Method, device and medium for predicting high-frequency force-thermal-magnetic-electric coupling dynamic response of magnetic shape memory alloy

Abstract

The application discloses a kind of magnetic shape memory alloy high-frequency force-thermal-magnetic-electric coupling dynamic response prediction method, equipment and medium, method includes: the first Hamiltonian action functional of magnetic shape memory alloy sample without considering thermal effect is established;According to the first Hamiltonian action functional, the first control equation group of magnetic shape memory alloy sample is derived;The second Hamiltonian action functional of magnetic shape memory alloy sample considering thermal effect is established, and the heat conduction equation is obtained according to the second Hamiltonian action functional;According to control equation group and heat conduction equation, the second control equation group of model is constructed, and the prediction result is obtained by solving the second control equation group.The scheme proposed in the present application considers the influence of temperature, as well as the influence of the excitation magnetic field generated under high-frequency magnetic field loading conditions, fully simulates the force-thermal-magnetic-electric coupling dynamic response of magnetic shape memory alloy under high-frequency force magnetic coupling loading conditions, and has important application prospect and value.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of prediction of force-thermal-magnetic-electric coupling dynamic response of magnetic shape memory alloy material under high-frequency force magnetic coupling loading and design and development of magnetic intelligent devices, and particularly relates to a prediction method, device and medium for high-frequency force-thermal-magnetic-electric coupling dynamic response of a magnetic shape memory alloy. BACKGROUND

[0002] Magnetic shape memory alloys (MSMAs) have attracted extensive attention due to their outstanding material properties. Under the action of magnetic field and external force loading, MSMA can exhibit reversible deformation, with a strain range of 6%-10%, which is much higher than that of ordinary magnetostrictive materials. Compared with traditional thermal shape memory materials, the response frequency of MSMA can reach 10 3 Hz, which makes them potential materials for manufacturing new high-frequency driving devices, such as actuators, energy harvesters, sensors, etc.

[0003] In the past few decades, many MSMAs (such as Ni-Mn-Ga, Fe-Pd, Fe-Pt, Co-Ni-Al, Co-Ni-Ga) have been reported. Among them, single-crystal Ni-Mn-Ga alloy is one of the most common materials. For single-crystal Ni-Mn-Ga alloy, the reason for having significant reversible strain is the reorientation of martensite variants with different lattice orientations. In order to fully understand the special properties of MSMA, researchers have carried out systematic experimental work and proposed different theoretical models. Early work in this field mainly focused on the quasi-static or low-frequency response of MSMA. However, in order to meet the requirements of sensing or driving in practical applications, the high-frequency dynamic response of MSMA is also worth studying.

[0004] In terms of theoretical modeling, LaMaster et al. proposed a model to describe the response of MSMA samples under magnetic-force loading. Haldar and Lagoudas developed a multi-field coupling theoretical model and proposed an algorithm that can effectively solve the system of control equations. On this basis, some important physical quantities such as variant volume fraction, eddy current density and Joule heat can be predicted. In order to better understand the internal coupling mechanism, Chen and He proposed a more comprehensive coupled thermomagnetic mechanical model. This model takes into account the effects of magnetic field and temperature on the phase transition and martensite reorientation of MSMA samples under high-frequency magnetic loading. Based on this, they also conducted numerical analysis and predicted the evolution curves of temperature, strain and volume fraction of austenite and martensite phases.

[0005] In the field of application research and development, Kohl et al. developed MSMA thin film brake for two-dimensional optical scanning; Riccardi et al. designed a precision displacement sensor based on MSMA feedback control; Lu Jun et al. developed a MSMA vibration sensor that can convert mechanical energy into electrical energy; Zhang Qingxin et al. developed a new type of vibration energy harvesting system using MSMA and conducted performance test; Shi Hu et al. designed a high-speed switch hydraulic valve driven by MSMA; Tao Fuquan et al. introduced the basic structure and working principle of a MSMA active shock absorber and carried out simulation analysis on its performance.

[0006] Although there are a large number of works in this field by predecessors, the current research on the dynamic response of MSMA is still in its infancy. The existing model rarely considers the orientation and movement of twin boundary in MSMA, which is an important feature in the process of variant reorientation. In addition, the influence of electromagnetic field distribution on MSMA sample is often ignored. SUMMARY

[0007] To at least partially solve one of the technical problems existing in the prior art, the purpose of the present application is to provide a method, device and medium for predicting the high-frequency force-thermal-magnetic-electric coupling dynamic response of magnetic shape memory alloy.

[0008] The first technical solution adopted by the present application is:

[0009] A method for predicting the high-frequency force-thermal-magnetic-electric coupling dynamic response of magnetic shape memory alloy, comprising the following steps:

[0010] establishing a first Hamiltonian action functional of the magnetic shape memory alloy sample without considering thermal effect;

[0011] According to the first Hamiltonian action functional, the first control equation set of the magnetic shape memory alloy sample is derived by variational method;

[0012] establishing a second Hamiltonian action functional of the magnetic shape memory alloy sample considering thermal effect, and obtaining a heat conduction equation according to the second Hamiltonian action functional;

[0013] According to the first control equation set and the heat conduction equation, the second control equation set of the model is constructed, and the force-thermal-magnetic-electric dynamic response of the MSMA sample under high-frequency force magnetic coupling loading condition is predicted by solving the second control equation set.

