Electromagnetic protection material failure and crack evolution calculation method

Abstract

The invention belongs to the technical field of electromagnetic protection, and discloses an electromagnetic protection material failure and crack evolution calculation method which comprises the following steps: establishing a free energy form for describing force heat and fracture response of an electromagnetic protection material; based on a Coleman-Nell process, analyzing and deducing a constitutive theory of electromagnetic, force, heat and fracture phase field coupling derived in a free energy form; combining a constitutive theory with a momentum conservation equation, a heat conduction equation, a fracture phase field evolution equation and a Maxwell equation set, and obtaining a solvable weak form of a total partial differential equation set based on a variational method; and analyzing, studying and judging the weak form, and developing a numerical solution method and a template. According to the method for calculating the failure and crack evolution of the electromagnetic protection material, the design level of the thermal protection material is improved, the development period of a new material is remarkably shortened, the cost is reduced, and conversion and application of the novel thermal protection material on a thermal protection system of a next-generation hypersonic aircraft are promoted.

Description

Technical Field

[0001] The present invention relates to the field of electromagnetic protection technology, and in particular to a method for calculating failure and crack evolution of electromagnetic protection materials. Background Art

[0002] With the continuous development of information technology and communication equipment, the complexity and interference of the electromagnetic environment are becoming increasingly serious. High-intensity electromagnetic fields can cause great damage to electronic equipment, communication systems and other critical infrastructure under some extreme environmental conditions, such as electromagnetic pulse (EMP), nuclear explosions, and electromagnetic weapons.

[0003] Most of the existing electromagnetic protection materials are based on metal shielding and absorbing materials, and their design methods usually focus on the optimization of a single function, such as only considering electromagnetic shielding or absorbing performance. However, in some special application environments, traditional electromagnetic protection materials have the following major problems: 1) The protection effect is limited and cannot provide stable protection in a wide band and multiple electromagnetic environments; 2) The weight of the material is large, which affects the lightweight design of the overall equipment; 3) The thermal management ability of the protective material is poor, and the material performance is easily degraded due to high temperature or other extreme environmental conditions.

[0004] The design and development of electromagnetic protection materials have long relied on experimental verification and semi-empirical models, and have been optimized through a combination of experiments and numerical simulations. However, this "trial and error" method and semi-empirical model approach lacks overall consideration of multifunctional synergistic performance in the material design process, resulting in low design efficiency, long cycle, and high R&D costs. In addition, existing design methods usually ignore the comprehensive performance requirements of materials in extreme electromagnetic environments, such as the unified optimization of protection, thermal management, and lightweight, which limits the widespread application of electromagnetic protection materials.

[0005] Therefore, it is urgent to propose a mathematical model and simulation method for electromagnetic protection materials that takes into account electromagnetic, force, and thermal coupling in order to achieve all-round optimization of electromagnetic protection materials. Summary of the invention

[0006] The purpose of the present invention is to provide a calculation method for failure and crack evolution of electromagnetic protection materials, which can not only improve the design level of electromagnetic protection materials, but also effectively shorten the research and development cycle, reduce research and development costs, and promote the application and development of electromagnetic protection materials in extreme environments.

[0007] To achieve the above object, the present invention provides a method for calculating failure and crack evolution of electromagnetic protection materials, comprising the following steps:

[0008] Step S1, considering the coupled mathematical model of electromagnetic field, temperature field, fracture phase field and force field, establishing a free energy form for describing the mechanical, thermal and fracture response of electromagnetic protection materials;

[0009] Step S2: Based on the Coleman-Noll process, the special physical and mechanical properties and usage scenarios of electromagnetic protection materials are taken into consideration, and the constitutive theory of electromagnetic, force, heat and fracture phase field coupling derived from the free energy form of step S1 is analyzed and derived;

[0010] Step S3, combining the constitutive theory of step S2 with the momentum conservation equation, the heat conduction equation, the fracture phase field evolution equation and the Maxwell equations, and obtaining a solvable weak form of the overall partial differential equations based on the variational method;

[0011] Step S4, analyze and judge the weak form given in step S3, develop numerical solution methods and templates, and realize efficient calculation and simulation of the mechanical, thermal, and fracture phase field coupling of the protective material under electromagnetic action, thereby realizing the prediction of mechanical and thermal failure and crack evolution process of the electromagnetic protective material.

