CN109960875B - Numerical simulation method for projectile penetration metal/rock composite target plate - Google Patents

Numerical simulation method for projectile penetration metal/rock composite target plate Download PDF

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CN109960875B
CN109960875B CN201910227180.XA CN201910227180A CN109960875B CN 109960875 B CN109960875 B CN 109960875B CN 201910227180 A CN201910227180 A CN 201910227180A CN 109960875 B CN109960875 B CN 109960875B
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target plate
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crush
metal
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CN109960875A (en
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杨建超
何翔
高杰
高伟亮
孙桂娟
王新颖
孔德锋
王晓峰
王幸
郭丹丹
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Institute of Engineering Protection National Defense Engineering Research Institute Academy of Military Sciences of PLA
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Abstract

The invention relates to a numerical simulation method of a projectile penetration metal/rock composite material target plate, which comprises the following steps: step S1: calculating penetration of the projectile body and the target plate by adopting a symmetric penalty function method, wherein the contact type is surface-to-surface erosion contact; step S2: establishing mathematical models of materials, including a target plate metal material model, a projectile body metal material model and a rock block material model in the target plate; step S3: establishing a finite element model of the material; step S4: and (4) carrying out numerical simulation. The beneficial effects of the invention are: the numerical simulation method provided by the invention is designed according to the structural characteristics of the metal matrix block stone composite material, the designed material constitutive model can better reflect the real performance of the material, and compared with the results of a large number of tests, the simulation result is basically consistent with the test result, and the whole process of penetration of a projectile into a metal/block stone composite material target plate can be better reflected.

Description

Numerical simulation method for projectile penetration metal/rock composite target plate
Technical Field
The invention relates to a numerical simulation technology of penetration-resistant materials, in particular to a numerical simulation method of a projectile penetration-resistant metal/rock composite material target plate.
Background
In the research of the protection engineering technology, the penetration resistance of the protection material is a key factor for determining the protection effect of the engineering. In order to obtain various penetration-resistant performance parameters of the protective material, a large number of experiments and calculations are needed, the penetration process of the projectile body to the material comprises the problems of high-speed collision, penetration, explosion, metal forming and other nonlinear dynamic impact of a two-dimensional and three-dimensional nonlinear structure, although the experimental result can well reflect the penetration-resistant effect of the material, the construction cost is high, and the experimental process is difficult to reproduce. The numerical simulation of the experimental process not only can reproduce the experimental process, but also can predict and estimate the tests which are not carried out, and has important significance for the research of modern protection technology.
At present, a metal/rock composite material is a novel protective material which is being developed and researched, and the structure of the metal/rock composite material is different from that of a single-material protective material, so that the metal/rock composite material is a macroscopically combined metal-based composite material with an uneven structure, and the whole penetration resistance process cannot be reasonably shown by an original numerical simulation method applied to the single material and a numerical simulation method applied to a microscopically reinforced metal-based composite material. Therefore, it is necessary to develop a numerical simulation method applied to a projectile penetration metal/rock composite target plate.
Disclosure of Invention
The invention aims to provide a numerical simulation method for a projectile penetration metal/block stone composite material target plate, which is based on an explicit nonlinear dynamic analysis finite element program LS-DYNA proposed by the American LSTC company, selects a proper contact collision algorithm, and respectively establishes constitutive models of a metal material and a block stone material and finite element models of the projectile and the target plate, thereby realizing the numerical simulation of the whole process of the projectile penetration metal/block stone composite material target plate.