[0014] Further, the first Hamiltonian action functional of the magnetic shape memory alloy sample without considering thermal effect comprises:

[0015] Assuming that the object of study is a single crystal MSMA sample, at the initial time t0, the sample occupies the reference configuration Ω r, whose surface boundary is denoted by ; the free space around the sample region r is denoted by , whose outer boundary is at infinity; in r , the position vector of a material point is denoted by X;

[0016] In the current model, only the reorientation between two variants, i.e. variant 1 and variant 2, is considered; at time t ∈ [t0, t1], variant 1 and variant 2 occupy in the sample and have and and ; the twin boundary is denoted by ; there can be multiple twin boundaries in the sample, thus and are composed of several separate regions; at the outer boundary ∞ of the sample, x = X,

[0017] At time t ∈ [t0, t1], an electromagnetic field is applied in the whole space , which has vector potential A a and scalar potential a ; a mechanical load (traction) t a is applied on the surface of the sample ; the electromagnetic field and the mechanical load induce the deformation of the MSMA sample from the reference configuration r to the current configuration t , whose surface boundary is denoted by ; accordingly, the surrounding region becomes ; the position vector of a material point in t is denoted by x(X, t); the total deformation gradient tensor and velocity v are obtained by taking the derivative of x(X, t);

[0018] The potential functions A a and a of the applied electromagnetic field are Eulerian vector fields, which are sufficiently smooth in the space-time region ; the magnetic induction B a , magnetic field H a , electric field E a and electric displacement D a are calculated;

[0019] The applied electromagnetic field can induce the effective magnetization of the MSMA sample; the Eulerian form of the magnetization vector field (per unit mass) is denoted by M(x, t);

[0020] In the sample, electromagnetic field is also excited, the vector potential and scalar potential of the excited electromagnetic field are denoted as A s and φ s , assuming that A s (x,t) and φ s are continuous in the first order and the second order derivatives of the potentials in the space-time region , based on the potential functions, the magnetic induction intensity B s , the magnetic field H s , the electric field E s and the electric displacement D s are calculated;

[0021] When an external magnetic field is applied, the movement of magnetic domain wall and the rotation of local magnetization vector of the magnetic shape memory alloy occur, in order to capture the experimental characteristics, the following constitutive form of the effective magnetization vector M i in the variant region :

[0022]

[0023] In the formula, α i is the volume fraction of two magnetic domains, is the unit vector along the local magnetization vector; the conduction current J c will generate Joule heat and cause significant temperature change of the MSMA sample;

[0024] Finally, the energy density functional of the magnetic shape memory alloy sample is obtained as wherein the subscript r represents under the reference (initial) configuration.

[0025] Further, the calculation formula of the total deformation gradient tensor and the velocity v is as follows:

[0026]

[0027] Wherein, the subscript “,t” represents the time derivative of the substance (i.e. the time derivative at fixed X);

[0028] The calculation formula of the magnetic induction intensity B a , the magnetic field H a , the electric field E a and the electric displacement D a is as follows:

[0029] B a (x,t)=rot(A a (x,t))

[0030]

[0031] D a (x,t) = ∈0E a (x,t)

[0032] where μ0 represents the vacuum permeability and ∈0 is the vacuum permittivity;

[0033] magnetic induction B s , magnetic field H s , electric field E s and electric displacement D s are calculated as follows:

[0034] B s (x,t) = rot(A s (x,t))

[0035]

[0036]

[0037] D s (x,t) = ∈0E s (x,t)

[0038] where ρ is the material density of the sample in the current configuration.

[0039] Further, in order to simulate the elastic response of the MSMA sample, the following elastic strain-energy density functions of the two martensitic variants are adopted:

[0040]

[0041] where, is the Lagrangian strain tensor, is the total deformation gradient tensor, is the inverse of the variant reorientation strain tensor, is the second order identity tensor; is the second order elastic modulus.

[0042] Further, the first set of control equations of the magnetic shape memory alloy sample is derived from the first Hamiltonian action functional by the variational method, comprising:

[0043] the variational derivative of is the control equation group in the form of Gauss's law of the electric field in Maxwell's equations;

[0044] the variational derivative of is the control equation group of Ampere's circuit law in Maxwell's equations;

[0045] the variational derivative of x is the motion control equation group of the magnetic-force coupling;

[0046] For α i and The evolution equations of the internal variables are obtained by taking the variational equations;

[0047] right The variational equation for Ohm's law is obtained.

[0048] The migration criterion of the twin interface is obtained by variational analysis of Π(t).

[0049] Furthermore, the second Hamiltonian action functional The expression is:

[0050]

[0051] In the formula, c is the specific heat capacity, k is the thermal conductivity, and R is the volumetric heat source within the MSMA sample; ρ r Where is the density of the sample; T is the temperature field; dV is the square of the derivative of the temperature field with respect to time; Grad represents the gradient operator under the reference configuration; dV is the infinitesimal change in volume at a point within the sample; dS is the infinitesimal change in volume at a point on the sample surface; r is time; q r and q t The heat flux density is at the sample boundary and the twin interface within the sample; the parameter τ represents the thermal relaxation time of the material, i.e., the finite thermal interaction time between material particles.