[0012] Preferably, in step S1, the electromagnetic process, temperature conduction, fracture phase field evolution and force-displacement process in the real physical process of failure and fracture of the electromagnetic protection material are all included in the consideration and derivation of establishing the free energy form, and the Helmholtz free energy form describing the evolution mode of the electromagnetic protection material system is as follows:

[0013]

[0014] Among them, B e is the elastic part of the left Cauchy-Green tensor; e and b are the electric and magnetic field vectors respectively; d, is the order parameter and its spatial gradient that characterize the fracture phase field state; T is the thermodynamic temperature; ζ is the dissipative internal variable determined by the free energy form and conservation law of the current electromagnetic protection material; ψ s , ψ e , ψ c , ψ t They are the Helmholtz free energy forms of displacement field / stress field, electromagnetic field, fracture phase field, and temperature field;

[0015] B e =F e ·F eT ;

[0016] Where F is the deformation gradient; F e is the elastic deformation part in its multiplication decomposition; F eT F e The transpose of

[0017] F=F e ·F p ·F t ;

[0018] Among them, F p 、Ft They are the plastic deformation part and the thermal deformation part of the deformation gradient respectively.

[0019] Preferably, in step S2, based on the Coleman-Noll process, the special physical and mechanical properties and usage scenarios of the electromagnetic protection material are taken into consideration, and the constitutive theory of electromagnetic, force, heat, and fracture phase field coupling derived from the free energy form of step S1 is analyzed and derived. The specific process is as follows:

[0020] Step S21, considering the energy conservation form of electromagnetic, force and thermal coupling, as shown below:

[0021]

[0022] Where ε is the total energy per unit mass; ρ is the mass density; σ is the Cauchy stress; is the velocity; q is the heat flux; f b is the physical strength in the current configuration; is the rate of change of total energy density; r is the heat source term; It is defined as electromotive force, where e and b are electric and magnetic field vectors respectively; Defined as magnetic field intensity; h and d are magnetic field and electric displacement field respectively; the outer product of electromotive force and magnetic field intensity It is a representation of the density of electromagnetic energy flux;

[0023] Step S22, consider the phase field evolution equation, as shown below:

[0024]

[0025] Where d is the fracture phase field order parameter; ρ d is the density that characterizes the inertial effect of the fracture phase field; η d The viscosity is used to characterize the viscous effect of the fracture phase field; is the gradient operator defined in the reference configuration; ρ0 is the density defined in the reference configuration; is the exogenous micro-force source term for controlling the phase field;

[0026] Step S23: Based on the Coleman-Noll process, the constitutive theory and entropy inequality are derived as follows:

[0027] η=-ψ T +α t trτ / ρ;

[0028] Where η is entropy; ψ T is the partial derivative of free energy with respect to temperature T; α t is the thermal expansion coefficient of the material; tr represents the trace of the second-order tensor; τ is the Kirchhoff stress;

[0029]

[0030] Among them, g is the generalized momentum density; ∈0 is the permittivity;

[0031] p=-ρψ e ,m=-ρψ b ;

[0032] Where p is the polarization field; ψ e is the partial derivative of free energy with respect to the electric field e; m is the magnetization field, ψ b is the partial derivative of free energy with respect to magnetic field b;

[0033]

[0034] Where μ0 is the magnetic permeability; I is the second-order unit tensor;

[0035]

[0036] in, is the elastic part B of the left Cauchy-Green tensor of the free energy e The partial derivative of

[0037]

[0038] in, Characterize the energy dissipation caused by the phase field; is the phase field evolution rate;

[0039]

[0040] in, (F p ) -1 is the plastic deformation rate; ψ ξ is the partial derivative of free energy with respect to the micro-force ξ; is the rate of change of micro-force; is the conductivity density; is the gradient of temperature T.

