A simulation method of warhead shell expansion and fracture based on smoothed particle dynamics

Abstract

The present invention belongs to the technical field of coupling algorithms, and discloses a warhead shell expansion fracture simulation method based on smooth particle dynamics, comprising the following steps: discretizing explosives and metal shells into SPH particles carrying physical information; calculating a correction matrix of the smooth function derivative of the SPH particles according to the spatial position of the discretized particles; calculating the stress of the SPH particles at the spatial position; reconstructing the stress of the SPH particles and their neighboring particles; updating the density and internal energy of the SPH particles at the spatial position; and updating the velocity and spatial position of the SPH particles. The present invention adopts the above-mentioned warhead shell expansion fracture simulation method based on smooth particle dynamics, introduces the reconstructed stress into the conservation equation and corrects the continuity equation. Under the premise of ensuring the velocity continuity condition, it can effectively handle complex fracture problems such as warhead shell expansion fracture, and has higher accuracy and robustness.

Description

Technical Field

[0001] The invention relates to the technical field of coupling algorithms, and in particular to a warhead shell expansion and fracture simulation method based on smooth particle dynamics. Background Art

[0002] The anti-explosive warhead is a type of warhead widely used in various weapon systems, and its outer part is covered with a metal shell of a certain thickness. These shells are used to contain explosives and produce high-speed fragments after explosion to kill targets within the combat radius. Therefore, studying the rupture of the shell is crucial to evaluating the damage effect of the warhead. With the continuous improvement of computer computing speed, numerical research has gradually become an efficient research method. For warhead explosions involving ultra-high-speed flow of materials and large deformation fracture, traditional finite element and finite difference methods often cannot simulate the complete process of the shell from detonation to expansion fracture well. In contrast, the meshless (Smoothed Particle Hydrodynamics, SPH) algorithm, as a pure Lagrangian method, has natural advantages in interface capture and large deformation material fracture, so it is very suitable for simulating the expansion fracture process of the warhead shell.

[0003] After the charge inside the shell is detonated, the effect of the high-pressure detonation products on the metal shell forms a typical gas-solid coupling problem. Gas-solid coupling has always been a hot spot and difficulty in the SPH algorithm. The traditional SPH method does not consider the existence of discontinuous interfaces and fails to meet the velocity continuity conditions between the explosive and the metal, which leads to inaccurate SPH particle velocity gradients near the interface, thereby introducing errors in the calculation of solid external forces and stresses. Since material fracture is closely related to its stress state, these errors may lead to inaccurate simulation of the expansion and fracture process of the warhead shell. In addition, the movement of the shell driven by explosives is a high-pressure and high-strain rate process. At this time, the shell often presents a mixed tensile-shear fracture rather than a simple tensile fracture. Existing solid SPH fracture simulation methods, such as those based on pseudo-springs and particle splitting, are only effective for simple tensile fractures. For complex tensile-shear mixed fracture problems, they cannot deal well with the squeezing effect that may occur between failed particles, which ultimately leads to the emergence of computational divergence problems. Summary of the invention

[0004] The purpose of the present invention is to provide a warhead shell expansion fracture simulation method based on smooth particle dynamics, which can effectively simulate the complete process of the warhead from detonation to the tensile-shear mixed fracture of the shell driven by detonation, introduce the reconstructed stress into the conservation equation and correct the continuity equation, and effectively handle complex fracture problems such as warhead shell expansion fracture under the premise of ensuring velocity continuity conditions, thereby ensuring the accuracy of solid structure stress calculation, thereby solving the numerical divergence problem caused by the instability phenomenon between failed particles, having higher accuracy and robustness, and providing important technical support for engineering and scientific research in related fields.

[0005] To achieve the above object, the present invention provides a warhead shell expansion fracture simulation method based on smooth particle dynamics, comprising the following steps:

[0006] S1. Discretize the explosive and metal shell into SPH particles carrying physical information;

[0007] S2, according to the discrete particle space position Calculating SPH particles Correction matrix of the smooth function derivative;

[0008] S3. Calculate spatial position SPH particles stress;

[0009] S4. Reconstruction of SPH particles and its neighboring particles stress;

[0010] S5. Update spatial position The density and internal energy of the SPH particle at ;

[0011] S6. Update SPH particles Speed ​​and spatial position .

[0012] Preferably, in step S1, the physical information includes volume, density, internal energy, pressure, and velocity.