[0052] Furthermore, the process of obtaining the heat conduction equation based on the second Hamiltonian action functional includes:

[0053] Find the variation with respect to T and then substitute it into R and q. r and q t Thus, the heat conduction equation and boundary conditions are obtained:

[0054]

[0055] In the formula, ΔT is the change in temperature; J -1 Represents the total deformation gradient The inverse of the determinant; N represents the conduction current density under the current configuration. r For the sample region Ω r Pointing to the surrounding area Ω′ r The unit normal vector; k1 is the heat exchange coefficient; N is the twin interface. The unit normal vector; D ± This is the critical value of the driving force required to activate twin interface movement during the forward and reverse variant reorientation process; It represents the difference in physical quantities on both sides of the twin interface from the negative direction (the direction in which the normal vector N is turned away) to the positive direction (the direction in which the normal vector N is turned towards).

[0056] Further, the second control equation set solving step comprises:

[0057] establishing a geometric model of the sample and external air;

[0058] selecting elastic and magnetic constitutive of the sample and external air model;

[0059] inputting boundary conditions and basic parameters of materials;

[0060] calculating deformation of the sample under high-frequency force-thermal-magnetic-electric coupling.

[0061] The second technical solution adopted by the present application is:

[0062] An electronic device, comprising a processor and a memory, the memory storing at least one instruction, at least one program, a code set or an instruction set, the at least one instruction, the at least one program, the code set or the instruction set being loaded and executed by the processor to implement the magnetic shape memory alloy high-frequency force-thermal-magnetic-electric coupling dynamic response prediction method as described above.

[0063] The third technical solution adopted by the present application is:

[0064] A computer readable storage medium, the storage medium storing at least one instruction, at least one program, a code set or an instruction set, the at least one instruction, the at least one program, the code set or the instruction set being loaded and executed by a processor to implement the magnetic shape memory alloy high-frequency force-thermal-magnetic-electric coupling dynamic response prediction method as described above.

[0065] The fourth technical solution adopted by the present application is:

[0066] A computer program product or computer program, the computer program product or computer program comprising computer instructions stored in a computer readable storage medium. The processor of the computer device can read the computer instructions from the computer readable storage medium, and the processor executes the computer instructions, so that the computer device executes the above method.

[0067] The present application has the following beneficial effects: the scheme proposed in the present application considers the influence of temperature and the influence of the excited magnetic field generated under the high-frequency magnetic field loading condition, can fully simulate the force-thermal-magnetic-electric coupling dynamic response of the magnetic shape memory alloy under the high-frequency force magnetic coupling loading condition, and has important application prospect and value in the field of magnetic shape memory alloy driver and the like. BRIEF DESCRIPTION OF DRAWINGS

[0068] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following introduces the drawings of the related technical solutions in the embodiments of the present application or the prior art. It should be understood that the drawings in the following introduction are only for facilitating the clear description of part of the embodiments of the technical solutions of the present application, and for those skilled in the art, other drawings can also be obtained without paying creative labor on the premise.

[0069] Figure 1 Boundary constraint and loading condition for the magnetic shape memory alloy sample.

[0070] Figure 2 Comsol simulation flowchart in numerical simulation.

[0071] Figure 3 Comparison chart of numerical simulation result and experimental result of the magnetic shape memory alloy sample at a convection velocity of 15 m / s.

[0072] Figure 4 Comparison chart of numerical simulation result and experimental result of the magnetic shape memory alloy sample at a convection velocity of 35 m / s.

[0073] Figure 5 Comparison chart of numerical simulation result and experimental result of the magnetic shape memory alloy sample at a convection velocity of 60 m / s.

[0074] Figure 6 Step flowchart of the prediction method of high-frequency force-thermal-magnetic-electric coupling dynamic response of the magnetic shape memory alloy provided in the embodiments of the present application. DETAILED DESCRIPTION

[0075] The embodiments of the present application are described in detail below, and examples of the embodiments are shown in the drawings, wherein the same or similar notations represent the same or similar elements or elements with the same or similar functions throughout. The embodiments described below with reference to the drawings are exemplary and are only used to explain the present application, and cannot be understood as a limitation of the present application. For the step numbers in the following embodiments, they are only set for facilitating the description and explanation, and the order between the steps is not limited in any way, and the execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0076] In the description of the present application, it should be understood that the orientation description, such as the orientation or position relationship indicated by up, down, front, back, left, right, etc. is based on the orientation or position relationship shown in the drawings, and is only for facilitating the description of the present application and simplifying the description, and cannot be understood as indicating or implying that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation of the present application.

[0077] In the description of the present application, the meaning of one or more is one or more, the meaning of multiple is two or more, greater than, less than, more than, etc. are understood as not including the number, above, below, within, etc. are understood as including the number. If the first, second is described, it is only for the purpose of distinguishing technical features, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of indicated technical features or the sequence of indicated technical features.

[0078] In the description of the present application, unless otherwise explicitly limited, the words such as setting, installing, connecting, etc. should be broadly understood, and those skilled in the art can reasonably determine the specific meaning of the above words in the present application in combination with the specific content of the technical scheme.

[0079] In view of the existing technical problems, the present application aims to provide a scheme for predicting the force-thermal-magnetic-electric coupling dynamic response of a magnetic shape memory alloy under high-frequency magnetic coupling loading and obtaining the average temperature evolution of the sample during the loading process. The scheme can predict the force-thermal-magnetic-electric coupling dynamic response of a magnetic shape memory alloy sample under high-frequency magnetic coupling loading, and therefore has important application prospects and value in the field of magnetic shape memory alloy drivers and other fields.

