Prediction method and device for high-frequency force-heat-magnetism-electricity coupling dynamic response of magnetic shape memory alloy and medium

Abstract

The invention discloses a method and equipment for predicting high-frequency force-heat-magnetism-electricity coupling dynamic response of magnetic shape memory alloy and a medium. The method comprises the following steps: establishing a first Hamiltonian action functional of a magnetic shape memory alloy sample without considering a heat effect; deducing a first control equation set of the magnetic shape memory alloy sample according to the first Hamiltonian action functional; establishing a second Hamiltonian action functional of the magnetic shape memory alloy sample considering the heat effect, and obtaining a heat conduction equation according to the second Hamiltonian action functional; and constructing a second control equation set of the model according to the control equation set and the heat conduction equation, and obtaining a prediction result by solving the second control equation set. According to the scheme provided by the invention, the influence of temperature and the influence of the excitation magnetic field generated under the high-frequency magnetic field loading condition are considered, the force-heat-magnetic-electric coupling dynamic response of the magnetic shape memory alloy under the high-frequency force-magnetic coupling loading condition is fully simulated, and the method has important application prospect and value.

Description

Technical Field

[0001] The present invention relates to the technical field of prediction of force-heat-magnetic-electric coupling dynamic response of magnetic shape memory alloy materials under high-frequency force-magnetic coupling loading and design and development of magnetic intelligent devices, and in particular to a prediction method, device and medium for the high-frequency force-heat-magnetic-electric coupling dynamic response of a magnetic shape memory alloy. Background Art

[0002] Magnetic shape memory alloy (MSMA) has attracted wide attention due to its outstanding material properties. Under the action of magnetic field and external force load, MSMA can show reversible deformation with 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 making new high-frequency driven 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-crystalline Ni-Mn-Ga alloy is one of the most common materials. For single-crystalline Ni-Mn-Ga alloy, the reason for the significant reversible strain is that the martensitic variants with different lattice orientations inside it undergo deformation and reorientation. In order to fully understand the special properties of MSMA, researchers have conducted systematic experimental work and proposed different theoretical models. Early work in this field 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-mechanical loads. Haldar and Lagoudas developed a multi-field coupling theoretical model and proposed an algorithm that can effectively solve the system of governing equations. On this basis, some important physical quantities such as variant volume fraction, eddy current density and Joule heating can be predicted. In order to better understand its inherent 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 transformation and martensite change redirection of MSMA samples under high-frequency magnetic loads. Based on this, they also performed numerical analysis and predicted the evolution curves of temperature, strain and volume fraction of austenite and martensite phases.

[0005] In the field of applied research and development, Kohl et al. developed an 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 an MSMA vibration sensor that can convert mechanical energy into electrical energy; Zhang Qingxin et al. used MSMA to develop a new vibration energy harvesting system and conducted performance tests; Shi Hu et al. designed an MSMA-driven high-speed switching hydraulic valve; Tu Fuquan et al. introduced the basic structure and working principle of an MSMA active shock absorber and simulated and analyzed its performance.

[0006] Despite a large amount of previous work in this field, research on the dynamic response of MSMA is still in its infancy. Existing models rarely consider the orientation and movement of twin interfaces in MSMA, which is an important feature of the variant reorientation process. In addition, the effect of electromagnetic field distribution on MSMA samples is often ignored. Summary of the invention

[0007] In order to solve at least one of the technical problems existing in the prior art to a certain extent, the purpose of the present invention is to provide a method, device and medium for predicting the high-frequency mechanical-thermal-magnetic-electric coupled dynamic response of a magnetic shape memory alloy.

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

[0009] A method for predicting the high-frequency mechanical-thermal-magnetic-electrical coupled dynamic response of a magnetic shape memory alloy comprises the following steps:

[0010] The first Hamiltonian action functional of magnetic shape memory alloy samples without considering thermal effect is established;

[0011] According to the first Hamiltonian action functional, the first governing equations of the magnetic shape memory alloy sample are derived by the variational method;

[0012] The second Hamiltonian action functional of the magnetic shape memory alloy sample considering the thermal effect is established, and the heat conduction equation is obtained according to the second Hamiltonian action functional;

[0013] The second control equation group of the model is constructed according to the first control equation group and the heat conduction equation. By solving the second control equation group, the force-heat-magnetic-electric dynamic response of the MSMA sample under high-frequency force-magnetic coupling loading conditions is predicted.