In order to achieve the purpose, the invention adopts the following technical scheme:
a numerical simulation method for a projectile penetration metal/rock composite target plate comprises the following steps:
step S1: calculating penetration of the projectile body and the target plate by adopting a symmetric penalty function method, wherein the contact type is surface-to-surface erosion contact;
step S2: establishing mathematical models of materials, including a target plate metal material model, a projectile body metal material model and a rock block material model in the target plate;
the target plate metal material strength model and the elastomer metal material strength model are both:
Figure BDA0002005559020000021
in the above formula: A. b, C, n and m are material constants; epsilon p Is equivalent plastic strain;
Figure BDA0002005559020000022
is a dimensionless strain rate wherein
Figure BDA0002005559020000023
In order to achieve an equivalent strain rate,
Figure BDA0002005559020000024
quasi-static reference strain rate; t is * ＝(T-T r )/(T m -T r ) Is a dimensionless temperature, wherein T is the temperature, T m Is the material melting temperature, T r Is at room temperature;
the crushing of the material is determined by accumulated damage, the damage factor D is between 0 and 1, and the material is not damaged when D is 0; when D is 1, the material is completely damaged, and the damage factor is
Figure BDA0002005559020000025
In the above formula,. DELTA.. di p Increase in plastic strain, epsilon, for a time step f For the failure strain of the current time step, the expression is
Figure BDA0002005559020000031
In the above formula, σ * ＝p/σ eq Is the ratio of hydrostatic pressure to equivalent stress; d 1 ～D 5 Is the material constant;
the state equations of the target plate metal material strength model and the elastomer metal material are as follows:
Figure BDA0002005559020000032
in the above formula, e is the unit volume internal energy of the material; c. C 0 Is v is s -v p The intercept of the curve; s. the 1 、S 2 And S 3 Is v s -v p The coefficient of the slope of the curve, which can be approximated to be linear (i.e. S) 2 And S 3 Zero); v. of s Is the velocity of the shock wave, v p Is the particle velocity; gamma ray 0 Is the Gr neisen coefficient; a is to gamma 0 First order volume correction; mu-rho/rho 0 -1, ρ is the current density, ρ 0 Is the initial density.
The strength and dimensionless equivalent stress equation of the stone material model in the target plate is as follows:
Figure BDA0002005559020000033
in the above formula, σ * ＝σ/f c Is a dimensionless equivalent stress, where σ is the actual equivalent stress, f c Quasi-static uniaxial compressive strength; A. b, C, N is the material constant; p is a radical of formula * ＝p/f c Is a dimensionless pressure, where p is the true pressure;
Figure BDA0002005559020000041
is a dimensionless strain rate wherein
Figure BDA0002005559020000042
In order to be a true strain rate,
Figure BDA0002005559020000043
for reference strain rate, D is a damage factor, obtained by adding equivalent plastic strain and plastic volume strain, and the expression is:
Figure BDA0002005559020000044
in the above formula,. DELTA.. di p Is the equivalent plastic strain increment; Δ μ p Is a plastic volume strain increment; t is * ＝T/f c Is the dimensionless maximum stretch hydrostatic pressure, where T is the maximum stretch hydrostatic pressure; d 1 And D 2 Is the material damage constant; in the process of calculation
Figure BDA0002005559020000045
Wherein the constant EFMIN is the minimum fracture plastic strain;
the relationship between the pressure p and the volume strain mu of the concrete is described by a rock block material model in the target plate by adopting a three-stage state equation of a porous material, and the concrete method comprises the following steps:
(1) the linear elasticity stage, the state equation of loading or unloading in the stage is as follows:
p＝K e μ (7)，
K e ＝p crush /μ crush (8)，
in the above formula, mu is more than or equal to 0 and less than or equal to mu crush ，K e Is the bulk modulus; p is a radical of crush And mu crush Respectively crushing volume pressure and crushing volume strain of a uniaxial compression experiment; mu-rho/rho 0 -1 is the cell standard volume strain, ρ is the current density, ρ 0 Is the initial density;
(2) and (3) a plastic deformation stage, wherein the loading state equation of the stage is as follows:
p＝K P (μ-μ crush )+p crush (9)，
Figure BDA0002005559020000051
in the above formula,. mu. crush ≤μ≤μ plock ，K p Is the plastic bulk modulus; p is a radical of formula lock Is the compaction pressure; mu.s lock ＝ρ grain /ρ 0 -1 is the compacted volume strain, where p grain Is the density of the particles, which corresponds to the density of the material without air gaps at all; mu.s plock Is at P lock The volume strain of (a) is,referred to as permanent crush volume strain;
the unloading state equation at this stage is:
p＝[(1-F)K e +FK P ](μ-μ max )+p max (11)
in the above formula, F ═ mu max -μ crush )/(μ plock -μ crush ) Is an interpolation factor; mu.s max And p max Is the maximum volume strain and maximum pressure reached before unloading.
(3) In the compacting stage, the concrete material in the stage is completely crushed, and the loaded state equation is as follows:
Figure BDA0002005559020000052
in the above-mentioned formula, the compound has the following structure,
Figure BDA0002005559020000061
to a corrected volume strain; k 1 、K 2 And K 3 Is a material constant;
the unloading state equation at this stage is:
Figure BDA0002005559020000062
step S3: establishing a finite element model of a material, wherein the method comprises the following steps: establishing finite element solid models of various materials in millimeter, gram and millisecond units according to the actual size in the designed test, and performing modeling calculation by a quarter model according to the symmetry of the structure and the load when the target plate is modeled; then, setting symmetrical constraint on the symmetrical surface of the whole model, setting fixed constraint on the periphery of the concrete substrate of the target body, setting surface-to-surface erosion contact between the bullets and the target body, and finally applying a certain initial speed to the bullets to finish the establishment of the whole calculation model;
step S4: and (4) performing numerical simulation, inputting various material parameters of the designed test, solving a linear equation set corresponding to each finite element model, and displaying the obtained result.