[0080] Embodiment 1

[0081] As Figure 6 shown, the present embodiment provides a method for predicting the high-frequency force-thermal-magnetic-electric coupling dynamic response of a magnetic shape memory alloy, comprising the following steps:

[0082] S1, establish the first Hamiltonian action functional of the magnetic shape memory alloy sample without considering the thermal effect.

[0083] First, the Hamiltonian action functional of the magnetic shape memory alloy sample without considering the thermal effect is established First, we study a single crystal MSMA sample. At the initial time t0, the sample occupies the reference configuration Ω r , whose surface boundary is represented by . In the vicinity of the sample region Ω r , the surrounding free space is represented by , and the outer boundary is at infinity. In Ω r , the position vector of a material point is denoted as X.

[0084] For simplicity, in the current model, we only consider the reorientation between two variants, i.e. variant 1 and variant 2. At time t∈[t0,t1], variant 1 and variant 2 occupy in the sample and and and between is a twin boundary, there can be multiple twin boundaries in the sample, thus and is composed of several separate regions. Furthermore, at the boundary at infinity Ω ∞ there is x = X, at time t ∈ [t0, t1] an electromagnetic field is applied in the whole space with vector potential A a and scalar potential φ a . In addition, a mechanical load (traction) t a is applied on the surface of the sample . The electromagnetic field and the mechanical load cause the deformation of the MSMA sample from the reference configuration Ω r to the current configuration Ω t , whose surface boundary is denoted by . Accordingly, the surrounding region becomes Ω t The position vector of a material point in Ω r is denoted by x(X, t). We assume that x(X, t) has piecewise continuous first and second derivatives in Ω a × [t0, t1]. According to the position vector field x(X, t), the deformation gradient tensor and the velocity v are respectively:

[0085]

[0086] Here, the subscript “,t” denotes the time derivative of the material (i.e., the time derivative at fixed X). The potential functions A a and φ a of the applied electromagnetic field are Euler vector fields, which are sufficiently smooth in the space-time region . Based on these potential functions, the magnetic induction B a , the magnetic field H a , the electric field E a and the electric displacement D -7 can be calculated:

[0087]

[0088] where μ0 represents the vacuum permeability (μ0= 4π × 10 2 N / A -12 and ∈0is the vacuum permittivity (∈0= 8.854 × 10F / m). The applied electromagnetic field can induce the effective magnetization of the MSMA sample (without considering the polarization of MSMA). The Euler form of the magnetization vector field (per unit mass) is denoted by M(x, t). In addition, some free charges and free currents can also be excited in the sample. These physical quantities will further induce the distribution of the excited electromagnetic field in the whole space. The Euler forms of the vector potential and scalar potential of these excited electromagnetic fields are denoted by A s and φ s , respectively. We also assume that A s (x, t) and φ s (x, t) are continuous in the first and second order derivatives in the space-time region Based on these potential functions, the magnetic induction B s , the magnetic field H s , the electric field E s and the electric displacement D s can be calculated as follows:

[0089]

[0090] ρ is the material density of the sample in the current configuration.

[0091] To simulate the elastic response of the MSMA sample, we adopt the following two elastic strain-energy densities of martensitic variants

[0092]

[0093] where L is the Lagrangian strain tensor, is the second-order elastic modulus. When the external magnetic field is applied, the motion of the magnetic domain wall and the rotation of the local magnetization vector of the MSMA will occur. In order to capture these experimental characteristics, the following constitutive form of the effective magnetization vector M i in the variant region

[0094]

[0095] where a i (i = 1, 2) is the volume fraction of the two magnetic domains, is the unit vector along the local magnetization vector. The conduction current J c will generate Joule heat and cause significant temperature changes in the MSMA sample. The value of the Joule heat P h is calculated by:

[0096]

[0097] where σ is the electrical conductivity of the material.

[0098] ​Energy density total functional of a magnetic shape memory alloy sample Here we ignore the thermal effect and obtain the energy density functional of a magnetic shape memory alloy sample where α i and, is an internal variable related to the effective magnetization.

[0099] S2, derive the first control equation set of the magnetic shape memory alloy sample by variational method according to the first Hamiltonian action functional.

[0100] Specifically, step S2 specifically includes the following steps:

[0101] S21, take the variation of to obtain the control equation set in the form of Gauss's law of electric field in Maxwell's equation.

[0102]

[0103] where subscript "r" represents being in the reference (initial) configuration, represents the electric displacement excited by the initial configuration sample; double brackets represent the size of the jump of the corresponding quantity at the interface between the sample and the air. N r is the unit normal vector on the surface, and N is the unit normal vector on the twin boundary. and is the free volume charge and the free surface charge density of the MSMA sample in the reference configuration Ω r .

[0104] S22, take the variation of to obtain the control equation set of Ampere's circuit law in Maxwell's equation.

[0105]

[0106] where is the magnetic field intensity excited by the initial configuration sample, V is the velocity of the sample in the initial configuration, and W n is the velocity of the twin boundary motion.

[0107] S23, take the variation of x to obtain the motion control equation set of magnetic-force coupling.

[0108]

[0109] where x ,tt is the acceleration of the sample motion, is the nominal stress tensor. and The expressions are as follows:

[0110]

[0111] S24, for a i and Variation of the internal variable to get the evolution equation.

[0112]

[0113] Where:

[0114]

[0115] Where:

[0116]

[0117] S25, for a Variation of the internal variable to get the Ohm's law equation.

