Electromagnetic shielding material failure and crack evolution calculation method

Abstract

The application belongs to the technical field of electromagnetic protection, and discloses a kind of electromagnetic protection material failure and crack evolution calculation method, comprising the following steps: establishing the free energy form for describing the force-thermal, fracture response of electromagnetic protection material;Based on Coleman-Noll process, analyze and deduce the constitutive theory of electromagnetic, force, thermal, fracture phase field coupling derived from free energy form;Constitute theory is combined with momentum conservation equation, heat conduction equation, fracture phase field evolution equation and Maxwell equation group, and the solvable weak form of overall partial differential equation group is obtained based on variational method;Weak form is analyzed and judged, and numerical solution method and template are developed.The electromagnetic protection material failure and crack evolution calculation method disclosed by the application is used to improve the design level of thermal protection material, significantly shorten the new material development cycle and reduce the cost, promote the transformation and application of new thermal protection material in the next generation of hypersonic aircraft thermal protection system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of electromagnetic protection, and in particular to a method for calculating failure and crack evolution of electromagnetic protection materials. BACKGROUND

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

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

[0004] The design and research and development of electromagnetic protection materials have long relied on experimental verification and semi-empirical models, and optimization is carried out through a combination of experiments and numerical simulations. However, this "trial and error method" and semi-empirical model method lacks overall consideration of multi-functional synergistic performance in the material design process, resulting in low design efficiency, long cycle, and high research and development cost. In addition, the existing design method usually ignores the comprehensive performance requirements of the material in extreme electromagnetic environments, such as the unified optimization of protection, thermal management and lightweight, which limits the wide application of electromagnetic protection materials.

[0005] Therefore, it is urgent to propose a mathematical model and simulation method of electromagnetic protection materials considering electromagnetic, force and thermal coupling to realize all-around optimization of electromagnetic protection materials. SUMMARY

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

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

[0008] Step S1, a coupling mathematical model considering electromagnetic field, temperature field, fracture phase field and force field is considered, and a free energy form for describing the force-thermal and fracture response of electromagnetic protection materials is established;

[0009] Step S2, based on the Coleman-Noll process, the special physical, mechanical properties of electromagnetic protection materials and the use scenarios are taken into account, 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 deduced;

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

[0011] Step S4, the weak form given in step S3 is analyzed and judged, and the numerical solution method and template are developed, and the efficient calculation and simulation of the force, heat, and fracture phase field coupling of the protection material under electromagnetic action are realized, so as to realize the prediction of the force-thermal failure and crack evolution process of the electromagnetic protection 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 electromagnetic protection material failure and fracture are all taken into account in the establishment of the free energy form and the deduction, and the Helmholtz free energy form describing the evolution mode of the electromagnetic protection material system is as follows:

[0013]

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

[0015] B e =F e ·F eT ;

[0016] Wherein, F is the deformation gradient; F e is the elastic deformation part in the multiplicative decomposition of F eT ; F e is the transpose of F e ;

[0017] F=F e ·F p ·F t ;

[0018] Wherein, F p , Ft respectively are the plastic deformation part and the thermal deformation part of the deformation gradient.

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

[0020] Step S21, considering the energy conservation form of electromagnetic, force, and heat coupling, as follows:

[0021]

[0022] Wherein, 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 density; f b is the body force under the current configuration; is the rate of change of total energy density; r is the heat source term; is defined as the electric force, e and b are the electric field and magnetic field vectors respectively; is defined as the magnetic field intensity; h and d are the magnetic field and electric displacement field respectively; the outer product of the electric force and the magnetic field intensity is the representation of the electromagnetic energy flow density;

[0023] Step S22, considering the phase field evolution equation, as follows:

[0024]

[0025] Wherein, d is the fracture phase field order parameter; ρ d is the density representing the inertial effect of the fracture phase field; η d is the viscosity representing 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 the entropy inequality are deduced, as follows:

