for shaped jet formation in a meshless axisymmetric coordinate system, comprising the following steps: S1. In r - z Geometric modeling of the shaped charge penetrating warhead structure is performed in an axisymmetric coordinate system. Finite element meshing is performed on the problem domain, and meshless geometric initialization is performed to obtain the initialized nodes and material points. The time domain is divided into several time steps. S2. In r - z Mass and volume weights of material points in an axisymmetric coordinate system; S3. Construct point shape functions for each substance and apply boundary conditions simultaneously; S4. Calculate the deformation gradient of each material point based on the displacement of each node, substitute the deformation gradient into the material constitutive model, update the stress of each material point, and use the numerical stabilization method to stabilize the paraxial region; use shape functions to discretize the stress of each material point onto each node to obtain the nodal force of each node, calculate the acceleration of the node based on the nodal force and the mass of each node, and update the nodal velocity. S5. Update the coordinates, neighborhood, shape function, and derivative of the shape function of the material point; update the position of the node. S6. Determine if the current time step is the last time step. If not, return to S4. If yes, output the physical information and dynamic data of each time step to complete the shaped jet forming simulation.

[0006] Preferably, the specific step of S1 is: to... r - z The structural domain in an axisymmetric coordinate system is meshed using finite element methods. Based on the finite element mesh, spatial discretization is performed using the optimal transport meshless method. Nodes in the finite element mesh are transformed into nodes in the optimal transport meshless method, and integration points in the finite element mesh are transformed into material points in the optimal transport meshless method.

[0007] Preferably, in step S2, the volume weight calculation method is as follows: the equivalent area of ​​each material point is calculated using a finite element mesh. and the radius of the material point Calculate volume weight for: .

[0008] Preferably, when calculating the volume weight in step S2, a smoothing scale is set. If the radius of the material point The effective radius is calculated as follows: The initial material point radius is adjusted using a smooth substitution method. Replace with effective radius The volume weight is calculated as follows: .

[0009] Preferably, the specific steps for applying boundary conditions in S3 are as follows: applying radial constraints to nodes on the axis of symmetry and applying rigid planar constraints at the axis of symmetry.

[0010] Preferably, the formula for calculating the deformation gradient in S4 is: , in, For deformation gradient, The radial displacement of each material point. This represents the axial displacement of the material point. This is the radial partial derivative of the radial displacement. This is the partial derivative of the radial displacement in the axial direction. This is the radial partial derivative of the axial displacement. This is the partial derivative of the axial displacement in the axial direction. and These are the initial radius and the radius after deformation of the material point, respectively.

[0011] Preferably, the step of stabilizing the paraxial region using a numerical stabilization method in S4 is as follows: setting a smoothing scale. If the radius of the material point Calculate the mass of each substance point. ,in, For material density, Let be the equivalent area of ​​the material point; if the radius of the material point is... The effective radius is calculated as follows: The initial material point radius is adjusted using a smooth substitution method. Replace with effective radius Calculate the mass of the substance point, that is, the mass of the substance point is... .

[0012] Preferably, the radial and axial node forces of each node in S4 are expressed as follows: , in, Radial nodal force, For axial nodal forces, For matter points radial coordinates, For matter points Volume weight, For matter points Jacobi, For matter points radial stress, For shape functions, For indexing material points, For matter points tangential stress, Let be the axial coordinates of the material point. For matter points Circumferential stress, For matter points Axial stress.

[0013] Preferably, in step S5, after updating the node position, a weighted smoothing method is used to perform paraxial correction on the material points, i.e., a smoothing scale is set. ,like The effective radius is calculated as follows: The effective radius is used as the radius of the material point; at the same time, an appropriate artificial viscosity is applied to suppress numerical oscillations in the paraxial region.

[0014] Preferably, step S4 further predicts the temperature distribution of the material during the focused jet forming process; wherein the temperature of the material is determined by the plastic heat of generation of the material, which is: , in, For plastic heat generation, The heat generation coefficient, For equivalent plastic stress, Equivalent plastic strain; The temperature of the material Represented as: , in, The initial temperature of the material. This represents the specific heat capacity of the material.

[0015] Compared with the prior art, the present invention has the following beneficial effects: 1. The present invention is in r - z Geometric modeling of the shaped charge penetrator structure is performed in an axisymmetric coordinate system, and mass and volume weights of the material points are constructed. r - z By constructing material points and nodes with axisymmetric volume weights in the plane, the robustness of the optimal transport meshless method to large deformations is maintained, while the original three-dimensional problem is reduced to two dimensions, significantly reducing the number of degrees of freedom and improving computational efficiency.

[0016] 2. This invention avoids numerical oscillations caused by the singularity of the volume integral in the region where the radius r of the material point approaches 0 by using weight correction and stability control methods for the paraxial region, thus ensuring the conservation of mass, momentum and energy and improving the accuracy of stress and strain prediction in the paraxial region.