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

[0015] Assume 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 boundaries are Indicated by; near the sample area X, the surrounding free space is represented by Indicates that its outer boundary At infinity; at Ω r In the equation, the position vector of a material point is denoted as X;

[0016] In the current model, only the redirection between two variants is considered, namely variant 1 and variant 2; at time t∈[t0,t1], variant 1 and variant 2 occupy In the sample And there is and Between is the twin interface. There may be multiple twin interfaces in the sample, so and is composed of several separate regions; at the infinite boundary Ω ∞ At x=X,

[0017] At time t∈[t0,t1], in the entire space An electromagnetic field is applied in the a and the scalar potential φ a On the sample surface Apply mechanical load (traction) t a ; The electromagnetic field and mechanical load caused the MSMA sample to change from the reference configuration Ω r To the current configuration Ω t The deformation of its surface boundary is Indicates that; accordingly, the surrounding area becomes Ω t The position vector of a material point in is represented by x(X, t); the total deformation gradient tensor is obtained by taking the derivative of x(X, t) and speed v;

[0018] Potential function A of the applied electromagnetic field a and φ a are Euler vector fields, which are in the spacetime region The inside is smooth enough to calculate the magnetic induction intensity B a , magnetic field H a 、Electric field E a and electric displacement D a ;

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

[0020] Electromagnetic fields are also excited in the sample. The Euler forms of the vector potential and scalar potential of these excited electromagnetic fields are denoted as A s and φ s , assuming A s (x,t) and φ s In the space-time region The first and second order derivatives in are continuous. Based on these potential functions, the magnetic induction intensity B is calculated. s , magnetic field H s 、Electric field E s and electric displacement D s ;

[0021] When an external magnetic field is applied, magnetic shape memory alloys will experience the movement of magnetic domain walls and the rotation of local magnetization vectors. In order to capture these experimental characteristics, The effective magnetization vector M i The following constitutive form:

[0022]

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

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

[0025] Furthermore, the total deformation gradient tensor The calculation formula of the velocity v is:

[0026]

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

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

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

[0030]

[0031] Da (x,t)=∈0E a (x,t)

[0032] In the formula, μ0 represents the vacuum magnetic permeability, ∈0 is the vacuum dielectric constant;

[0033] Magnetic induction intensity B s , magnetic field H s 、Electric field E s and electric displacement D s The calculation formula is as follows:

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

[0035]

[0036] D s (x,t)=∈0E s (x,t)

[0037] where ρ is the material density of the sample in the current configuration.

[0038] Furthermore, in order to simulate the elastic response of MSMA samples, the following elastic strain-energy density of two martensitic variants are used:

[0039]

[0040] In the formula, is the Lagrangian strain tensor, is the total deformation gradient tensor, is the inverse of the deformation reorientation strain tensor, is the second-order unit tensor; is the second-order elastic modulus.

[0041] Furthermore, the first control equations of the magnetic shape memory alloy sample are derived by variational method according to the first Hamiltonian action functional, including:

[0042] right The Gaussian law governing equations of the electric field in Maxwell's equations are obtained by solving the variational equations;

[0043] right The variational equations are used to obtain the governing equations of Ampere's circuit law in Maxwell's equations;

[0044] By varying x, we can obtain the motion control equations of magnetic-mechanical coupling;

[0045] To α i and The evolution equation of the internal variables is obtained by solving the variation equation;

[0046] right Solving the variation gives the Ohm's law equation;

[0047] The migration criterion of the twin interface is obtained by taking the variation of Π(t).

[0048] Furthermore, the second Hamiltonian action functional The expression is:

[0049]

[0050] Where c is the specific heat capacity, k is the thermal conductivity, R is the volume heat source in the MSMA sample; ρ r is the density of the sample; T is the temperature field; is the quadratic derivative of the temperature field with respect to time; Grad represents the gradient operator under the reference configuration; dV is the small change in volume at a certain point in the sample; dS is the small change in volume at a certain point on the surface of the sample; t is time; q r and q t is the heat flux density on the sample boundary and the twin interface within the sample; the parameter τ represents the thermal relaxation time of the material, that is, the limited thermal interaction time between material particles.