[0041] Preferably, in step S3, the constitutive theory of step S2 is combined with the momentum conservation equation, the heat conduction equation, the fracture phase field evolution equation and the Maxwell equations, and based on the variational method, a solvable weak form of the overall partial differential equations is obtained. The specific process is as follows:

[0042] Step S31, consider the electromagnetic field equation, as shown below:

[0043]

[0044] Where, j is the current density; q is the charge density;

[0045] Step S32: introducing the generalized electromagnetic-force coupling momentum density into the conservation law. In the electromagnetic protection material, the momentum conservation form is as follows:

[0046]

[0047] Where ρ is the mass density; g is the generalized momentum density under electromagnetic-force coupling; σ is the Cauchy stress; f b is the physical strength in the current configuration;

[0048] The form of conservation of angular momentum is as follows:

[0049]

[0050] Where x is the position vector of the current configuration; σ is still the Cauchy stress;

[0051] The form of mass conservation is as follows:

[0052]

[0053] Step S33, consider the phase field evolution equation, as shown below:

[0054]

[0055] in, is the historical variable that characterizes the crack driving force; W e+ is the positive definition of elastic strain energy; W p is the plastic work; W0 is the energy threshold for crack initiation; χ is the thermal-plastic work conversion coefficient; G c is the critical energy release rate of fracture; l c is the crack characteristic width of the fracture phase field method;

[0056] Step S34: Combining the variational method, the following weak form group is obtained:

[0057]

[0058] Among them, Ω represents the computational space; δ u is the variation of displacement; To calculate the surface force on the boundary Γ;

[0059]

[0060] Where c is the specific heat; δ T is the variation of temperature; k is the thermal conductivity related to the fracture phase field;

[0061]

[0062] Among them, η dCharacterizes the fracture phase field viscosity, δ d is the variation of the fracture phase field;

[0063]

[0064] Among them, δ A is the variation of magnetic potential field; A is the magnetic potential field; defined as is the divergence of the magnetic potential field.

[0065] Preferably, in step S4, the weak form given in step S3 is analyzed and judged, and a numerical solution method and template are developed. The specific process is as follows:

[0066] Step S41: Considering the plastic constitutive theory and numerical calculation method, a plastic yield criterion is given as follows:

[0067]

[0068] Where, s = dev (σ) is the deviatoric stress; is the current rate-dependent, temperature-dependent and damage-dependent yield strength of the material;

[0069] Step S42: In each incremental step, the equivalent plastic strain increment is completed according to the conventional process. and plastic strain increment dε p After the calculation, the total elastic strain of the current calculation step is obtained as follows:

[0070] ε n+1 =ε n +dε-dε p ;

[0071] Step S43, decomposing the strain according to the decomposition principle, calculating the stress and elastic strain energy according to the current tangent modulus and elastic material parameters, realizing the decoupling of tensile and compressive elastic-plastic deformation, and preventing damage to the electromagnetic protection material and non-physical healing of cracks.

[0072] Therefore, the present invention adopts the above-mentioned calculation method for failure and crack evolution of electromagnetic protection materials, which provides a solid mathematical explanation for the damage, failure and crack evolution of protection materials under the coupling of electromagnetic, force and heat, and on this basis establishes an efficient and accurate numerical method and simulation process to achieve accurate prediction of the mechanical and thermal response of electromagnetic protection materials.

[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 flowchart of the steps of the method for calculating failure and crack evolution of electromagnetic protection materials of the present invention;

[0075] Figure 2 Schematic diagram of the type II fracture failure mode of the Ti-6Al-4V material in Example 1 of the present invention;

[0076] Figure 3 This is a cloud diagram of the equivalent plastic strain distribution of the aluminum metal plastic thick cylinder in Example 2 of the present invention;

[0077] Figure 4 This is the inner wall displacement-loading curve of the aluminum metal plastic thick cylindrical tube in Example 2 of the present invention. DETAILED DESCRIPTION

[0078] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0079] like Figure 1 As shown, the present invention provides a method for calculating failure and crack evolution of electromagnetic protection materials, comprising the following steps:

[0080] Step S1, considering the coupled mathematical model of electromagnetic field, temperature field, fracture phase field and force field, establishing a free energy form for describing the mechanical, thermal and fracture response of electromagnetic protection materials.

[0081] The electromagnetic process, temperature conduction, fracture phase field evolution and force-displacement process in the real physical process of failure and fracture of electromagnetic protection materials are all taken into consideration and deduction in establishing the free energy form.