[0017] 3. This invention, through constructing an axisymmetric stress update and contact processing algorithm, can stably simulate the dynamic responses such as large plastic deformation, high strain rate, plastic heat generation, and thermo-mechanical coupling in the shaped jet forming process, and can accurately predict the jet forming process and its velocity and temperature distribution. Attached Figure Description

[0018] Figure 1 This is a schematic diagram illustrating the spatial discretization of a geometric model in an axisymmetric coordinate system using a combination of material points and nodes, as described in this invention. Figure 2 This is a schematic diagram of the paraxial region smooth transition algorithm of the present invention; Figure 3 The geometric features and axisymmetric simplification of the jet-penetrating warhead of Embodiment 2 of the present invention; Figure 4 This is a diagram illustrating the detonation wave propagation process in Embodiment 2 of the present invention; Figure 5 This is a prediction of the results of focused jet forming in Embodiment 2 of the present invention. Detailed Implementation

[0019] The technical solution of the present invention will be further described in detail below through embodiments. These embodiments are for illustrative purposes only and are not intended to limit the present invention. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0020] Example 1: A meshless simulation method for shaped jet formation in an axisymmetric coordinate system, comprising the following steps: S1. In r - z Geometric modeling of the shaped charge penetrator structure is performed in an axisymmetric coordinate system, and the computational model is initialized. r-z In an axisymmetric coordinate system, the structure of a shaped charge penetrator is geometrically modeled and meshed using a finite element method (FEA) and then spatially discretized using the optimal transport meshless method (OTM). This involves discretizing the geometric model into a set of material points and a set of nodes. Specifically, the nodes in the OTM method are initialized using the nodes of the finite element mesh, and the material points in the OTM method are initialized using the center points of each element in the finite element mesh. Figure 1 As shown, the problem domain is meshed using finite element methods (FEM), and then the original nodes and material points of the FEM are converted into initialized nodes and material points. Hollow points represent nodes. ( Here, is the node index number in the discrete domain, representing which node it is. (This represents the nth time step; the time step size and number of steps are controlled by the user.) Solid triangles represent matter points. ( This is the index number of a material point in the discrete domain, representing which material point it is. (This represents the nth time step). Then the time domain is divided into several time steps.

[0021] S2. In r - z Constructing mass and volume weights for material points in an axisymmetric coordinate system. The volume weights of material points are constructed by assigning mass, volume, material parameters, and axial weights to each point, such that the integral of any physical quantity in the axisymmetric coordinate system can be obtained. r-z In the plane, the weighted summation is used to obtain the values. The method for constructing the volume weights of the material points is as follows: [Calculation...] r-z Area of ​​finite element in coordinate system s The initial radius of the material point in this unit is . r Then its volume weight is For material points near the axis of rotation, their volume weights are adjusted to determine a smooth scale. ,in, Let be the minimum equivalent radius of a material point when it is spatially discrete. This is an empirical parameter, typically ranging from 1.0 to 2.0. When the radius of a material point... When, its effective radius is The volume weight of the material point at this location is This method can eliminate singularities in the denominator of volume fractions.

[0022] S3. Settings The shape function of each material point is constructed. A dynamic search algorithm is used to determine the neighborhood range of each material point, centered on the initial search radius. All nodes within this neighborhood are then designated as the neighborhood of the material point. Based on these neighborhoods, the shape function of each material point is calculated. and the derivative of the point shape function of matter Simultaneously, boundary conditions are applied, with axisymmetric boundary conditions applied at the axis, consisting of two parts: 1) Constraints are applied to the nodes on the axis, restricting their radial degrees of freedom, allowing them to move only in the axial direction; at the same time, rigid surface constraint boundary conditions are applied at the axis, restricting other nodes and material points from penetrating the axis.

[0023] S4. Calculate the deformation gradient of each material point based on the displacement of each node. The formula for calculating the deformation gradient is: , in, For deformation gradient, The radial displacement of each material point. This represents the axial displacement of the material point. This is the radial partial derivative of the radial displacement. This is the partial derivative of the radial displacement in the axial direction. This is the radial partial derivative of the axial displacement. This is the partial derivative of the axial displacement in the axial direction. and These are the initial radius and the radius after deformation of the material point, respectively; Substitute the deformation gradient into the material constitutive model to update the stress at each material point; The stress at each material point is discretized to each node using shape functions, yielding the nodal forces at each node. The radial and axial nodal forces are expressed as follows: , in, For the radial internal force of the node, For axial nodal forces, For matter points radial coordinates, For matter points Volume weight, For matter points Jacobi, For matter points radial stress, For shape functions, For indexing material points, For matter points Tangential stress in the rz plane For axial coordinates, For matter points Circumferential stress, For matter points Axial stress.