[0051] Furthermore, obtaining the heat conduction equation according to the second Hamiltonian action functional includes:

[0052] After calculating the variation of T, substitute it into R and q r and q t , we get the heat conduction equation and boundary conditions:

[0053]

[0054] Where ΔT is the change in temperature; J -1 represents the total deformation gradient Inverse of a determinant; is the conduction current density under the current configuration; N r is the sample area 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 of ± is the critical value of the driving force required to activate the twin interface motion during the reorientation process for both the forward and reverse variants; It represents the difference of the physical quantities on both sides of the twin interface from the negative direction (the direction opposite to the normal vector N) to the positive direction (the direction positive to the normal vector N).

[0055] Furthermore, the second control equations solving step includes:

[0056] Establish the geometric model of the sample and the external air;

[0057] Select elastic and magnetic constitutive models for the sample and external air model;

[0058] Input boundary conditions and basic material parameters;

[0059] Calculate the deformation of samples under high-frequency mechanical-thermal-magnetic-electric coupling.

[0060] The second technical solution adopted by the present invention is:

[0061] An electronic device comprises a processor and a memory, wherein the memory stores at least one instruction, at least one program, a code set or an instruction set, and the at least one instruction, at least one program, the code set or the instruction set is loaded and executed by the processor to implement a method for predicting the high-frequency force-heat-magnetic-electric coupling dynamic response of a magnetic shape memory alloy as described above.

[0062] The third technical solution adopted by the present invention is:

[0063] A computer-readable storage medium stores at least one instruction, at least one program, a code set or an instruction set, wherein the at least one instruction, the at least one program, the code set or the instruction set is loaded and executed by a processor to implement a method for predicting the high-frequency force-heat-magnetic-electric coupling dynamic response of a magnetic shape memory alloy as described above.

[0064] The fourth technical solution adopted by the present invention is:

[0065] A computer program product or a computer program includes computer instructions stored in a computer-readable storage medium. A processor of a 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.

[0066] The beneficial effects of the present invention are as follows: the scheme proposed in the present invention takes into account the influence of temperature and the influence of the excitation magnetic field generated under high-frequency magnetic field loading conditions, and can fully simulate the force-heat-magnetic-electric coupling dynamic response of magnetic shape memory alloys under high-frequency force-magnetic coupling loading conditions, and has important application prospects and value in the fields of magnetic shape memory alloy drives and the like. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the embodiments of the present invention or the drawings of related technical solutions in the prior art are introduced below. It should be understood that the drawings introduced below are only for the convenience of clearly describing some embodiments of the technical solutions of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work.

[0068] Figure 1 Boundary constraints and loading conditions for the magnetic shape memory alloy sample.

[0069] Figure 2 This is the comsol simulation flow chart in numerical simulation.

[0070] Figure 3 This is a comparison chart between the numerical simulation results and the experimental results of the magnetic shape memory alloy sample at a convection velocity of 15m / s.

[0071] Figure 4 This is a comparison chart between the numerical simulation results and the experimental results of the magnetic shape memory alloy sample at a convection velocity of 35m / s.

[0072] Figure 5 This is a comparison chart between the numerical simulation results and the experimental results of the magnetic shape memory alloy sample at a convection velocity of 60m / s.

[0073] Figure 6 The present invention provides a flowchart of the steps of a method for predicting the high-frequency mechanical-thermal-magnetic-electrical coupled dynamic response of a magnetic shape memory alloy in an embodiment of the present invention. DETAILED DESCRIPTION

[0074] The embodiments of the present invention are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and are not to be construed as limitations of the present invention. For the step numbers in the following embodiments, they are only provided for the convenience of explanation, and the order between the steps is not limited in any way, and the execution order of each step in the embodiment can be adaptively adjusted according to the understanding of those skilled in the art.

[0075] In the description of the present invention, it should be understood that descriptions involving orientations, such as up, down, front, back, left, right, etc., and orientations or positional relationships indicated are based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present invention.