[0027] η = -ψ T + α t trτ / ρ;

[0028] Wherein, η is the entropy; ψ T is the partial derivative of the 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] where 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 the free energy with respect to the electric field e; m is the magnetization field, ψ b is the partial derivative of the free energy with respect to the magnetic field b;

[0033]

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

[0035]

[0036] where, is the partial derivative of the free energy with respect to the elastic part B e of the left Cauchy-Green tensor;

[0037]

[0038] where, characterizes the energy dissipation caused by the phase field; is the evolution rate of the phase field;

[0039]

[0040] where, (F p ) -1 is the plastic deformation rate; ψ ξ is the partial derivative of the free energy with respect to the microforce ξ; is the rate of change of the microforce; is the conduction 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 evolution equation of the fracture phase field, and the Maxwell equation set to obtain a solvable weak form of the overall partial differential equation set based on the variational method, and the specific process is as follows:

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

[0043]

[0044] where j is the current density; q is the charge density;

[0045] Step S32, introduce the generalized electromagnetic-force coupled momentum density to the conservation law, in the electromagnetic protective material, the momentum conservation form is as follows:

[0046]

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

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

[0049]

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

[0051] The mass conservation form is as follows:

[0052]

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

[0054]

[0055] Where, is a historical variable representing 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 of 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, combined with the variational method, the following weak form group is obtained:

[0057]

[0058] Where, Ω represents the calculation space; δ u is the variation of displacement; is the surface force on the calculation 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] Where, η dcharacterizing the fracture phase field viscosity, δ d is the variation of the fracture phase field;

[0063]

[0064] where δ A is the variation of the 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 to develop a numerical solution method and template, and the specific process is as follows:

[0066] Step S41, considering the plastic constitutive theory and numerical calculation method, the 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 increment step, after the calculation of the equivalent plastic strain increment and the plastic strain increment dε p , 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, the strain is decomposed by the decomposition principle, and the stress and elastic strain energy are calculated by the current tangent modulus and elastic material parameters, realizing the decoupling of tension-compression elastic-plastic deformation, preventing the non-physical healing of electromagnetic protective material damage and crack.

[0072] Therefore, the electromagnetic protective material failure and crack evolution calculation method provided in the application provides a solid mathematical explanation for the damage, failure and crack evolution of the protective material under the coupling action of electromagnetism, force and heat, and on this basis, an efficient and accurate numerical method and simulation process are established to realize accurate prediction of the force and heat response of the electromagnetic protective material.

[0073] The technical solutions of the application will be further described in detail below with reference to the drawings and examples. BRIEF DESCRIPTION OF DRAWINGS

[0074] Figure 1 is the step flow chart of the electromagnetic protective material failure and crack evolution calculation method of the application;

[0075] Figure 2 This is a schematic diagram of the type II fracture failure mode of the Ti–6Al–4V material in Embodiment 1 of the present invention;

[0076] Figure 3 This is an equivalent plastic strain distribution cloud map of the aluminum metal plastic thick cylindrical tube in Embodiment 2 of the present invention;

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

[0078] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

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

[0080] Step S1: Consider the coupled mathematical model of electromagnetic field, temperature field, fracture phase field and force field, and establish the free energy form to describe the mechanical and thermal and fracture response of electromagnetic protection materials.

[0081] The electromagnetic processes, temperature conduction, fracture phase field evolution, and force-displacement processes involved in the actual physical processes of electromagnetic shielding material failure and fracture are all incorporated into the consideration and derivation of the free energy form.

[0082] The Helmholtz free energy form describing the evolution of electromagnetic shielding material systems is shown below:

[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 The elastic part of the left Cauchy-Green tensor; e and b are the electric and magnetic field vectors, respectively; d, The order parameter and its spatial gradient 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 shielding material; ψ s , ψ e , ψ c , ψ t These are the Helmholtz free energy forms for the displacement / 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 multiplicative decomposition, F eT is the transpose of F e .