[0024] Calculate the acceleration of the nodes based on the nodal forces and the mass of each node. And update the node speed based on the node's acceleration. .

[0025] S5. Update the coordinates of the matter point. ,in, The neighborhood of the matter point; update the neighborhood of the matter point according to step S3. Update the material point shape function ,in, Update the derivative of the shape function of the matter points to the total number of matter points. Update node position , For time step.

[0026] Paraxial region stability control is performed based on the node's location. For example... Figure 2As shown, nodes on the z-axis are represented by blue nodes. Displacement constraints are applied, and rigid surface constraints are also applied on the z-axis; key dimensions are taken. , r Locations with coordinates smaller than this critical dimension are represented by yellow areas, and material points within these areas are represented by green material points. A weighted smoothing method is needed to perform paraxial correction on these green material points, i.e., when the radius of the material point... When, its effective radius is The effective radius is then used as the radius of the material point. This radius is substituted into the calculation process of deformation gradient, stress, and nodal forces to complete the volume reconstruction of the paraxial region. At the same time, appropriate artificial viscosity is applied to suppress numerical oscillations in the paraxial region.

[0027] S6. Determine if the current time step is the last time step. If not, return to S4. If yes, output the physical information and dynamic data of each time step, including the position, velocity, acceleration, strain, stress, temperature and other field variables of each node and material point. Obtain the shape, velocity distribution and temperature distribution of the shaped jet formation, complete the dynamic response analysis of the material, and realize the simulation of shaped jet formation.

[0028] The temperature of a material is determined by the plastic heat generated by the material, which is: , in, For plastic heat generation, The heat generation coefficient, For equivalent plastic stress, Equivalent plastic strain; The temperature of the material Represented as: , in, The initial temperature of the material. This represents the specific heat capacity of the material.

[0029] Example 2 illustrates the meshless simulation method for shaped jet formation in an axisymmetric coordinate system using the jet formation simulation process of a shaped jet warhead as an example. The structure of the shaped jet warhead is as follows: Figure 3 As shown, it includes a shaped charge liner filled with explosives.

[0030] This embodiment describes the shaped charge jet formation process of a jet-piercing armor-piercing warhead with a diameter of 14 cm and a height of 14.5 cm. For example... Figure 4As shown, the detonation zone is located on the outermost radial side of the warhead's tail. First, the geometric model is meshed using finite element methods, and the mesh is then converted into the nodes and material points used in this invention. Constraints are set at the axis to restrict the radial degrees of freedom of the nodes on the axis, and a rigid surface is applied at the axis to prevent possible node / material point penetration of the axis.

[0031] In this embodiment, a high-energy explosive model is used for the charge, and the detonation products satisfy the JWL equation of state as follows:

[0032] In the formula, p For pressure; Relative volume; For the internal energy of the material, A , B , R 1. R 2. These are constants calibrated through experiments. The JWL equation of state and its isentropic equation consist of three terms: the first term plays a major role in the high-pressure region, the second term plays a major role in the medium-pressure region, and the third term plays a major role in the low-pressure region.

[0033] The metal shaped charge liner is modeled using a high-strain-rate elastoplastic model, in which the Mie-Gruneisen equation of state is used to describe the thermodynamic state of the metallic material, and the relationship is as follows:

[0034] , in, These are all parameters related to the thermal behavior of metallic materials, calibrated through experiments. For the initial density, For material density, The elastic modulus is used. The model still uses a thermo-visco-plastic model to describe the mechanical behavior of the explosive, covering strain hardening, strain rate dependence, and high-temperature softening that may occur during the simulation. In this model, the equivalent yield stress follows a power-law relationship: , In the formula, y Yield strength; For effective plastic strain; This is the equivalent plastic strain rate; T Absolute temperature; 0 represents the initial quasi-static yield stress; and For reference, effective plastic strain and strain rate; n To strengthen the index;m The strain rate index; T 0 is the reference temperature; T m It is the melting temperature; q This is the thermal softening index.

[0035] After the explosive detonates, the detonation wave propagates spherically within the charge and converges and collides at the axis, forming an extremely high-pressure zone that compresses the shaped charge liner, ultimately forming a shaped charge jet. Applying the meshless simulation method for shaped charge jet formation in an axisymmetric coordinate system proposed in this invention, the propagation of the detonation wave within the charge during the detonation process can be accurately simulated. Figure 4 As shown; it can also simulate the entire process of detonation wave impacting the shaped charge liner during jet formation, the shaped charge liner undergoing extreme plastic deformation, temperature rise, and finally forming a metal jet, recording the jet's shape, velocity distribution, and temperature distribution, such as... Figure 5 As shown, this provides initial conditions for the subsequent jet penetration process.