In step S3, the contact interfaces between different materials in the model are all connected by common joints, that is, the metal casing and the nylon filler inside the projectile body are connected by common joints, and the metal box, the rock block and the concrete substrate in the target body are also connected by common joints.
The invention has the beneficial effects that: the numerical simulation method provided by the invention is designed according to the structural characteristics of the metal matrix block stone composite material, the designed material constitutive model can better reflect the real performance of the material, and compared with the results of a large number of tests, the simulation result is basically consistent with the test result, and the whole process of penetration of a projectile body into a metal/block stone composite material target plate can be better reflected.
Drawings
FIG. 1 is a flow chart of the present invention.
Fig. 2 is a time course graph of the projectile velocity in example 1.
Fig. 3 is a graph of the time course of projectile displacement in example 1.
Fig. 4 is a graph showing a simulation of the projectile of example 1 at 0.45 milliseconds of penetration.
Fig. 5 is a simulation display of the projectile of example 1 at 4.3 milliseconds during penetration.
Detailed Description
The present invention will be described in further detail with reference to the flow charts in the drawings.
The numerical simulation is carried out by adopting LS-DYNA software, LS-DYNA is an explicit nonlinear dynamic analysis finite element program which is introduced by the American LSTC company, the numerical simulation object is the whole process that a projectile penetrates through a metal-block stone composite material target plate, the involved materials comprise a metal projectile, a metal box body, block stones and concrete, and the involved algorithm is mainly a contact collision algorithm.
The invention provides a numerical simulation method of a projectile penetration metal/rock composite material target plate, which comprises the following steps:
step S1: calculating penetration of the projectile body and the target plate by adopting a symmetric penalty function method, wherein the contact type is surface-to-surface erosion contact; the principle of the symmetric penalty function method is simple: the method comprises the steps of checking whether a slave node penetrates through a main surface or not at each time step, if the slave node does not penetrate through the main surface, processing is not carried out, and if the slave node penetrates through the main surface, a large interface contact force is introduced between the node and the penetrated main surface, wherein the magnitude of the large interface contact force is in direct proportion to the penetration depth and the rigidity of a main sheet and is called a penalty function value, so that the penetration of the node on a contact surface is limited. The symmetric penalty function method is called because the penalty function processing is performed on the master node as well as the slave node. The size of the penalty function is limited by stability and can be adjusted by enlarging the penalty function value or reducing the time step if significant breakthrough occurs in the calculation. The symmetric penalty function method has the advantages of simple principle, easy programming, little arousing of grid hourglass effect, no numerical noise and accurate conservation of algorithm momentum, thereby having wide application.
Step S2: establishing mathematical models of materials, including a target plate metal material model, a projectile body metal material model and a rock block material model in the target plate;
the target plate metal material strength model and the elastomer metal material strength model are both as follows:
Figure BDA0002005559020000081
in the above formula: A. b, C, n and m are material constants; epsilon p Is equivalent plastic strain;
Figure BDA0002005559020000082
is a dimensionless strain rate wherein
Figure BDA0002005559020000083
In order to achieve an equivalent strain rate,
Figure BDA0002005559020000084
quasi-static reference strain rate; t is * ＝(T-T r )/(T m -T r ) Is a dimensionless temperature, wherein T is the temperature, T m Is the material melting temperature, T r Is at room temperature;
the crushing of the material is determined by accumulated damage, the damage factor D is between 0 and 1, and the material is not damaged when the D is 0; when D is 1, the material is completely damaged, and the damage factor is
Figure BDA0002005559020000085
In the above formula,. DELTA.. di p Increment of plastic strain, epsilon, for one time step f For the failure strain at the current time step, the expression is:
Figure BDA0002005559020000086
in the above formula, σ * ＝p/σ eq Is the ratio of hydrostatic pressure to equivalent stress; d 1 ～D 5 Is a material constant;
the state equations of the target plate metal material strength model and the elastomer metal material are as follows:
Figure BDA0002005559020000091
in the above formula, e is the unit volume internal energy of the material; c. C 0 Is v is s -v p The intercept of the curve; s. the 1 、S 2 And S 3 Is v is s -v p The coefficient of the slope of the curve, which can approximate a linear relationship (i.e., S) 2 And S 3 Zero); v. of s Is the velocity of the shock wave, v p Is the particle velocity; gamma ray 0 Gr ü neisen coefficient; a is to gamma 0 First order volume correction; mu-rho/rho 0 -1, ρ is the current density, ρ 0 Is the initial density.