[0087] F = F e · F p · F t ;

[0088] where F p , F t are the plastic and thermal deformation parts of the deformation gradient, respectively.

[0089] Step S2, based on the Coleman-Noll procedure, the special physical, mechanical properties of the electromagnetic protection material and the use scene 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 deduced.

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

[0091]

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

[0093] Step S22, considering the phase field evolution equation, as follows:

[0094]

[0095] where d is the fracture phase field order parameter; p d is the density representing the inertial effect of the fracture phase field; η d is the viscosity representing the viscous effect of the fracture phase field; is the gradient operator defined in the reference configuration; p0 is the density defined in the reference configuration; is the exogenous micro-force source term controlling the phase field.

[0096] Step S23, based on the Coleman-Noll procedure, derive the constitutive theory and entropy inequality as follows:

[0097] η = -ψ T + α t trτ / ρ;

[0098] where η is the entropy; ψ T is the partial derivative of the 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, ∈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 the free energy with respect to the electric field e, m is the magnetization field, ψ b is the partial derivative of the free energy with respect to the magnetic field b;

[0103]

[0104] where μ0 is the magnetic permeability, I is the second order identity tensor;

[0105]

[0106] where, is the partial derivative of the free energy with respect to the elastic part B e of the left Cauchy-Green tensor;

[0107]

[0108] where, characterizes the energy dissipation caused by the phase field, is the evolution rate of the phase field;

[0109]

[0110] where, is the plastic deformation rate, ψ ξ is the partial derivative of the free energy with respect to the microforce ξ, is the rate of change of the microforce, is the flux density; is the gradient of temperature T.

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

[0112] Step S31, the electromagnetic field equation is considered, as follows:

[0113]

[0114] Wherein, j is the current density; q is the charge density.

[0115] In view of the basic properties and common working state of electromagnetic protection materials, focus is put on the last term of the above equation set, i.e. the magnetic field Gauss law reflecting the magnetic field passivity. The formula shows that the magnetic field must be the curl of a certain order tensor field A, i.e. According to the analysis convention, the A field is called magnetic potential.

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

[0117]

[0118] Wherein, ρ is the mass density, g is the generalized momentum density under the electromagnetic-force coupling, σ is the Cauchy stress, f b is the body force under the current configuration.

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

[0120]

[0121] Wherein, x is the position vector under the current configuration, and σ is still the Cauchy stress. Unlike the traditional continuous medium theory, due to the electromagnetic coupling and the specific form of the constitutive relation, the Cauchy stress tensor no longer has symmetry.

[0122] Wherein, the mass conservation form is as follows:

[0123]

[0124] Step S33, the phase field evolution equation is considered, as follows:

[0125]

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

[0127] Step S34: Combining the variational method, the following set of weak forms is obtained:

[0128]

[0129] Where Ω represents the computational space, δ u For the variation of displacement, To calculate the surface forces on the boundary Γ;

[0130]

[0131] Where c is the specific heat, δ T For temperature variation, k is the thermal conductivity related to the fracture phase field;

[0132]

[0133] Where, η d Characterizing the "viscosity" of the fracture phase field, δ d The variation of the fracture phase field;

[0134]

[0135] Where, δ A Let A be the variation of the magnetic potential field, defined as follows: Obviously, Let be the divergence of the magnetic potential field.

[0136] Step S4: Analyze and assess 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 the force, heat, and fracture phase field coupling of protective materials under electromagnetic action, and thus realize accurate prediction of the force and heat failure and crack evolution process of electromagnetic protective materials.

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

[0138]

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

[0140] Step S42: In each incremental step, complete the equivalent plastic strain increment 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] In step S43, the strain is decomposed by the decomposition principle, and the stress and elastic strain energy are calculated by the current tangent modulus and elastic material parameters, so that the decoupling of tensile and compressive elastic-plastic deformation is realized, and the non-physical healing of damage and cracks of the electromagnetic protection material is prevented.