[0118]

[0119] Where

[0120] S26, for a Variation of the internal variable to get the migration criterion of twin boundary.

[0121]

[0122] Where is the configuration force, which plays a driving role. We express the energy dissipation density (per unit volume) in the forward and reverse reorientation processes as and

[0123] S3, establish the second Hamiltonian action functional of the magnetic shape memory alloy sample considering thermal effects, and obtain the heat conduction equation according to the second Hamiltonian action functional.

[0124] Hamiltonian action functional of the magnetic shape memory alloy sample considering thermal effects

[0125]

[0126] Where c is the specific heat capacity (unit mass), k is the thermal conductivity coefficient, R is the volume heat source inside the MSMA sample; q r and q T are the heat flux density on the sample boundary and the twin boundary inside the sample; The parameter τ (τ≥0) represents the thermal relaxation time of the material, that is, the limited thermal interaction time between particles of the material.

[0127] After variation of T, R, q r and q tThe heat conduction equation and boundary conditions are as follows:

[0128]

[0129] S4, constructing a second control equation group based on the control equation group and the heat conduction equation, and obtaining a prediction result by solving the second control equation group.

[0130] In summary, the heat conduction equation (18), the Maxwell equations (7) and (8), the dynamic magnetic-force motion equation (9), the evolution law of the internal variables (11) and (14), the Ohm's law (15), and the twin boundary motion criterion (16) constitute the control equation group of the current model. By solving the control equation group, the force-heat-magnetic-electric dynamic response of the MSMA sample under high-frequency force-magnetic coupling loading can be predicted.

[0131] Exemplarily, the solving process of the control equation group based on the commercial finite element software COMSOL Multiphysics will be introduced. The equation group is solved by using the "solid mechanics", "magnetic field (current)", and "solid heat transfer" modules in the software. The main steps are as follows:

[0132] S41, establishing a geometric model of the sample and the external air;

[0133] S42, selecting the elastic and magnetic constitutive of the sample and the external air model;

[0134] S43, inputting boundary conditions and basic parameters of materials;

[0135] S44, calculating the deformation of the sample under high-frequency force-heat-magnetic-electric coupling.

[0136] The above method will be further described in combination with the accompanying drawings and specific embodiments.

[0137] The method of the present embodiment aims to provide a method for predicting the force-heat-magnetic-electric coupling dynamic response of a magnetic shape memory alloy under high-frequency magnetic force coupling loading, which can obtain the evolution curves of the force-heat-magnetic-electric coupling dynamic response and the average temperature of the sample during the loading process. For ease of demonstration, we take a five-layer modulated (5M) Ni-Mn-Ga alloy as an example. The content of the scheme includes predicting the dynamic mechanical response of the Ni-Mn-Ga alloy under multi-field coupling after giving the material, shape, and magnetization vector parameters of the Ni-Mn-Ga alloy sample. It should be noted that the research and development of MSMA functional devices often need to utilize the dynamic response characteristics of materials under multi-field coupling. The prediction process specifically includes the following steps:

[0138] Step 1: setting material parameters (length, width, height of the Ni-Mn-Ga alloy sample, material parameters, and magnetic field parameters (external magnetic field size Ba Magnetization amplitude M of the alloy sample s ) and so on.

[0139] Step 2: According to the control equation set obtained by solving, the body force and the surface force at the boundary of the sample are set. The constraint setting at the boundary of the sample is shown in Figure 1

[0140]

[0141] Step 3: According to the settings in step 1 and step 2, the parameters are input into the finite element software COMSOL Multiphysics for calculation to obtain numerical results. Thus, the force-thermal-magnetic-electric dynamic mechanical response of the magnetic shape memory alloy under the action of different high-frequency force magnetic coupling is predicted. In the numerical calculation, the initial configuration of the sample is selected as Ω r = 15 mm x 2 mm x 3 mm, the external magnetic field (air) model configuration is selected as Ω r = 75 mm x 10 mm x 15 mm, and the numerical calculation flow chart is shown in Figure 2 The specific operation steps of the software are as follows:

[0142] 3.1) Select "solid mechanics" and "magnetic field (current)", "solid heat transfer" modules for simulation. In the "solid mechanics" module, set the elastic constitutive of the sample, and set the constitutive of the region except the sample as the built-in air (Air) constitutive of the software. The boundary condition setting of the alloy sample is shown in Figure 1 According to the derived boundary condition, the body force and surface force of the magnetic field acting on the sample are applied to the sample. Linear elements are selected in this module for simulation.

[0143] 3.2) In the "magnetic field (current)" module, first set the "reduced field" option to calculate the demagnetizing field of the magnetic field, and give the size of the uniform background magnetic flux density. Set the magnetic constitutive relationship of the sample and the external region as B = μ (H + M), where μ = 4π x 10 -7 is the vacuum permeability, and the magnetization vector M of the sample region is set by formula (5), and the magnetization vector M of the external region is 0. Finally, select "external magnetic vector potential" and "A field specification fixed" options to specify the boundary condition of the external magnetic field. In this module, the magnetic vector potential is linear.

[0144] 3.3) In the "solid heat conduction" module, set the reference temperature to 16℃, set the sample as a generalized heat source, use the volume consumption density, and set the heat flux type as "convective heat flux". The heat transfer coefficient adopts "external forced convection" and "plate, average transfer coefficient", and the convection velocities are set to 15, 35 and 60 m / s respectively.