[0013] Preferably, in step S2, according to the discrete particle spatial position Calculating SPH particles The correction matrix of the smooth function derivative is as follows:

[0014] ;

[0015] in, To correct the rectangle, For SPH particles The correction matrix of is the spatial position of the SPH particle; Represents SPH particles Supports the first Neighborhood SPH particles; For SPH particles The initial position of For SPH particles The initial position of For particles and particles The distance between represents a smooth function, which is the Wendland function; represents the volume of the SPH particle, Indicates The volume of a neighborhood SPH particle; is the gradient operator, For SPH particles The gradient operator of is the symbol for the vector outer product.

[0016] Preferably, in step S3, the spatial position is calculated SPH particles The specific process is as follows:

[0017] S31. Calculation of SPH particles The velocity gradient is as follows:

[0018] ;

[0019] in, For speed, For SPH particles speed, For the The speed of the neighboring SPH particles; is the velocity gradient, For SPH particles The velocity gradient;

[0020] S32. Calculate SPH particles The strain rate tensor and rotation rate tensor of are as follows:

[0021] ;

[0022] in, and are the strain rate tensor and the rotation rate tensor, respectively. For SPH particles The strain rate tensor, For SPH particles The rotation rate tensor of T is the matrix transpose operator;

[0023] S33. Calculation of SPH particles The rate of change of the deviator stress is as follows:

[0024] ;

[0025] in, and are the deviatoric stress and the rate of change of deviatoric stress, respectively. Represents SPH particles The deviator stress, Represents SPH particles The rate of change of the deviator stress, is the shear modulus, I is the identity matrix, represents the trace of a matrix;

[0026] S34. Calculate SPH particles The pressure includes:

[0027] S341. If the material is explosive, then the SPH particles The pressure is as follows:

[0028] ;

[0029] in, Represents SPH particles pressure; , is the initial density of the material, is the material density; E represents the internal energy, A , B , , as well as All are material constants;

[0030] S342. If the material is a metal shell, then the SPH particles The pressure is as follows:

[0031] ;

[0032] in, , a , C 0. , S 1. S 2 and S 3 are all constants;

[0033] S35. Calculation of SPH particles The stress is as follows:

[0034] ;

[0035] in, For SPH particles The stress, is the stress of the SPH particle.

[0036] Preferably, in step S4, the SPH particles are reconstructed and its neighboring particles The specific process is as follows:

[0037] S41. Calculation of SPH particles The damage factor is as follows:

[0038] ;

[0039] in, represents the damage factor, Represents SPH particles The damage factor, For particles The plastic strain, For particles The fracture strain;

[0040] S42. Computational characterization of SPH particles and SPH particles The parameters of the movement trend are as follows:

[0041] ;

[0042] in, Represents SPH particles and SPH particles The parameters of the movement trend between Represents particles and particles have a tendency to approach each other. Represents particles and particles have a tendency to move away from each other;

[0043] S43. Calculation of SPH particles and SPH particles pressure and deviatoric stresses after reconstruction;

[0044] S431, if If established, then the particle and particles The reconstructed pressure and deviatoric stress are shown below:

[0045] ;

[0046] in, For SPH particles The damage factor, For SPH particles pressure, For SPH particles The pressure after reconstruction, For SPH particles The pressure after reconstruction, For SPH particles The deviator stress, For SPH particles The reconstructed deviatoric stress, For SPH particles deviatoric stress after reconstruction;

[0047] S432, if If this is not true, then the particle and particles The reconstructed pressure and deviatoric stress are:

[0048] ;

[0049] S44. Calculation of SPH particles and SPH particles The reconstructed stress is as follows:

[0050] ;

[0051] in, For SPH particles The stress after reconstruction, For SPH particles Stress after reconstruction.

[0052] Preferably, in step S5, the spatial position is updated The density and internal energy of the SPH particles are as follows:

[0053] S51. Calculation of SPH particles and SPH particles The density change rate scaling factor between is as follows:

[0054] ;

[0055] S52. Calculate SPH particles The density change rate and internal energy change rate are as follows:

[0056] ;

[0057] in, Represents SPH particles The density change rate, For SPH particles The density of For SPH particles The density of For SPH particles The internal energy, For SPH particles The rate of change of internal energy;

[0058] S53. Update SPH particles The density and internal energy are as follows:

[0059] ;

[0060] in, dt is the time step.