[0143] Embodiment 1

[0144] Based on the electromagnetic protection material failure and crack evolution calculation method proposed in the application, the Ti-6Al-4V material is considered in this embodiment, and in this embodiment, the model size is 10mm*4mm, the pre-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, and fracture critical energy release rate 30kJ / m 2 , and the fracture energy threshold is 15MPa.

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

[0146] Embodiment 2

[0147] In this embodiment, the plastic numerical process is implemented alone. 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 cylindrical cylinder is 1.0mm, and the outer diameter is 1.3mm, and the implementation results are shown in Figure 3 and Figure 4 .

[0148] Therefore, the electromagnetic protection material failure and crack evolution calculation method is adopted, which provides a solid mathematical explanation for the damage, failure and crack evolution of the protection material under the coupling action of electromagnetic force and heat, and on this basis, a high-efficiency and accurate numerical method and simulation process are established, and the accurate prediction of the electromagnetic protection material force and heat response is realized.

[0149] It should be pointed out finally that the above examples are only used to illustrate the technical solutions of the present application but not to limit it, and although the present application has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solutions of the present application can still be modified or replaced equivalently, and these modifications or equivalent replacements should not make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present application.

Claims

1. A method for calculating the failure and crack evolution of electromagnetic protection materials, characterized in that, Includes the following steps: Step S1: Consider the coupled mathematical model of electromagnetic field, temperature field, fracture phase field and force field, and establish the free energy form to describe the mechanical and thermal and fracture response of electromagnetic shielding materials; Step S2: Based on the Coleman-Noll process, the special physical and mechanical properties and application scenarios of electromagnetic shielding materials are taken into consideration, and the constitutive theory of electromagnetic, mechanical, thermal and fracture phase-field coupling derived from the free energy form in step S1 is analyzed and derived. Step S3: Combine the constitutive theory from step S2 with the momentum conservation equation, heat conduction equation, fracture phase field evolution equation and Maxwell's equations, and derive the solvable weak form of the global partial differential equations based on the variational method. Step S4: Analyze and assess the weak form given in Step S3, develop numerical solution methods and templates, and realize efficient calculation and simulation of the force, heat, and fracture phase field coupling of the protective material under electromagnetic action, thereby enabling the prediction of the force and heat failure and crack evolution process of electromagnetic protective materials.

2. The method for calculating the failure and crack evolution of electromagnetic protection materials according to claim 1, characterized in that, In step S1, the electromagnetic processes, temperature conduction, fracture phase field evolution, and force-displacement processes involved in the actual physical processes of electromagnetic shielding material failure and fracture are all incorporated into the consideration and derivation of the free energy form. The Helmholtz free energy form describing the evolution of the electromagnetic shielding material system is shown below: ； in, The elastic part of the left Cauchy-Green tensor; , These are the electric field and magnetic field vectors, respectively. , The order parameters and their spatial gradients characterize the state of the fracture phase field. Thermodynamic temperature; This refers to the dissipative internal variable determined by the free energy form and conservation law of current electromagnetic protection materials. , , , These are the Helmholtz free energy forms for displacement / stress field, electromagnetic field, fracture phase field, and temperature field, respectively. ； in, For deformation gradient; This is the elastic deformation part in its multiplicative decomposition; for Transpose of; ； in, , These are the plastic deformation portion and the thermal deformation portion of the deformation gradient, respectively.