[0082] The Helmholtz free energy form that describes the evolution of the electromagnetic protection material system is as follows:

[0083] ψ=ψ(B e ,e,b,d,▽d,T,ζ)=ψ s (B e ,e,b,d,ζ)+ψ e (e,b)+ψ c (d,▽d)+ψ t (T);

[0084] Among them, B e is the elastic part of the left Cauchy-Green tensor; e and b are the electric and magnetic field vectors respectively; d, is the order parameter and its spatial gradient that characterize the fracture phase field state; T is the thermodynamic temperature; ζ is the dissipative internal variable determined by the free energy form and conservation law of the current electromagnetic protection material; ψ s , ψ e , ψ c , ψ t They are the Helmholtz free energy forms of displacement field / stress field, electromagnetic field, fracture phase field, and temperature field respectively.

[0085] Be =F e ·F eT ;

[0086] Where F is the deformation gradient, F e is the elastic deformation part in its multiplication decomposition, F eT F e The transpose of .

[0087] F=F e ·F p ·F t ;

[0088] Among them, F p 、F t They are the plastic deformation part and the thermal deformation part of the deformation gradient respectively.

[0089] Step S2: Based on the Coleman-Noll process, the special physical and mechanical properties and usage scenarios of electromagnetic protection materials are taken into consideration, and the constitutive theory of electromagnetic, force, heat, and fracture phase field coupling derived from the free energy form of step S1 is analyzed and derived.

[0090] Step S21, considering the energy conservation form of electromagnetic, force and thermal coupling, as shown below:

[0091]

[0092] Where ε is the total energy per unit mass; ρ is the mass density; σ is the Cauchy stress; is the velocity; q is the heat flux; f b is the physical strength in the current configuration; is the rate of change of total energy density; r is the heat source term; It is defined as electromotive force, where e and b are electric and magnetic field vectors respectively; Defined as magnetic field intensity, h and d are magnetic field and electric displacement field respectively; the outer product of electromotive force and magnetic field intensity It is a representation of the density of electromagnetic energy flow.

[0093] Step S22, consider the phase field evolution equation, as shown below:

[0094]

[0095] Where d is the fracture phase field order parameter; ρ d is the density that characterizes the inertial effect of the fracture phase field; η d The viscosity is used to characterize the viscous effect of the fracture phase field; is the gradient operator defined in the reference configuration; ρ0 is the density defined in the reference configuration; is the exogenous micro-force source term that controls the phase field.

[0096] Step S23: Based on the Coleman-Noll process, the constitutive theory and entropy inequality are derived as follows:

[0097] η=-ψ T +α t trτ / ρ;

[0098] Where η is entropy; ψ T is the partial derivative of free energy with respect to temperature T; α t is the thermal expansion coefficient of the material; tr represents the trace of the second-order tensor; τ is the Kirchhoff stress.

[0099]

[0100] Where g is the generalized momentum density and ∈0 is the permittivity.

[0101] p=-ρψ e ,m=-ρψ b ;

[0102] Where p is the polarization field, ψ e is the partial derivative of free energy with respect to the electric field e, m is the magnetization field, ψ b is the partial derivative of free energy with respect to magnetic field b;

[0103]

[0104] Among them, μ0 is the magnetic permeability, I is the second-order unit tensor;

[0105]

[0106] in, is the elastic part B of the left Cauchy-Green tensor of the free energy e The partial derivative of

[0107]

[0108] in, Characterize the energy dissipation caused by the phase field, is the phase field evolution rate;

[0109]

[0110] in, is the plastic deformation rate, ψ ξ is the partial derivative of the free energy with respect to the micro-force ξ, is the rate of change of the microforce, is the conductivity density; is the gradient of temperature T.

[0111] Step S3, combining the constitutive theory of step S2 with the momentum conservation equation, the heat conduction equation, the fracture phase field evolution equation and the Maxwell equations, and obtaining a solvable weak form of the overall partial differential equations based on the variational method.

[0112] Step S31, consider the electromagnetic field equation, as shown below:

[0113]

[0114] Where j is the current density and q is the charge density.