[0061] Preferably, in step S6, the SPH particles are updated Speed ​​and spatial position , the specific process is as follows:

[0062] S61. Calculation of SPH particles The acceleration is as follows:

[0063] ;

[0064] in, For SPH particles The acceleration of To be applied to particles Artificial viscosity between

[0065] S62. Update SPH particles The speed is as follows:

[0066] ;

[0067] ;

[0068] Among them, the superscript n is the number of time steps for calculating the moment, For the n Particles in time steps i speed, For the n +1 time step velocity of particle i, For the n The acceleration of the particle in each time step is is the velocity correction term for one time step, c is a constant coefficient, which is 0.1;

[0069] S63. Update SPH particles The spatial position is as follows:

[0070] ;

[0071] in, For the n Particles in time steps i spatial location, For the n +1 time step particles i spatial location.

[0072] Therefore, the present invention adopts the above-mentioned warhead shell expansion fracture simulation method based on smooth particle dynamics, which can effectively simulate the complete process of the warhead from detonation to the tensile-shear mixed fracture of the shell driven by detonation, introduce the reconstructed stress into the conservation equation and correct the continuity equation. Under the premise of ensuring the velocity continuity condition, it can effectively deal with complex fracture problems such as warhead shell expansion fracture, ensure the accuracy of solid structure stress calculation, thereby solving the numerical divergence problem caused by the instability phenomenon between failed particles, and has higher accuracy and robustness, providing important technical support for engineering and scientific research in related fields.

[0073] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 It is a schematic diagram of the fracture and separation of SPH structure particles of a warhead shell expansion fracture simulation method based on smooth particle dynamics of the present invention;

[0075] Figure 2 It is a schematic diagram of a typical two-dimensional plane strain warhead calculation example in an embodiment of a warhead shell expansion fracture simulation method based on smooth particle dynamics of the present invention;

[0076] Figure 3 It is a flow field velocity profile diagram obtained by different simulation methods in an embodiment of a warhead shell expansion and fracture simulation method based on smooth particle dynamics of the present invention;

[0077] Figure 4 Different simulation methods in the embodiment of the warhead shell expansion fracture simulation method based on smooth particle dynamics of the present invention obtain t=12.4 Shell fracture damage cloud diagram; wherein, (a) is the calculation result of the pseudo-spring method; (b) is the calculation result of the present invention;

[0078] Figure 5 Different simulation methods in the embodiment of the warhead shell expansion fracture simulation method based on smooth particle dynamics of the present invention obtain t=22 Shell fracture damage cloud map; wherein, (a) is the calculation result without introducing the density change rate scaling factor; (b) is the calculation result of the method of the present invention;

[0079] Figure 6 The present invention is a flow chart of a method for simulating warhead shell expansion and fracture based on smooth particle dynamics. DETAILED DESCRIPTION

[0080] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0081] like Figure 6 As shown, the present invention provides a warhead shell expansion fracture simulation method based on smooth particle dynamics, comprising the following steps:

[0082] S1. Discrete the explosive and metal shell into a certain number of SPH particles carrying physical information, including volume, density, internal energy, pressure, velocity, etc.

[0083] S2, according to the discrete particle space position Calculating SPH particles The correction matrix of the smooth function derivative is as follows:

[0084] ;

[0085] in, To correct the rectangle, For SPH particles The correction matrix of is the spatial position of the SPH particle; Represents SPH particles Supports the first Neighborhood SPH particles; For SPH particles The initial position of For SPH particles The initial position of For particles and particles The distance between represents a smooth function, which is the Wendland function; represents the volume of the SPH particle, Indicates The volume of a neighborhood SPH particle; is the gradient operator, For SPH particles The gradient operator of is the symbol for the vector outer product.

[0086] S3. Calculate spatial position SPH particles The specific process is as follows:

[0087] S31. Calculation of SPH particles The velocity gradient is as follows:

[0088] ;

[0089] in, For speed, For SPH particles speed, For the The speed of the neighboring SPH particles; is the velocity gradient, For SPH particles velocity gradient.

[0090] S32. Calculate SPH particles The strain rate tensor and rotation rate tensor of are as follows:

[0091] ;

[0092] in, and are the strain rate tensor and the rotation rate tensor, respectively. For SPH particles The strain rate tensor, For SPH particles The rotation rate tensor of T is the matrix transpose operator.

[0093] S33. Calculation of SPH particles The rate of change of the deviator stress is as follows:

[0094] ;

[0095] in, and are the deviatoric stress and the rate of change of deviatoric stress, respectively. Represents SPH particles The deviator stress, Represents SPH particles The rate of change of the deviator stress, is the shear modulus, I is the identity matrix, Represents the trace of the matrix.