[0076] In the description of the present invention, "several" means one or more, "more" means more than two, "greater than", "less than", "exceed" etc. are understood as not including the number itself, and "above", "below", "within" etc. are understood as including the number itself. If there is a description of "first" or "second", it is only used for the purpose of distinguishing the technical features, and cannot be understood as indicating or implying the relative importance or implicitly indicating the number of the indicated technical features or implicitly indicating the order of the indicated technical features.

[0077] In the description of the present invention, unless otherwise clearly defined, terms such as setting, installing, connecting, etc. should be understood in a broad sense, and technicians in the relevant technical field can reasonably determine the specific meanings of the above terms in the present invention based on the specific content of the technical solution.

[0078] In view of the existing technical problems, the present invention aims to propose a scheme for predicting the force-heat-magnetic-electric coupling dynamic response of magnetic shape memory alloys 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-heat-magnetic-electric coupling dynamic response of magnetic shape memory alloy samples under high-frequency magnetic coupling loading, and therefore has important application prospects and value in the fields of magnetic shape memory alloy actuators.

[0079] Example 1

[0080] like Figure 6 As shown, this embodiment provides a method for predicting the high-frequency mechanical-thermal-magnetic-electrical coupled dynamic response of a magnetic shape memory alloy, comprising the following steps:

[0081] S1. Establish the first Hamiltonian action functional of the magnetic shape memory alloy sample without considering the thermal effect.

[0082] First, the Hamiltonian action functional of the magnetic shape memory alloy sample without considering the thermal effect is established. First, the object of our study is a single crystal MSMA sample. At the initial time t0, the sample occupies the reference configuration Ω r , whose surface boundaries are Indicates. In the sample area Ω r Nearby, free space around Indicates that its outer boundary At infinity. At Ω r In the equation, the position vector of a material point is denoted by X.

[0083] For simplicity, in the current model, we only consider the redirection between two variants, namely variant 1 and variant 2. At time t∈[t0,t1], variant 1 and variant 2 occupy In the sample And there is and Between is the twin interface. There may be multiple twin interfaces in the sample, so and is composed of several separate regions. In addition, at the infinite boundary Ω ∞ At x=X, At time t∈[t0,t1], in the entire space An electromagnetic field is applied in the a and the scalar potential φ a In addition, on the sample surface A mechanical load (traction) is also applied to a The electromagnetic field and mechanical load caused the MSMA sample to change from the reference configuration Ω r To the current configuration Ω t The deformation of its surface boundary is Correspondingly, the surrounding area becomes Ω t The position vector of a material point in Ω is denoted by x(X,t). We assume that x(X,t) is in Ω r ×[t0,t1] has piecewise continuous first-order and second-order derivatives. According to the position vector field x(X,t), the deformation gradient tensor and speed v are:

[0084]

[0085] Here, the subscript ",t" refers to the time derivative of the material (i.e., the time derivative at a fixed point X). The potential function A of the applied electromagnetic field a and φ a are Euler vector fields, which are in the spacetime region The inside is smooth enough. Based on these potential functions, the magnetic induction intensity B can be calculated a , magnetic field H a 、Electric field E a and electric displacement D a :

[0086]

[0087] Where μ0 represents the vacuum magnetic permeability (μ0 = 4π×10 -7 N / A 2 ), ∈0 is the dielectric constant of vacuum (∈0=8.854×10 -12F / m). The applied electromagnetic field can induce effective magnetization of the MSMA sample (without considering the polarization of MSMA). The Euler form of the magnetization vector field (unit mass) is represented by M(x, t). In addition, some free charges and free currents can be excited in the sample. These physical quantities will further induce the distribution of the excited electromagnetic field in the entire space. The Euler form of the vector potential and scalar potential of these excited electromagnetic fields is recorded as A s and φ s , we also assume that A s (x,t) and φ s In the space-time region The first and second order derivatives in are continuous. Based on these potential functions, the magnetic induction intensity B can be calculated. s , magnetic field H s 、Electric field E s and electric displacement D s :

[0088]

[0089] ρ is the material density of the sample in the current configuration.