[0115] In view of the basic properties and common working conditions of electromagnetic protection materials, we focus on the last term of the above equations, which is the Gaussian law of magnetic field that reflects the passivity of the magnetic field. This formula shows that the magnetic field must be the curl of a tensor field A of a certain order, that is, According to analytical convention, field A is called magnetic potential.

[0116] Step S32: introduce generalized electromagnetic-force coupling momentum density into the conservation law to replace the usual definition of velocity. In electromagnetic protection materials, the momentum conservation form is as follows:

[0117]

[0118] Where ρ is the mass density, g is the generalized momentum density under electromagnetic-force coupling, σ is the Cauchy stress, and f b It is the physical strength of the current configuration.

[0119] The form of conservation of angular momentum is as follows:

[0120]

[0121] Among them, x is the position vector under the current configuration, and σ is still the Cauchy stress. Different from the traditional continuum theory, due to the electromagnetic coupling and the specific form of the constitutive structure, the Cauchy stress tensor no longer retains symmetry.

[0122] The form of mass conservation is as follows:

[0123]

[0124] Step S33, consider the phase field evolution equation, as shown below:

[0125]

[0126] in, is the historical variable representing the crack driving force, W e+ is a “positive” definition of elastic strain energy; W p is the plastic work, W0 is the energy threshold for crack initiation; χ is the thermal-plastic work conversion coefficient, Gc is the critical energy release rate of fracture, l c is the crack characteristic width of the fracture phase field method;

[0127] Step S34: Combining the variational method, the following weak form group is obtained:

[0128]

[0129] Among them, Ω represents the computational space, δ u is the variation of displacement, To calculate the surface force on the boundary Γ;

[0130]

[0131] Where c is the specific heat, δ T is the variation of temperature, k is the thermal conductivity associated with the fracture phase field;

[0132]

[0133] Among them, η d Characterize the "viscosity" of the fracture phase field, δ d is the variation of the fracture phase field;

[0134]

[0135] Among them, δ A is the variation of the magnetic potential field, A is the magnetic potential field, and is defined as Obviously, is the divergence of the magnetic potential field.

[0136] Step S4, analyze and judge the weak form given in step S3, develop effective and accurate numerical solution methods and templates for specific problems, realize efficient calculation and simulation of mechanical, thermal, and fracture phase field coupling of protective materials under electromagnetic action, and thus realize accurate prediction of mechanical and thermal failure and crack evolution process of electromagnetic protective materials.

[0137] Step S41: Considering the plastic constitutive theory and numerical calculation method, a plastic yield criterion is given as follows:

[0138]

[0139] Where, s = dev (σ) is the deviatoric stress; is the current rate-dependent, temperature-dependent and damage-dependent yield strength of the material.

[0140] Step S42: In each incremental step, the equivalent plastic strain increment is completed according to the conventional process. and plastic strain increment dε pAfter the calculation, the total elastic strain of the current calculation step is obtained as follows:

[0141] ε n+1 =ε n +dε-dε p ;

[0142] Step S43, decomposing the strain according to the decomposition principle, calculating the stress and elastic strain energy according to the current tangent modulus and elastic material parameters, realizing the decoupling of tensile and compressive elastic-plastic deformation, and preventing damage to the electromagnetic protection material and non-physical healing of cracks.

[0143] Example 1

[0144] Based on the electromagnetic protection material failure and crack evolution calculation method proposed in the present invention, this embodiment considers Ti-6Al-4V material. In this embodiment, the model size is 10mm×4mm, the prefabricated crack width is 4mm, and the main material parameters are: density 4430kg / m 3 , elastic modulus 110GPa, Poisson's ratio 0.35, initial yield strength 1098MPa, hardening coefficient 1092MPa, rate hardening coefficient 0.014, hardening index 0.93, thermal softening index 1.1, reference temperature 298K, material melting point 1878K, critical fracture energy release rate 30kJ / m 2 , the fracture energy threshold is 15MPa.

[0145] According to the above process and materials, the simulation was completed and the type II fracture and failure mode of the electromagnetic protection material was obtained, such as Figure 2 shown.