[0096] S34. Calculate SPH particles The pressure includes:

[0097] S341. If the material is explosive, then the SPH particles The pressure is as follows:

[0098] ;

[0099] in, Represents SPH particles pressure; , is the initial density of the material, is the material density; E represents the internal energy, A , B , , as well as are material constants.

[0100] S342. If the material is a metal shell, then the SPH particles The pressure is as follows:

[0101] ;

[0102] in, , a , C 0. , S 1. S 2 and S 3 are all constants.

[0103] S35. Calculation of SPH particles The stress is as follows:

[0104] ;

[0105] in, For SPH particles The stress, is the stress of the SPH particle.

[0106] S4. Reconstruction of SPH particles and its neighboring particles The specific process is as follows:

[0107] S41. Calculation of SPH particles The damage factor is as follows:

[0108] ;

[0109] in, represents the damage factor, Represents SPH particles The damage factor, For particles The plastic strain, For particles The fracture strain.

[0110] S42. Computational characterization of SPH particles and SPH particles The parameters of the movement trend are as follows:

[0111] ;

[0112] in, Represents SPH particles and SPH particles The parameters of the movement trend between Represents particles and particles have a tendency to approach each other. Represents particles and particles Have a tendency to move away from each other.

[0113] S43. Calculation of SPH particles and SPH particles pressure and deviatoric stresses after reconstruction;

[0114] S431, if If established, then the particle and particles The reconstructed pressure and deviatoric stress are shown below:

[0115] ;

[0116] in, For SPH particles The damage factor, For SPH particles pressure, For SPH particles The pressure after reconstruction, For SPH particles The pressure after reconstruction, For SPH particles The deviator stress, For SPH particles The reconstructed deviatoric stress, For SPH particles Deviatoric stress after reconstruction.

[0117] S432, if If this is not true, then the particle and particles The reconstructed pressure and deviatoric stress are:

[0118] ;

[0119] S44. Calculation of SPH particles and SPH particles The reconstructed stress is as follows:

[0120] ;

[0121] in, For SPH particles The stress after reconstruction, For SPH particles Stress after reconstruction.

[0122] S5. Update spatial position The density and internal energy of the SPH particles are as follows:

[0123] S51. Calculation of SPH particles and SPH particles The density change rate scaling factor between is as follows:

[0124] ;

[0125] S52. Calculate SPH particles The density change rate and internal energy change rate are as follows:

[0126] ;

[0127] in, Represents SPH particles The density change rate, For SPH particles The density of For SPH particles The density of For SPH particles The internal energy, For SPH particles The rate of change of internal energy.

[0128] S53. Update SPH particles The density and internal energy are as follows:

[0129] ;

[0130] in, dtis the time step.

[0131] S6. Update SPH particles Speed ​​and spatial position , the specific process is as follows:

[0132] S61. Calculation of SPH particles The acceleration is as follows:

[0133] ;

[0134] in, For SPH particles The acceleration of To be applied to particles Artificial viscosity between.

[0135] S62. Update SPH particles The speed is as follows:

[0136] ;

[0137] ;

[0138] Among them, the superscript n is the number of time steps for calculating the moment, For the n Particles in time steps i speed, For the n +1 time step velocity of particle i, For the n The acceleration of the particle in each time step is is the velocity correction term for one time step, c is a constant coefficient, which is taken as 0.1.

[0139] S63. Update SPH particles The spatial position is as follows:

[0140] ;

[0141] in, For the n Particles in time steps i spatial location, For the n +1 time step particles i spatial location.

[0142] Example

[0143] A schematic diagram of the SPH structure particle fracture separation of a warhead shell expansion fracture simulation method based on smooth particle dynamics of the present invention is shown in FIG. Figure 1 Figure 2 shows the stress reconstruction of particles when the material fractures.

[0144] This embodiment uses a typical two-dimensional plane strain warhead as an example to verify the effectiveness of the present invention. Considering that the common charge structure of the warhead is a rotational axis symmetrical structure, the axial strain of the shell under the detonation drive is much smaller than the radial strain, so the warhead can be simplified into a two-dimensional plane strain model. Figure 2 As shown, the warhead radius r =2cm, the charge type is TNT, the outer coating thickness h =0.4cm 45 steel shell. The state equation of the explosive is JWL, and the specific parameters are shown in Table 1; the state equation of 45 steel is Mie–Grüneisen equation, and the specific parameters are shown in Table 2. The strength model adopts Johnson–Cook constitutive model, and the specific material parameters are shown in Table 3. The calculated particle spacing is 0.38mm.