[0036] This embodiment employs the shaped charge jet formation simulation method proposed in this invention, successfully predicting the entire jet formation process during the operation of an armor-piercing jet warhead. Compared to traditional jet formation simulation methods, the proposed method simplifies the jet formation process by simulating it in an axisymmetric coordinate system. Compared to three-dimensional jet formation simulation, this reduces the computational load by over 90%, significantly improving computational efficiency. Furthermore, it can accurately predict the entire process of charge initiation, detonation wave propagation, and metal jet formation during jet formation, providing the morphology, velocity distribution, and temperature distribution of the formed jet. This demonstrates the accuracy and stability of the proposed method in numerical simulation of jet formation problems.

[0037] The present invention has been described in detail above with reference to the embodiments, but the content described is only a preferred embodiment of the present invention and should not be considered as limiting the scope of the present invention. All equivalent changes and improvements made in accordance with the scope of the present invention should still fall within the patent coverage of the present invention.

Claims

1. A meshless-based simulation method for shaped charge jet formation in an axisymmetric coordinate system, characterized in that, Includes the following steps: S1. In r - z Geometric modeling of the shaped charge penetrating warhead structure is performed in an axisymmetric coordinate system. Finite element meshing is performed on the problem domain, and meshless geometric initialization is performed to obtain the initialized nodes and material points. The time domain is divided into several time steps. S2. In r - z Mass and volume weights of material points in an axisymmetric coordinate system; S3. Construct point shape functions for each substance and apply boundary conditions simultaneously; S4. Calculate the deformation gradient of each material point based on the displacement of each node, substitute the deformation gradient into the material constitutive model, update the stress of each material point, and perform stabilization processing on the paraxial region using a numerical stabilization method. The steps are: set the smoothing scale. If the radius of the material point Calculate the mass of each substance point. ,in, For material density, Let be the equivalent area of ​​the material point; if the radius of the material point is... The effective radius is calculated as follows: The initial material point radius is adjusted using a smooth substitution method. Replace with effective radius Calculate the mass of the substance point, that is, the mass of the substance point is... ; The stress at each material point is discretized to each node using shape functions to obtain the nodal force at each node. The acceleration of the node is calculated based on the nodal force and the mass of each node, and the nodal velocity is updated. S5. Update the coordinates, neighborhood, shape function, and derivative of the shape function of the material point; update the position of the node. S6. Determine if the current time step is the last time step. If not, return to S4. If yes, output the physical information and dynamic data of each time step to complete the shaped jet forming simulation.

2. The simulation method for shaped jet formation based on a meshless axisymmetric coordinate system according to claim 1, characterized in that: The specific steps of S1 are as follows: ... r - z The structural domain in an axisymmetric coordinate system is meshed using finite element methods. Based on the finite element mesh, spatial discretization is performed using the optimal transport meshless method. Nodes in the finite element mesh are transformed into nodes in the optimal transport meshless method, and integration points in the finite element mesh are transformed into material points in the optimal transport meshless method.

3. The simulation method for shaped jet formation based on a meshless axisymmetric coordinate system according to claim 1, characterized in that: In S2, the volume weight calculation method is as follows: the equivalent area of ​​each material point is calculated through a finite element mesh. and the radius of the material point Calculate volume weight for: .

4. The simulation method for shaped jet formation based on a meshless axisymmetric coordinate system according to claim 3, characterized in that: When S2 calculates the volume weight, a smoothing scale is set. If the radius of the material point The effective radius is calculated as follows: The initial material point radius is adjusted using a smooth substitution method. Replace with effective radius The volume weight is calculated as follows: .

5. The simulation method for shaped jet formation based on a meshless axisymmetric coordinate system according to claim 1, characterized in that: The specific steps for applying boundary conditions in S3 are as follows: apply radial constraints to nodes on the axis of symmetry, and apply rigid planar constraints at the axis of symmetry.

6. The simulation method for shaped jet formation based on a meshless axisymmetric coordinate system according to claim 1, characterized in that: The formula for calculating the deformation gradient in S4 is: ， in, For deformation gradient, The radial displacement of each material point. This represents the axial displacement of the material point. This is the radial partial derivative of the radial displacement. This is the partial derivative of the radial displacement in the axial direction. This is the partial derivative of the axial displacement in the radial direction. This is the partial derivative of the axial displacement in the axial direction. and These are the initial radius and the radius after deformation of the material point, respectively.

7. The simulation method for shaped jet formation based on a meshless axisymmetric coordinate system according to claim 4, characterized in that: In step S5, after updating the node positions, a weighted smoothing method is used to perform paraxial correction on the material points, i.e., a smoothing scale is set. ,like The effective radius is calculated as follows: The effective radius is used as the radius of the material point; at the same time, an appropriate artificial viscosity is applied to suppress numerical oscillations in the paraxial region.

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