[0145] The evolution curve results of the axial strain of the magnetic shape memory alloy sample under different air convection velocities are as follows:​Figure 3 , Figure 4 Figure 5 As shown in the figure, the corresponding convection velocities are 15, 35, and 60 m / s, respectively. The solid line represents the simulation result of this method, while the dashed line represents the experimental measurement result. The simulation results and experimental results are in excellent agreement, verifying the accuracy of this method.

[0146] The above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Therefore, any changes made in accordance with the shape and principle of the present invention should be covered within the protection scope of the present invention.

[0147] In summary, compared with the prior art, the present invention has at least the following advantages and beneficial effects:

[0148] (1) Many influencing factors need to be considered.

[0149] This invention proposes a two-step variational method to establish the governing equations for a magnetic shape memory alloy sample model. The first step involves establishing the Hamiltonian action functional. It involves not only the system's kinetic and potential energy, but also the energy dissipation and eddy current effects caused by variant redirection. The independent variables in the equation include the spatial position vector x and the scalar potential φ. r sum vector potential Conduction current density J c and the internal variable α associated with the effective magnetization vector. i and also, It also depends on the abnormal distribution Π(t) in the sample. In the second step, another Hamiltonian action functional is proposed. To study the distribution and evolution of the temperature field within an MSMA sample, temperature T is used as the state variable.

[0150] (2) The set of governing equations is complete.

[0151] Through Hamiltonian action functionals and Variational calculations of the independent variables yielded Maxwell's equations, Ohm's law, the dynamic magnetodynamic equations, the internal variable evolution equations, and the heat conduction equations. Furthermore, through calculations... The twin interface motion criterion in the MSMA sample can be obtained by relating it to the variation of the abnormal distribution Π(t). The above equations and the twin interface motion criterion constitute the governing equations of the current model, laying the foundation for modeling single-crystal MSMA samples under high-frequency thermo-magnetic-electrical-mechanical effects.

[0152] (3) Simple and easy-to-use numerical methods

[0153] In order to solve the control equations, a solution method based on the commercial software COMSOL Multiphysics is proposed. According to the numerical results, the dynamic mechanical behavior response of MSMA sample under high-frequency thermal-magnetic-electric-force loading conditions is obtained. Taking Ni-Mn-Ga alloy sample as an example, the force-thermal-magnetic-electric dynamic response of MSMA sample in the stress-assisted cyclic field loading test is studied. The dynamic response and the evolution curve of the average temperature of the sample in the loading process are predicted, which are in good agreement with the experimental data. In addition, the distribution of some important physical quantities (such as eddy current density) in the sample can also be simulated, which provides a comprehensive description of the response of MSMA sample under high-frequency field loading test.

[0154] Embodiment 2

[0155] The embodiments of the present application also provide an electronic device, which comprises a processor and a memory, and the memory stores at least one instruction, at least one program, a code set or an instruction set, which are loaded and executed by the processor to realize the method for predicting the high-frequency force-thermal-magnetic-electric coupling dynamic response of a magnetic shape memory alloy as shown in any one of the above method embodiments. Figure 6 The embodiments of the present application also provide an electronic device, which comprises a processor and a memory, and the memory stores at least one instruction, at least one program, a code set or an instruction set, which are loaded and executed by the processor to realize the method for predicting the high-frequency force-thermal-magnetic-electric coupling dynamic response of a magnetic shape memory alloy as shown in any one of the above method embodiments.

[0156] It can be understood that the memory can include a random access memory (RAM) and a read-only memory (ROM). Optionally, the memory includes a non-transitory computer-readable storage medium. The memory can be used to store instructions, programs, codes, code sets or instruction sets. The memory can include a program storage area and a data storage area, wherein the program storage area can store instructions for implementing an operating system, instructions for at least one function, instructions for implementing each of the above method embodiments, etc.; and the data storage area can store data created according to the use of the server, etc.

[0157] The processor can include one or more processing cores. The processor connects various parts within the entire server by various interfaces and lines, executes various functions of the server and processes data by running or executing instructions, programs, code sets or instruction sets stored in the memory, and calling data stored in the memory. Optionally, the processor can be implemented in at least one of a hardware form of a digital signal processing (DSP), a field-programmable gate array (FPGA), and a programmable logic array (PLA). The processor can be integrated with one or several combinations of a central processing unit (CPU) and a modem. Among them, the CPU mainly processes operating systems and application programs; the modem is used to process wireless communication. It can be understood that the above-mentioned modem can also not be integrated into the processor, but can be realized by a single chip.

[0158] Since the electronic device is an electronic device corresponding to the magnetic shape memory alloy high-frequency force-heat-magnetic-electric coupling dynamic response prediction method of the embodiments of the application, and the principle of solving problems of the electronic device is similar to that of the method, the implementation of the electronic device can be referred to the implementation process of the above-mentioned method embodiments, and the repeated parts will not be described here.

[0159] Embodiment 3

[0160] The embodiments of the application also provide a computer readable storage medium, wherein at least one instruction, at least one program, a code set or an instruction set are stored in the storage medium, and the at least one instruction, the at least one program, the code set or the instruction set are loaded and executed by a processor to realize the magnetic shape memory alloy high-frequency force-heat-magnetic-electric coupling dynamic response prediction method as shown in the above-mentioned embodiments. Figure 6 The embodiments of the application also provide a computer readable storage medium, wherein at least one instruction, at least one program, a code set or an instruction set are stored in the storage medium, and the at least one instruction, the at least one program, the code set or the instruction set are loaded and executed by a processor to realize the magnetic shape memory alloy high-frequency force-heat-magnetic-electric coupling dynamic response prediction method as shown in the above-mentioned embodiments.