[0145] Table 1 Parameters of JWL equation of state of explosives

[0146] ;

[0147] Table 2 Mie–Grüneisen state equation parameters for 45 steel

[0148] ;

[0149] Table 3 Johnson–Cook constitutive model parameters of 45 steel

[0150] ;

[0151] In order to evaluate the reliability of the present invention in ensuring the velocity continuity near the gas-solid interface, the calculation results of the method of the present invention are compared with the traditional SPH method which does not consider the velocity continuity condition. Figure 3 The figure shows the 8th Particle velocity distribution profile along the radius at each moment. It can be observed from the figure that the radial velocity calculated by the method of the present invention shows good continuity, while the velocity obtained by the traditional SPH method shows obvious disturbances, and even velocity discontinuities appear at certain positions. This shows that the method of the present invention can effectively suppress the velocity discontinuity problem of the flow field and the gas-solid interface, thereby ensuring the accuracy of the structural stress calculation.

[0152] In order to verify the effectiveness of the present invention in dealing with the interaction between failed particles in complex fracture problems, the calculation results of the present invention are compared with those of the pseudo-spring method. Figure 4 As shown, the explosive detonation is 12.4 Shell expansion fracture cloud diagrams obtained by two methods at the moment; Figure 4 (a) in the figure shows the calculation results of the pseudo-spring method. Figure 4 (b) in the figure shows the calculation results of the present invention. Overall, the shell fracture conditions obtained by the two methods are similar. However, it can be observed from the local figure that the pseudo-spring method shows the mutual aggregation and clustering phenomenon between the failed particles. This is because the fracture mode of the shell under the action of detonation drive is mainly shear fracture, and there is an extrusion effect between the fracture surface materials. However, the disclosed pseudo-spring method cannot effectively deal with the extrusion effect between the failed particles, especially when the failed particles are close to each other, it cannot provide appropriate force, resulting in particle aggregation. In this embodiment, the calculation of the pseudo-spring method showed a negative failed particle density value after time 12.4, which ultimately led to calculation divergence. In contrast, the failed shell particles calculated by the method of the present invention are more evenly distributed, without obvious aggregation or clustering. This clearly demonstrates the superiority of the method of the present invention in dealing with complex fracture problems and interactions between failed particles.

[0153] In order to illustrate the necessity of introducing the density change rate scaling factor in the present invention, the calculation results of the method of the present invention are compared with the calculation results without introducing the factor. Figure 5 The figure shows the explosion of the explosives 22 Shell expansion fracture cloud diagrams obtained by two methods at the moment; Figure 5 (a) shows the calculation result without introducing the density change rate scaling factor. Figure 5 (b) in the figure shows the calculation result of the method of the present invention. By comparison, it can be seen that when the density change rate scaling factor is not introduced, the particle distribution near the fracture surface is relatively disordered, connected to each other, and a clear fracture cannot be formed. In contrast, the method of the present invention obtains a clear fracture surface, and the particle distribution near the fracture surface is orderly. This shows that the introduction of the density change rate scaling factor can better simulate the fracture separation phenomenon of the metal shell material, making the calculation results more accurate and reliable.

[0154] Therefore, the present invention adopts the above-mentioned warhead shell expansion fracture simulation method based on smooth particle dynamics, which can effectively simulate the complete process of the warhead from detonation to the tensile-shear mixed fracture of the shell driven by detonation, introduce the reconstructed stress into the conservation equation and correct the continuity equation. Under the premise of ensuring the velocity continuity condition, it can effectively deal with complex fracture problems such as warhead shell expansion fracture, ensure the accuracy of solid structure stress calculation, thereby solving the numerical divergence problem caused by the instability phenomenon between failed particles, and has higher accuracy and robustness, providing important technical support for engineering and scientific research in related fields.