3. The method for calculating the 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 application scenarios of electromagnetic shielding materials are taken into consideration. The constitutive theory of electromagnetic, mechanical, thermal, and fracture phase-field coupling derived from the free energy form in step S1 is analyzed and derived. The specific process is as follows: Step S21: Consider the energy conservation form of electromagnetic, mechanical, and thermal coupling effects, as shown below: ； in, It is the total energy per unit mass; It is mass density; Cauchy stress; For speed; Heat flux density; For the current configuration of the body force; The rate of change of total energy density; For heat source items; Defined as electric power, , These are the vectors of electric field strength and magnetic field induction intensity, respectively; Defined as magnetic field strength, , These are the magnetic field and electric displacement field, respectively; and the outer product of the electrodynamic force and magnetic field strength. It is a characterization of electromagnetic energy flux density; Step S22: Consider the phase field evolution equation, as shown below: ； in, For fracture phase field sequence parameters; This represents the phase field evolution rate. The density used to characterize the inertial effect of the fracture phase field; Viscosity used to characterize the viscous effect of the fracture phase field; For the gradient operator defined in the reference configuration; Density defined in the reference configuration; To control the exogenous micro-force source term of the phase field; Step S23: Based on the Coleman-Noll process, derive the constitutive theory and entropy inequality, as shown below: ； in, Entropy; For free energy with respect to temperature The partial derivatives; The coefficient of thermal expansion of the material; This indicates taking the trace of a second-order tensor; Kirchhoff stress; ； in, Generalized momentum density; Permeability; ； in, For polarization field; Let be the partial derivative of the free energy with respect to the electric field e; For magnetization field, For free energy to magnetic field The partial derivatives; ； in, Permeability; It is a second-order unit tensor; ； in, The elastic part of the free energy with respect to the left Cauchy-Green tensor The partial derivatives; ； in, Characterizes the energy dissipation caused by the phase field; This represents the phase field evolution rate. ； in, This refers to the rate of plastic deformation. For free energy to micro force The partial derivatives; The rate of change of the infinitesimal force; For conductivity density; For temperature The gradient.

4. The method for calculating the failure and crack evolution of electromagnetic protection materials according to claim 1, characterized in that, In step S3, the constitutive theory from step S2 is combined with the momentum conservation equation, the heat conduction equation, the fracture phase field evolution equation, and Maxwell's equations. Based on the variational method, a solvable weak form of the global partial differential equations is obtained. The specific process is as follows: Step S31: Consider the electromagnetic field equations, as shown below: ； in, Current density; Charge density; Step S32: Introduce the generalized electromagnetic-force coupling momentum density into the conservation law. In electromagnetic shielding materials, the momentum conservation form is as follows: ； in, It is mass density; That is, the generalized momentum density under electromagnetic-force coupling; Cauchy stress; For the current configuration of the body force; The form of conservation of angular momentum is as follows: ； in, Still Cauchy stress; The form of mass conservation is as follows: ； Step S33: Consider the phase field evolution equation, as shown below: ； ； in, Historical variables characterizing crack driving forces; This is the positive definition of elastic strain energy; Plastic work; The energy threshold for crack initiation; The thermoplastic work conversion coefficient; The critical energy release rate at fracture; The characteristic width of the crack is given by the fracture phase field method; Step S34: Combining the variational method, the following set of weak forms is obtained: ； in, Representational computational space; For the variation of displacement; To calculate the boundary Surface forces on; ； in, Specific heat; For the variation of temperature; Thermal conductivity related to the fracture phase field; ； in, Characterizing the viscosity of the fracture phase field, The variation of the fracture phase field; ； in, For the variation of the magnetic potential field; For magnetic potential field; defined as ; Let be the divergence of the magnetic potential field.

5. The method for calculating the 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 evaluated, 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 methods, the plastic yield criterion is given as follows: ； in, It is a deviatoric stress; The yield strength is a material current rate-dependent, temperature-dependent, and damage-dependent property. Step S42: In each incremental step, complete the equivalent plastic strain increment according to the conventional process. and plastic strain increment After calculation, the total elastic strain of the current calculation step is obtained, as shown below: ； Step S43: Decompose the strain according to the decomposition principle. Calculate the stress and elastic strain energy from the current tangent modulus and elastic material parameters to achieve decoupling of tensile, compressive, elastic-plastic deformation and prevent non-physical healing of electromagnetic shielding material damage and cracks.

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