[0090] To simulate the elastic response of MSMA samples, we used the following elastic strain-energy density of two martensitic variants:

[0091]

[0092] in is the Lagrangian strain tensor, is the second-order elastic modulus. When an external magnetic field is applied, the magnetic shape memory alloy will undergo the movement of the magnetic domain wall and the rotation of the local magnetization vector. In order to capture these experimental characteristics, The effective magnetization vector M i The following constitutive form:

[0093]

[0094] where α 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 Joule heat will be generated, causing a significant temperature change in the MSMA sample. The Joule heat value P h Calculated by the following formula:

[0095]

[0096] where σ is the electrical conductivity of the material.

[0097] Total energy density functional of magnetic shape memory alloy samples Here we ignore the thermal effect and obtain the energy density functional of the magnetic shape memory alloy sample where α i and, is an internal variable related to the effective magnetization.

[0098] S2. Based on the first Hamiltonian action functional, the first control equation group of the magnetic shape memory alloy sample is derived by variational method.

[0099] Specifically, step S2 includes the following steps:

[0100] S21, yes The variational equations are obtained by Gauss's law governing the electric field in Maxwell's equations.

[0101]

[0102] The subscript "r" indicates that it is in the reference (initial) configuration. Indicates the electric displacement excited by the sample in the initial configuration; double brackets Indicates the size of the mutation at the interface between the sample and the air. r yes is the unit normal vector on the twin interface, and N is the unit normal vector on the twin interface. and is the MSMA sample in the reference configuration Ω r The free volume charge and free surface charge density under .

[0103] S22, yes The variational equations are obtained to obtain the governing equations of Ampere's circuit law in Maxwell's equations.

[0104]

[0105] in is the magnetic field strength excited by the sample in the initial configuration, V is the velocity of the sample in the initial configuration, W n is the velocity of the twin interface motion.

[0106] S23. Differentiate x to obtain the set of motion control equations for magnetic-mechanical coupling.

[0107]

[0108] where x ,tt is the acceleration of the sample motion, is the nominal stress tensor. and The expression is as follows:

[0109]

[0110] S24, for α i and The evolution equation of the internal variables is obtained by solving the variation.

[0111]

[0112] in:

[0113]

[0114] in:

[0115]

[0116] S25, yes Solving the variation gives the Ohm's law equation.

[0117]

[0118] in

[0119] S26. Take the variation of Π(t) to obtain the migration criterion of the twin interface.

[0120]

[0121] in 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

[0122] S3. Establish a second Hamiltonian action functional for the magnetic shape memory alloy sample taking thermal effects into account, and obtain a heat conduction equation based on the second Hamiltonian action functional.

[0123] Hamiltonian action functional of magnetic shape memory alloy samples considering thermal effects

[0124]

[0125] Where c is the specific heat capacity (unit mass), k is the thermal conductivity, and R is the volume heat source in the MSMA sample; q r and q T is the heat flux density on the sample boundary and the twin interface within the sample; the parameter τ (τ ≥ 0) represents the thermal relaxation time of the material, that is, the limited thermal interaction time between material particles.

[0126] After calculating the variation of T, substitute it into R and q r and q tThe heat conduction equation and boundary conditions are obtained:

[0127]

[0128] S4. Construct a second control equation group of the model according to the control equation group and the heat conduction equation, and obtain the prediction result by solving the second control equation group.

[0129] In summary, the heat conduction equation (18), Maxwell equations (7) and (8), dynamic magnetic-mechanical motion equations (9), the evolution laws of internal variables (11) and (14), Ohm's law (15) and the twin interface motion criterion (16) constitute the governing equations of the current model. By solving the governing equations, the mechano-thermal-magnetic-electrical dynamic response of the MSMA sample under high-frequency mechano-magnetic coupling loading conditions can be predicted.

[0130] By way of example, the process of solving the control equations based on the commercial finite element software COMSOL Multiphysics will be introduced. The equations are solved using the "Solid Mechanics", "Magnetic Field (Current)" and "Solid Heat Transfer" modules in the software. The main steps are as follows:

[0131] S41, establishing a geometric model of the sample and the external air;

[0132] S42, select the elastic constitutive model and magnetic constitutive model of the sample and the external air model;

[0133] S43. Input boundary conditions and basic material parameters;

[0134] S44. Calculate the deformation of the sample under high-frequency force-heat-magnetic-electric coupling.