[0155] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A warhead shell expansion fracture simulation method based on smooth particle dynamics, characterized in that: The following steps are involved: S1. Discretize the explosive and metal shell into SPH particles carrying physical information; the physical information includes volume, density, internal energy, pressure, and velocity; S2, according to the discrete particle space position Calculating SPH particles The correction matrix of the smooth function derivative is as follows: ； in, To correct the rectangle, For SPH particles The correction matrix of is the spatial position of the SPH particle; Represents SPH particles Supports the first Neighborhood SPH particles; For SPH particles The initial position of For SPH particles The initial position of For particles and particles The distance between represents a smooth function, which is the Wendland function; represents the volume of the SPH particle, Indicates The volume of a neighborhood SPH particle; is the gradient operator, For SPH particles The gradient operator of is the symbol for the vector outer product; S3. Calculate spatial position SPH particles The specific process is as follows: S31. Calculation of SPH particles The velocity gradient is as follows: ； in, For speed, For SPH particles speed, For the The speed of the neighboring SPH particles; is the velocity gradient, For SPH particles The velocity gradient; S32. Calculate SPH particles The strain rate tensor and rotation rate tensor of are as follows: ； in, and are the strain rate tensor and the rotation rate tensor, respectively. For SPH particles The strain rate tensor, For SPH particles The rotation rate tensor of T is the matrix transpose operator; S33. Calculation of SPH particles The rate of change of the deviator stress is as follows: ； in, and are the deviatoric stress and the rate of change of deviatoric stress, respectively. Represents SPH particles The deviator stress, Represents SPH particles The rate of change of the deviator stress, is the shear modulus, I is the identity matrix, represents the trace of a matrix; S34. Calculate SPH particles The pressure includes: S341. If the material is explosive, then the SPH particles The pressure is as follows: ； in, Represents SPH particles pressure; , is the initial density of the material, is the material density; E represents the internal energy, A , B , , as well as All are material constants; S342. If the material is a metal shell, then the SPH particles The pressure is as follows: ； in, , a , C 0. , S 1. S 2 and S 3 are all constants; S35. Calculation of SPH particles The stress is as follows: ； in, For SPH particles The stress, is the stress of the SPH particle; S4. Reconstruction of SPH particles and its neighboring particles stress; S5. Update spatial position The density and internal energy of the SPH particle at ; S6. Update SPH particles Speed ​​and spatial position .

2. The method for simulating warhead shell expansion fracture based on smooth particle dynamics according to claim 1, characterized in that: In step S4, the SPH particles are reconstructed and its neighboring particles The specific process is as follows: S41. Calculation of SPH particles The damage factor is as follows: ； in, represents the damage factor, Represents SPH particles The damage factor, For particles The plastic strain, For particles The fracture strain; S42. Computational characterization of SPH particles and SPH particles The parameters of the movement trend are as follows: ； in, Represents SPH particles and SPH particles The parameters of the movement trend between Represents particles and particles have a tendency to approach each other. Represents particles and particles have a tendency to move away from each other; S43. Calculation of SPH particles and SPH particles pressure and deviatoric stresses after reconstruction; S431, if If established, then the particle and particles The reconstructed pressure and deviatoric stress are shown below: ； in, For SPH particles The damage factor, For SPH particles pressure, For SPH particles The pressure after reconstruction, For SPH particles The pressure after reconstruction, For SPH particles The deviator stress, For SPH particles The reconstructed deviatoric stress, For SPH particles deviatoric stress after reconstruction; S432, if If this is not true, then the particle and particles The reconstructed pressure and deviatoric stress are: ； S44. Calculation of SPH particles and SPH particles The reconstructed stress is as follows: ； in, For SPH particles The stress after reconstruction, For SPH particles Stress after reconstruction.

3. The method for simulating warhead shell expansion fracture based on smooth particle dynamics according to claim 1, characterized in that: In step S5, the spatial position is updated The density and internal energy of the SPH particles are as follows: S51. Calculation of SPH particles and SPH particles The density change rate scaling factor between is as follows: ； S52. Calculate SPH particles The density change rate and internal energy change rate are as follows: ； in, Represents SPH particles The density change rate, For SPH particles The density of For SPH particles The density of For SPH particles The internal energy, For SPH particles The rate of change of internal energy; S53. Update SPH particles The density and internal energy are as follows: ； in, dt is the time step.

4. The method for simulating warhead shell expansion fracture based on smooth particle dynamics according to claim 1, characterized in that: In step S6, the SPH particles are updated Speed ​​and spatial position , the specific process is as follows: S61. Calculation of SPH particles The acceleration is as follows: ； in, For SPH particles The acceleration of To be applied to particles Artificial viscosity between S62. Update SPH particles The speed is as follows: ； ； Among them, the superscript n is the number of time steps for calculating the moment, For the n Particles in time steps i speed, For the n +1 time step velocity of particle i, For the n The acceleration of the particle in each time step is is the velocity correction term for one time step, c is a constant coefficient, which is 0.1; S63. Update SPH particles The spatial position is as follows: ； in, For the n Particles in time steps spatial location, For the n +1 time step particles spatial location.

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