[0161] Those skilled in the art can understand that all or part of the steps of various methods in the above embodiments can be completed by instructing the relevant hardware through a program, and the program can be stored in a computer readable storage medium, including Read-Only Memory (ROM), Random Access Memory (RAM), Programmable Read-only Memory (PROM), Erasable Programmable Read Only Memory (EPROM), One-time Programmable Read-Only Memory (OTPROM), Electrically-Erasable Programmable Read-Only Memory (EEPROM), Compact Disc Read-Only Memory (CD-ROM) or other optical disk storage, magnetic disk storage, magnetic tape storage, or any other medium that can be used to carry or store data which can be read by a computer.

[0162] Since the storage medium is a storage medium corresponding to the method for predicting the high-frequency force-thermal-magnetic-electric coupling dynamic response of a magnetic shape memory alloy, and the principle of solving the problem of the storage medium is similar to that of the method, the implementation of the storage medium can refer to the implementation process of the above method embodiments, and the repeated parts will not be described again.

[0163] Embodiment 4

[0164] In some possible implementation manners, various aspects of the method of the embodiments of the present application can also be implemented in the form of a program product, which includes program codes for causing a computer device to execute the steps of the method for predicting the high-frequency force-thermal-magnetic-electric coupling dynamic response of a magnetic shape memory alloy according to various exemplary embodiments of the present application described above in the specification when the program product is run on the computer device. Among them, the executable computer program code or "code" for executing various embodiments can be written in a high-level programming language such as C, C++, C#, Smalltalk, Java, JavaScript, Visual Basic, Structured Query Language (for example, Transact-SQL), Perl, or in various other programming languages.

[0165] It should be understood that various aspects of the application can be implemented in hardware, software, firmware or a combination of them. In the above embodiments, various steps or methods can be implemented in software or firmware which is stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, and in another embodiment, any of the following technologies, known in the art, or their combination, can be used: discrete logic circuitry having logic gates for implementing logic functions upon an application of data signals, application-specific integrated circuits having appropriate combinational logic gates, programmable gate arrays (PGA), field-programmable gate arrays (FPGA), and so forth.

[0166] In the description of the present specification, the description of the terms "one embodiment", "some embodiments", "an example", "a specific example", or "some examples" and the like means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the present specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Also, the specific features, structures, materials or characteristics described can be combined in any appropriate manner in one or more embodiments or examples. In addition, the person skilled in the art can combine and combine the different embodiments or examples described in the present specification and the features of the different embodiments or examples, without contradiction.

[0167] The above embodiments are only for the purpose of illustrating the technical concept and characteristics of the present application, and the purpose is to enable those skilled in the art to understand the content of the present application and to implement it, and cannot limit the protection scope of the present application. Any equivalent changes or modifications made according to the essence of the present application should be covered within the protection scope of the present application.

Claims

1. A method for predicting the dynamic response of a magnetic shape memory alloy in a high-frequency force-thermal-magnetic-electric coupling, characterized in that, Includes the following steps: Establish the first Hamiltonian action functional for magnetic shape memory alloy samples without considering thermal effects; Based on the first Hamiltonian action functional, the first set of governing equations for the magnetic shape memory alloy sample is derived by variational method; the second Hamiltonian action functional for the magnetic shape memory alloy sample considering thermal effects is established, and the heat conduction equation is obtained based on the second Hamiltonian action functional. The second set of governing equations for the model is constructed based on the first set of governing equations and the heat conduction equation. The prediction results are obtained by solving the second set of governing equations. The establishment of the first Hamiltonian action functional for the magnetic shape memory alloy sample without considering thermal effects includes: For a single-crystal MSMA sample, at the initial time t0, the sample occupies the reference configuration Ω. r Its surface boundary is used Indicates; in the sample region Ω r Nearby, surrounding free space It indicates its outer boundary At infinity; In Ω r In this context, the position vector of a material point is denoted as X; In the current model, only the reorientation between two variants, namely variant 1 and variant 2, is considered; at time t∈[t0,t1], variant 1 and variant 2 occupy […]. In the sample And there are and Between It is a twin interface. and It consists of several separate regions; at the infinite boundary Ω ∞ At a certain point, x = X. in, It is a second-order unit tensor; At time t∈[t0,t1], in the entire space An electromagnetic field is applied to a point, which has a vector potential A. a scalar potential φ a On the sample surface Applying a mechanical load t a Electromagnetic fields and mechanical loads caused the MSMA sample to deviate from the reference configuration Ω. r To the current configuration Ω t The deformation, its surface boundary is used This indicates that; correspondingly, the surrounding area became Ω t The position vector of a material point is denoted by x(X,t); the derivative of x(X,t) yields the total deformation gradient tensor. and velocity v; The potential function A of the applied electromagnetic field a and φ a These are Eulerian vector fields, and they exist in the spacetime region. The interior is sufficiently smooth; the magnetic flux density B is calculated. a Magnetic field H a Electric field E a and electric displacement D a ; An applied electromagnetic field can induce effective magnetization of the MSMA sample; the Eulerian form of the magnetization vector field is denoted by M(x,t); Electromagnetic fields were also excited in the sample; the vector and scalar potentials of these excited electromagnetic fields are denoted by A in Euler form. s and φ s Assume A s (x,t) and φ s In the spatiotemporal region The first and second derivatives are continuous. Based on these potential functions, the magnetic flux density B can be calculated. s Magnetic field H s Electric field E s and electric displacement D s ; When an external magnetic field is applied, magnetic shape memory alloys exhibit domain wall movement and local magnetization vector rotation. To capture these experimental characteristics, a variant region is designed. Effective magnetization vector M i It has the following constitutive forms: In the formula, α i These are the volume fractions of the two magnetic domains. It is a unit vector along the local magnetization vector; conduction current J c This will generate Joule heating and cause temperature changes in the MSMA sample; Finally, the Hamiltonian functional of the obtained magnetic shape memory alloy sample is: The subscript 'r' indicates the reference configuration.