[0146] Example 2

[0147] This example implements the plastic numerical process separately. Common aluminum metal is used as the target material, and a 1 / 4 model of a thick cylindrical wall is considered. The inner diameter of the cylinder is 1.0 mm, and the outer diameter is 1.3 mm. The implementation results are as follows: Figure 3 and Figure 4 shown.

[0148] Therefore, the present invention adopts the above-mentioned calculation method for failure and crack evolution of electromagnetic protection materials, which provides a solid mathematical explanation for the damage, failure and crack evolution of protection materials under the coupling of electromagnetic, force and heat, and on this basis establishes an efficient and accurate numerical method and simulation process to achieve accurate prediction of the mechanical and thermal response of electromagnetic protection materials.

[0149] 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 method for calculating failure and crack evolution of electromagnetic protection materials, characterized in that: The following steps are involved: Step S1, considering the coupled mathematical model of electromagnetic field, temperature field, fracture phase field and force field, establishing a free energy form for describing the mechanical, thermal and fracture response of electromagnetic protection materials; Step S2: Based on the Coleman-Noll process, the special physical and mechanical properties and usage scenarios of electromagnetic protection materials are taken into consideration, and the constitutive theory of electromagnetic, force, heat and fracture phase field coupling derived from the free energy form of step S1 is analyzed and derived; Step S3, combining the constitutive theory of step S2 with the momentum conservation equation, the heat conduction equation, the fracture phase field evolution equation and the Maxwell equations, and obtaining a solvable weak form of the overall partial differential equations based on the variational method; Step S4, analyze and judge the weak form given in step S3, develop numerical solution methods and templates, and realize efficient calculation and simulation of the mechanical, thermal, and fracture phase field coupling of the protective material under electromagnetic action, thereby realizing the prediction of mechanical and thermal failure and crack evolution process of the electromagnetic protective material.

2. The method for calculating failure and crack evolution of electromagnetic protection materials according to claim 1, characterized in that: In step S1, the electromagnetic process, temperature conduction, fracture phase field evolution and force-displacement process in the real physical process of failure and fracture of electromagnetic protection materials are all taken into consideration and derivation to establish the free energy form, and the Helmholtz free energy form describing the evolution of the electromagnetic protection material system is as follows: ψ=ψ(B e ,e,b,d,▽d,T,ζ)=ψ s (B e ,e,b,d,g)+ψ e (e,b)+ψ c (d,▽d)+ψ t (T); Among them, B e is the elastic part of the left Cauchy-Green tensor; e and b are the electric field and magnetic field vectors respectively; d and ▽d are the order parameters and their spatial gradients that characterize the fracture phase field state; T is the thermodynamic temperature; ζ is the dissipative internal variable determined by the free energy form and conservation law of the current electromagnetic protection material; ψ s , ψ e , ψ c , ψ t They are the Helmholtz free energy forms of displacement field / stress field, electromagnetic field, fracture phase field, and temperature field; B e =F e ·F eT ; Where F is the deformation gradient; F e is the elastic deformation part in its multiplication decomposition; F eT F e The transpose of F=F e ·F p ·F t ; Among them, F p 、F t They are the plastic deformation part and the thermal deformation part of the deformation gradient respectively.