The strength and dimensionless equivalent stress equation of the stone material model in the target plate is as follows:
Figure BDA0002005559020000092
in the above formula, σ * ＝σ/f c Is in no amountLine equivalent stress, where σ is the actual equivalent stress, f c Quasi-static uniaxial compressive strength; A. b, C, N is the material constant; p is a radical of formula * ＝p/f c Is a dimensionless pressure, where p is the true pressure;
Figure BDA0002005559020000093
is a dimensionless strain rate wherein
Figure BDA0002005559020000094
In order to be a true strain rate,
Figure BDA0002005559020000095
for reference strain rate, D is a damage factor, obtained by adding equivalent plastic strain and plastic volume strain, and the expression is:
Figure BDA0002005559020000096
in the above formula,. DELTA.. di p Is the equivalent plastic strain increment; Δ μ p Is the plastic volume strain increment; t is * ＝T/f c Is the dimensionless maximum stretch hydrostatic pressure, where T is the maximum stretch hydrostatic pressure; d 1 And D 2 Is the material damage constant; in the process of calculation
Figure BDA0002005559020000102
Wherein the constant EFMIN is the minimum fracture plastic strain;
the relationship between the pressure p and the volume strain mu of the concrete is described by a rock block material model in the target plate by adopting a three-stage state equation of a porous material, and the concrete steps are as follows:
(3) the linear elasticity stage, the state equation of loading or unloading in the stage is as follows:
p＝K e μ (7)，
K e ＝p crush /μ crush (8)，
in the above formula, 0 is less than or equal to mu and less than or equal to mu crush ，K e Is the bulk modulus; p is a radical of formula crush And mu crush The crushing volume pressure and the crushing volume strain of a uniaxial compression experiment are respectively; mu-rho/rho 0 -1 is the cell standard volume strain, ρ is the current density, ρ 0 Is the initial density;
(4) and (3) a plastic deformation stage, wherein the loading state equation of the stage is as follows:
p＝K P (μ-μ crush )+p crush (9)，
Figure BDA0002005559020000101
in the above formula,. mu. crush ≤μ≤μ plock ，K p Is the plastic bulk modulus; p is a radical of formula lock Is the compaction pressure; mu.s lock ＝ρ grain /ρ 0 -1 is the compacted volume strain, where p grain Is the density of the particles, which corresponds to the density of the material without air gaps at all; mu.s plock Is at P lock The volume strain at (a), referred to as permanent crush volume strain;
the unloading state equation at this stage is:
p＝[(1-F)K e +FK P ](μ-μ max )+p max (11)
in the above formula, F ═ mu max -μ crush )/(μ plock -μ crush ) Is an interpolation factor; mu.s max And p max Is the maximum volume strain and maximum pressure reached before unloading.
(3) In the compacting stage, the concrete material in the stage is completely crushed, and the loaded state equation is as follows:
Figure BDA0002005559020000111
in the above formula, the first and second carbon atoms are,
Figure BDA0002005559020000112
to a corrected volume strain; k 1 、K 2 And K 3 Is the material constant;
the unloading state equation at this stage is:
Figure BDA0002005559020000113
step S3: a finite element model of a material is established, and the method comprises the following steps: establishing finite element solid models of various materials by adopting millimeter, gram and millisecond units according to the actual size in the designed test, and performing modeling calculation by using a quarter model according to the symmetry of a structure and a load when the target plate is modeled; then, setting symmetrical constraint on the symmetrical surface of the whole model, setting fixed constraint on the periphery of the concrete substrate of the target body, setting surface-to-surface erosion contact between the bullets and the target body, and finally applying a certain initial speed to the bullets to finish the establishment of the whole calculation model;
step S4: and (3) performing numerical simulation, namely inputting various material parameters of a designed test, solving a linear equation set corresponding to each finite element model, and displaying an obtained result.
In step S3, all contact interfaces between different materials in the model are connected by common nodes, that is, the metal casing in the projectile body and the nylon filler inside are connected by common nodes, and the metal box body, the rock block and the concrete substrate in the target body are also connected by common nodes.