[0135] The above method is supplemented with reference to the accompanying drawings and specific embodiments.

[0136] The method of this embodiment aims to provide a method for predicting the force-heat-magnetic-electric coupling dynamic response of magnetic shape memory alloys under high-frequency magnetic-force coupling loading, which can obtain the evolution curve of the force-heat-magnetic-electric coupling dynamic response and the average temperature of the sample during the loading process. For the convenience of demonstration, we take the 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 parameters such as the material, shape and magnetization vector of the Ni-Mn-Ga alloy sample. It should be pointed out that the research and development of MSMA functional devices often requires the use of the dynamic response characteristics of materials under multi-field coupling conditions. The prediction process specifically includes the following steps:

[0137] Step 1: Set the material parameters (length, width, height of the Ni-Mn-Ga alloy sample, material parameters and magnetic field parameters (external magnetic field size Ba ,, alloy sample magnetization amplitude M s )wait.

[0138] Step 2: According to the solved control equations, set the body force on the sample and the surface force at the boundary. The constraint settings at the sample boundary are as follows: Figure 1 shown.

[0139]

[0140] Step 3: According to the settings in steps 1 and 2, the parameters are input into the finite element software COMSOL Multiphysics to calculate and obtain numerical results. In this way, the force-heat-magnetic-electric dynamic mechanical response of magnetic shape memory alloys under different high-frequency force-magnetic coupling is predicted. In the numerical calculation, the initial configuration of the sample is selected as Ω r =15mm×2mm×3mm, the external magnetic field (air) model configuration is selected as Ω r =75mm×10mm×15mm, the numerical calculation flow chart is as follows Figure 2 The specific operation steps of the software are as follows:

[0141] 3.1) Select the "Solid Mechanics", "Magnetic Field (Current)", and "Solid Heat Transfer" modules for simulation. In the "Solid Mechanics" module, set the elastic constitutive model of the sample, and set the constitutive model of the area other than the sample to the built-in air constitutive model of the software. The boundary conditions of the alloy sample are set as follows: Figure 1 As shown in Figure 2. According to the derived boundary conditions, the body force and surface force of the magnetic field on the sample are applied to the sample. Linear unit simulation is selected in this module.

[0142] 3.2) In the "Magnetic Field (Current)" module, first set the "Reduced Field" option to calculate the demagnetization field of the magnetic field, given the size of the uniform background magnetic flux density. Set the magnetic constitutive relationship between the sample and the external area to B = μ (H + M), where μ = 4π × 10 -7 is the vacuum permeability, the magnetization vector M of the sample region is set by formula (5), and the magnetization vector M of the external region is set to 0. Finally, select the "External magnetic vector potential" and "A field gauge fixed" options to specify the external magnetic field boundary conditions. The magnetic vector potential is linear in this module.

[0143] 3.3) In the "Solid Thermal Conductivity" module, set the reference temperature to 16 °C, set the sample to a generalized heat source, use volume consumption density, set the heat flux type to "convective heat flux", use "external forced convection" and "plate, average transfer coefficient" for the heat transfer coefficient, and set the convection speeds to 15, 35, and 60 m / s, respectively.

[0144] The evolution curves of the axial strain of the magnetic shape memory alloy samples under different air convection velocities are shown in the figure. Figure 3 , Figure 4 Figure 5 As shown in the figure, the corresponding convection velocities are 15, 35, and 60 m / s respectively. As can be seen from the figure, the solid line is the result of the simulation of this method, and the dotted line is the result of the experimental measurement. The simulation results of this method are very consistent with the experimental results, which verifies the accuracy of this method.

[0145] The above-described embodiments are only preferred embodiments of the present invention and are not intended to limit the scope of implementation of the present invention. Therefore, all changes made according to the shape and principle of the present invention should be included in the protection scope of the present invention.

[0146] In summary, compared with the prior art, the present invention has at least the following advantages and beneficial effects:

[0147] (1) Consider many influencing factors.

[0148] The method of the present invention proposes a two-step variational method to establish a control equation group of a magnetic shape memory alloy sample model. In the first step, the Hamiltonian action functional is established. It not only involves the kinetic energy and potential energy of the system, but also includes the energy dissipation and eddy effects caused by the redirection of the variant. The independent variables in include the spatial position vector x, the scalar potential φ r and vector potential Conduction current density J c , and the internal variable α related to 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 in the MSMA sample, it uses temperature T as the state variable.