3. The method for calculating failure and crack evolution of electromagnetic protection materials according to claim 1, characterized in that: In step S2, based on the Coleman-Noll process, the special physical and mechanical properties and usage scenarios of electromagnetic protection materials are taken into consideration, and the constitutive theory of electromagnetic, force, heat, and fracture phase field coupling derived from the free energy form of step S1 is analyzed and derived. The specific process is as follows: Step S21, considering the energy conservation form of electromagnetic, force and thermal coupling, as shown below: Where ε is the total energy per unit mass; ρ is the mass density; σ is the Cauchy stress; is the velocity; q is the heat flux; f b is the physical strength in the current configuration; is the rate of change of total energy density; r is the heat source term; It is defined as electromotive force, where e and b are electric and magnetic field vectors respectively; Defined as magnetic field intensity; h and d are magnetic field and electric displacement field respectively; the outer product of electromotive force and magnetic field intensity It is a representation of the density of electromagnetic energy flux; Step S22, consider the phase field evolution equation, as shown below: Where d is the fracture phase field order parameter; ρ d is the density that characterizes the inertial effect of the fracture phase field; η d is the viscosity that characterizes the viscous effect of the fracture phase field; ▽0 is the gradient operator defined in the reference configuration; ρ0 is the density defined in the reference configuration; is the exogenous micro-force source term for controlling the phase field; Step S23: Based on the Coleman-Noll process, the constitutive theory and entropy inequality are derived as follows: n = -ψ T +a t trt / r; Where η is entropy; ψ T is the partial derivative of free energy with respect to temperature T; α t is the thermal expansion coefficient of the material; tr represents the trace of the second-order tensor; τ is the Kirchhoff stress; Among them, g is the generalized momentum density; ∈0 is the permittivity; p=-ρψ e ,m=-ρψ b ; Where p is the polarization field; ψ e is the partial derivative of free energy with respect to the electric field e; m is the magnetization field, ψ b is the partial derivative of free energy with respect to magnetic field b; Where μ0 is the magnetic permeability; I is the second-order unit tensor; in, is the elastic part B of the left Cauchy-Green tensor of the free energy e The partial derivative of in, Characterize the energy dissipation caused by the phase field; is the phase field evolution rate; in, is the plastic deformation rate; ψ ξ is the partial derivative of free energy with respect to the micro-force ξ; is the rate of change of micro-force; is the conduction density; q▽T is the gradient of temperature T.

4. The method for calculating failure and crack evolution of electromagnetic protection materials according to claim 1, characterized in that: In step S3, the constitutive theory of step S2 is combined with the momentum conservation equation, the heat conduction equation, the fracture phase field evolution equation and the Maxwell equations, and based on the variational method, a solvable weak form of the overall partial differential equations is obtained. The specific process is as follows: Step S31, consider the electromagnetic field equation, as shown below: Where, j is the current density; q is the charge density; Step S32: introducing the generalized electromagnetic-force coupling momentum density into the conservation law. In the electromagnetic protection material, the momentum conservation form is as follows: Where ρ is the mass density; g is the generalized momentum density under electromagnetic-force coupling; σ is the Cauchy stress; f b is the physical strength in the current configuration; The form of conservation of angular momentum is as follows: Where x is the position vector of the current configuration; σ is still the Cauchy stress; The form of mass conservation is as follows: Step S33, consider the phase field evolution equation, as shown below: in, is the historical variable that characterizes the crack driving force; W e+ is the positive definition of elastic strain energy; W p is the plastic work; W0 is the energy threshold for crack initiation; χ is the thermal-plastic work conversion coefficient; G c is the critical energy release rate of fracture; l c is the crack characteristic width of the fracture phase field method; Step S34: Combining the variational method, the following weak form group is obtained: Among them, Ω represents the computational space; δ u is the variation of displacement; t is the surface force on the calculated boundary Γ; Where c is the specific heat; δ T is the variation of temperature; k is the thermal conductivity related to the fracture phase field; Among them, η d Characterizes the fracture phase field viscosity, δ d is the variation of the fracture phase field; Among them, δ A is the variation of the magnetic potential field; A is the magnetic potential field; it is defined as b=▽×A; ▽A is the divergence of the magnetic potential field.

5. The method for calculating failure and crack evolution of electromagnetic protection materials according to claim 1, characterized in that: In step S4, the weak form given in step S3 is analyzed and judged, and a numerical solution method and template are developed. The specific process is as follows: Step S41: Considering the plastic constitutive theory and numerical calculation method, a plastic yield criterion is given as follows: Where, s = dev (σ) is the deviatoric stress; is the current rate-dependent, temperature-dependent and damage-dependent yield strength of the material; Step S42: In each incremental step, the equivalent plastic strain increment is completed according to the conventional process. and plastic strain increment dε p After the calculation, the total elastic strain of the current calculation step is obtained as follows: ε n+1 s n +d-d-d p 100. Step S43, decomposing the strain according to the decomposition principle, calculating the stress and elastic strain energy according to the current tangent modulus and elastic material parameters, realizing the decoupling of tensile and compressive elastic-plastic deformation, and preventing damage to the electromagnetic protection material and non-physical healing of cracks.

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