According to the steps, the invention makes numerical simulation on the penetration test of the phi 60 elastomer, in the designed test, the metal box material is cast steel ZG45, the actually measured yield strength is 386MPa, the tensile strength is 676MPa, the elastic modulus is 204GPa, and the model parameters are shown in the table I:
table-metal box material model parameters
Figure BDA0002005559020000121
The elastomer material is 35CrMnSiA subjected to special heat treatment, the tensile strength is 1910MPa, the yield strength is 1570MPa, and the model parameters of the elastomer material are shown in the table II:
TABLE II elastomeric material model parameters
Figure BDA0002005559020000122
Figure BDA0002005559020000131
The target plate rock block material is C50 commercial concrete, the actually measured cubic compressive strength is 55MPa, and the values of model parameters are shown in the table III:
model parameters of Epimeri concrete HJC
Figure BDA0002005559020000132
The main simulation object of numerical simulation is an intrusion test of a phi 60 projectile, the length of the projectile is 360mm, the overall slenderness ratio is 6:1, and the slenderness ratio of a head is 2: 1; the target body selects a plain concrete cylindrical target with the diameter of 2000mm as a target plate substrate, and the strength grade of the concrete is C50. The metal/rock composite material target plate is embedded in a plain concrete surface layer, a 3mm thick steel plate is adopted to clamp the outside of a plain concrete target body, the length of the target body is 1.5m, the size of the rock in the metal/rock composite material target plate is a cube small block with the side length of 55mm, the wall thickness of a metal box body is 6mm, the thickness of a single-layer target plate is 116mm, and the metal volume content in the composite material target plate is 25.4%.
Example 1
When the landing speed of the projectile body is 780 m/s, the speed time-course curve of the projectile body is shown in figure 2, the displacement time-course curve of the projectile body is shown in figure 3, numerical simulation of the penetration process is shown in figures 4 and 5,
compared with the actual test result, the numerical simulation penetration depth is 784 mm, the actual measurement penetration depth is 785 mm, and the penetration depth error is 0.3%.
Example 2:
when the landing speed of the projectile body is 1275 m/s, the penetration depth of the numerical simulation is through the target plate, and the actually measured penetration depth is also through the target plate.
Example 3:
the invention also carries out numerical simulation on the process of the same projectile penetrating the same metal-block stone composite material target body at different speeds, and the result is shown in the fourth table:
table quaphi 60 elastomer penetration metal-block stone composite material target body numerical value simulation result
Figure BDA0002005559020000141
In conclusion, the numerical simulation method for the projectile penetration metal/rock composite target plate provided by the invention has the characteristics of good simulation effect and capability of visually displaying the whole penetration process.
The present invention is not described in detail in the prior art.

Claims (2)

1. A numerical simulation method for a projectile penetration metal/rock composite target plate is characterized by comprising the following steps: the method comprises the following steps:
step S1: calculating penetration of the projectile body and the target plate by adopting a symmetric penalty function method, wherein the contact type is surface-to-surface erosion contact;
step S2: establishing mathematical models of materials, including a target plate metal material model, a projectile body metal material model and a rock block material model in the target plate;
the target plate metal material strength model and the elastomer metal material strength model are both:
Figure FDA0002005559010000011
in the above formula: A. b, C, n and m are material constants; epsilon p Is the equivalent plastic strain;
Figure FDA0002005559010000012
is a dimensionless strain rate wherein
Figure FDA0002005559010000013
In order to obtain an equivalent strain rate,
Figure FDA0002005559010000014
quasi-static reference strain rate; t ═ T (T-T) r )/(T m -T r ) Is a dimensionless temperature, wherein T is the temperature, T m Is the material melting temperature, T r Is at room temperature;
the crushing of the material is also determined by accumulated damage, the damage factor D is between 0 and 1, and the material is not damaged when D is 0; when D is 1, the material is completely damaged, and the damage factor is
Figure FDA0002005559010000015
In the above formula,. DELTA.. di-elect cons p Increase in plastic strain, epsilon, for a time step f For the failure strain of the current time step, the expression is
Figure FDA0002005559010000021
In the above formula, σ * ＝p/σ eq Is the ratio of hydrostatic pressure to equivalent stress; d 1 ～D 5 Is a material constant;
the state equations of the target plate metal material strength model and the elastomer metal material are as follows:
Figure FDA0002005559010000022
in the above formula, e is the unit volume internal energy of the material; c. C 0 Is v is s -v p The intercept of the curve; s 1 、S 2 And S 3 Is v is s -v p The coefficient of the slope of the curve, which can be approximated to be linear (i.e. S) 2 And S 3 Zero); v. of s Is the velocity of the shock wave, v p Is the particle velocity; gamma ray 0 Gr ü neisen coefficient; a is to gamma 0 First order volume ofCorrecting; mu-rho/rho 0 -1, ρ is the current density, ρ 0 Is the initial density;
the strength and dimensionless equivalent stress equation of the stone material model in the target plate is as follows:
Figure FDA0002005559010000023
in the above formula, σ * ＝σ/f c Is a dimensionless equivalent stress, where σ is the actual equivalent stress, f c Quasi-static uniaxial compressive strength; A. b, C, N is the material constant; p is a radical of formula * ＝p/f c Is a dimensionless pressure, where p is the true pressure;
Figure FDA0002005559010000024
is a dimensionless strain rate wherein
Figure FDA0002005559010000031
In order to be a true strain rate,
Figure FDA0002005559010000032
for reference strain rate, D is a damage factor, obtained by adding equivalent plastic strain and plastic volume strain, and the expression is:
Figure FDA0002005559010000033
in the above formula,. DELTA.. di p Is the equivalent plastic strain increment; Δ μ p Is a plastic volume strain increment; t is * ＝T/f c Is the dimensionless maximum stretch hydrostatic pressure, where T is the maximum stretch hydrostatic pressure; d 1 And D 2 Is the material damage constant; in the process of calculation
Figure FDA0002005559010000034
Wherein the constant EFMIN is the minimum fracture plastic strain;
the relationship between the pressure p and the volume strain mu of the concrete is described by a rock block material model in the target plate by adopting a three-stage state equation of a porous material, and the concrete steps are as follows:
(1) the linear elasticity stage, the state equation of loading or unloading in the stage is as follows:
p＝K e μ (7)，
K e ＝p crush /μ crush (8)，
in the above formula, mu is more than or equal to 0 and less than or equal to mu crush ，K e Is the bulk modulus; p is a radical of crush And mu crush Respectively crushing volume pressure and crushing volume strain of a uniaxial compression experiment; mu-rho/rho 0 -1 is the cell standard volume strain, ρ is the current density, ρ 0 Is the initial density;
(2) and (3) a plastic deformation stage, wherein the loading state equation of the stage is as follows:
p＝K P (μ-μ crush )+p crush (9)，
Figure FDA0002005559010000044
in the above formula,. mu. crush ≤μ≤μ plock ，K p Is the plastic bulk modulus; p is a radical of formula lock Is the compaction pressure; mu.s lock ＝ρ grain /ρ 0 -1 is the compacted volume strain, where p grain Is the density of the particles, which corresponds to the density of the material without air gaps at all; mu.s plock Is at P lock The volume strain at (a), referred to as permanent crush volume strain;
the unloading state equation at this stage is:
p＝[(1-F)K e +FK P ](μ-μ max )+p max (11)
in the above formula, F ═ mu max -μ crush )/(μ plock -μ crush ) Is an interpolation factor; mu.s max And p max Is the maximum volume strain and maximum pressure reached before unloading;
(3) and in the compaction stage, the concrete material is completely crushed in the stage, and the loaded state equation is as follows:
Figure FDA0002005559010000041
in the above formula, the first and second carbon atoms are,
Figure FDA0002005559010000042
to a corrected volume strain; k 1 、K 2 And K 3 Is a material constant;
the unloading state equation at this stage is:
Figure FDA0002005559010000043
step S3: a finite element model of a material is established, and the method comprises the following steps: establishing finite element solid models of various materials in millimeter, gram and millisecond units according to the actual size in the designed test, and performing modeling calculation by a quarter model according to the symmetry of the structure and the load when the target plate is modeled; then, setting symmetrical constraint on the symmetrical surface of the whole model, setting fixed constraint on the periphery of the concrete matrix of the target body, setting surface-to-surface erosion contact between the bullets and the target body, and finally applying a certain initial speed to the bullets to finish the establishment of the whole calculation model;
step S4: and (4) performing numerical simulation, inputting various material parameters of the designed test, solving a linear equation set corresponding to each finite element model, and displaying the obtained result.
2. The method of claim 1, wherein the method comprises the steps of: in step S3, the contact interfaces between different materials in the model are all connected by common joints, that is, the metal casing and the nylon filler inside the projectile body are connected by common joints, and the metal box, the rock block and the concrete substrate in the target body are also connected by common joints.
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