2. The method for predicting the high-frequency force-thermal-magnetic-electric coupling dynamic response of a magnetic shape memory alloy according to claim 1, characterized in that, Total Deformation Gradient Tensor The formula for calculating velocity v is: Where the subscript ",t" represents the time derivative of the substance; Magnetic induction intensity B a Magnetic field H a Electric field E a and electric displacement D a The calculation formula is as follows: B a (x,t)=rot(A a (x,t)) D a (x,t)=∈0E a (x,t) In the formula, μ0 represents the vacuum permeability, and ∈0 is the vacuum permittivity; Magnetic induction intensity B s Magnetic field H s Electric field E s and electric displacement D s The calculation formula is as follows: B s (x,t)=rot(A s (x,t)) D s (x,t)=∈0E s (x,t) In the formula, ρ is the material density of the sample in the current configuration.

3. The method for predicting the high-frequency force-thermal-magnetic-electric coupling dynamic response of a magnetic shape memory alloy according to claim 1, characterized in that, To simulate the elastic response of MSMA samples, the elastic strain-energy density of the following two martensitic variants was used. In the formula, It is the Lagrange strain tensor. It is the total deformation gradient tensor. It is the inverse of the weight-oriented strain tensor. It is a second-order unit tensor; It is the second-order elastic modulus.

4. The method for predicting the high-frequency force-thermal-magnetic-electric coupling dynamic response of a magnetic shape memory alloy according to claim 1, characterized in that, The first set of governing equations for the magnetic shape memory alloy sample, derived by variational method based on the first Hamiltonian action functional, includes: right By taking variational methods, we obtain the set of governing equations for the electric field in the Gaussian law form of Maxwell's equations. right By taking variational solutions, we obtain the set of governing equations for Ampere's circuit law in Maxwell's equations; Taking variational equations with respect to x yields the set of motion control equations for magnetic-mechanical coupling. For α i and The evolution equations of the internal variables are obtained by taking the variational equations; right The variational equation for Ohm's law is obtained. The migration criterion of the twin interface is obtained by variational analysis of Π(t).

5. The method for predicting the high-frequency force-thermal-magnetic-electric coupling dynamic response of a magnetic shape memory alloy according to claim 1, characterized in that, The second Hamiltonian action functional The expression is: In the formula, c is the specific heat capacity, k is the thermal conductivity, and R is the volumetric heat source within the MSMA sample; ρ r Where is the density of the sample; T is the temperature field; dV is the square of the derivative of the temperature field with respect to time; Grad represents the gradient operator under the reference configuration; dV is the infinitesimal change in volume at a point within the sample; dS is the infinitesimal change in volume at a point on the sample surface; t is time; q r and q t The heat flux density is at the sample boundary and the twin interface within the sample; the parameter τ represents the thermal relaxation time of the material, i.e., the finite thermal interaction time between material particles.

6. The method for predicting the high-frequency force-thermal-magnetic-electric coupling dynamic response of a magnetic shape memory alloy according to claim 5. Its features are, The process of obtaining the heat conduction equation based on the second Hamiltonian action functional includes: Find the variation with respect to T and then substitute it into R and q. r and q t Thus, the heat conduction equation and boundary conditions are obtained: In the formula, ΔT is the change in temperature; J -1 Represents the total deformation gradient The inverse of the determinant; N represents the conduction current density under the current configuration. r For the sample region Ω r Pointing to the surrounding area Ω' r The unit normal vector; k1 is the heat exchange coefficient; N is the twin interface. The unit normal vector; D ± This is the critical value of the driving force required to activate twin interface movement during the forward and reverse variant reorientation process; It represents the difference in physical quantities on both sides of the twin interface from the negative direction to the positive direction.

7. The method for predicting the high-frequency force-thermal-magnetic-electric coupling dynamic response of a magnetic shape memory alloy according to claim 1. Its features are, The steps for solving the second set of governing equations include: Establish a geometric model of the sample and the external air; Select the elastic and magnetic constitutive models of the sample and the external air model; Input the boundary conditions and basic material parameters; Calculate the deformation of the sample under high-frequency force-thermal-magnetic-electric coupling.

8. An electronic device, characterized in that, The electronic device includes a processor and a memory, the memory storing at least one program, which is loaded and executed by the processor to implement the method as described in any one of claims 1 to 7.

9. A computer-readable storage medium, characterized in that, The storage medium stores at least one program segment, which is loaded and executed by a processor to implement the method as described in any one of claims 1 to 7.

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