[0149] (2) The control equations are complete.

[0150] Hamiltonian action functional and By calculating the variation of the independent variables, we obtain Maxwell's equations, Ohm's law, dynamic magnetomechanics equations, internal variable evolution equations and heat conduction equations. The twin interface motion criterion in the MSMA sample can be obtained relative to the change of the deformation distribution Π(t). The above equations and the twin interface motion criterion constitute the control equation group of the current model, which lays the foundation for modeling single crystal MSMA samples under high-frequency thermal-magnetic-electrical-mechanical effects.

[0151] (3) Simple and easy-to-use numerical method

[0152] In order to solve the governing equations, a solution method based on the commercial software COMSOL Multiphysics is proposed. According to the numerical results, the dynamic mechanical behavior response of the MSMA sample under high-frequency thermal-magnetic-electrical-mechanical loading conditions is obtained. Taking the Ni-Mn-Ga alloy sample as an example, the mechanical-thermal-magnetic-electrical dynamic response of the MSMA sample in the stress-assisted cyclic field loading test is studied. The dynamic response of the sample during the loading process and the evolution curve of the average temperature are predicted, which are in good agreement with the experimental data. In addition, the distribution of some important physical quantities in the sample (such as eddy current density) can also be simulated, providing a comprehensive description of the response of the MSMA sample under high-frequency field loading test.

[0153] Example 2

[0154] An embodiment of the present invention further provides an electronic device, the 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 following Figure 6 A prediction method for high-frequency mechanical-thermal-magnetic-electric coupled dynamic response of a magnetic shape memory alloy is shown.

[0155] It is understood that the memory may include a random access memory (RAM) or a read-only memory (ROM). Optionally, the memory includes a non-transitory computer-readable storage medium. The memory may be used to store instructions, programs, codes, code sets, or instruction sets. The memory may include a program storage area and a data storage area, wherein the program storage area may store instructions for implementing an operating system, instructions for at least one function, instructions for implementing the above-mentioned various method embodiments, etc.; the data storage area may store data created according to the use of the server, etc.

[0156] The processor may include one or more processing cores. The processor uses various interfaces and lines to connect the various parts of the entire server, and 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 hardware form of digital signal processing (DSP), field programmable gate array (FPGA), and programmable logic array (PLA). The processor can integrate one or a combination of a central processing unit (CPU) and a modem. Among them, the CPU mainly processes the operating system and application programs; the modem is used to process wireless communications. It can be understood that the above-mentioned modem may not be integrated into the processor, but implemented separately through a chip.

[0157] Since the electronic device is an electronic device corresponding to the method for predicting the high-frequency force-heat-magnetic-electric coupling dynamic response of a magnetic shape memory alloy in an embodiment of the present invention, and the principle of solving the problem by the electronic device is similar to that of the method, the implementation of the electronic device can refer to the implementation process of the above-mentioned method embodiment, and the repeated parts will not be repeated.

[0158] Example 3

[0159] The embodiment of the present invention further provides a computer-readable storage medium, wherein the storage medium stores at least one instruction, at least one program, code set or instruction set, and the at least one instruction, the at least one program, the code set or instruction set is loaded and executed by a processor to implement the following Figure 6 A prediction method for high-frequency mechanical-thermal-magnetic-electric coupled dynamic response of a magnetic shape memory alloy is shown.

[0160] Those skilled in the art can understand that all or part of the steps in the various methods of the above embodiments can be completed by instructing related hardware through a program, and the program can be stored in a computer-readable storage medium, and the storage medium includes a read-only memory (ROM), a random access memory (RAM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), a one-time programmable read-only memory (OTPROM), an electronically erasable rewritable read-only memory (EEPROM), a compact disc (CD-ROM) or other optical disc storage, magnetic disk storage, magnetic tape storage, or any other computer-readable medium that can be used to carry or store data.

[0161] Since the storage medium is the storage medium corresponding to the method for predicting the high-frequency force-heat-magnetic-electric coupling dynamic response of a magnetic shape memory alloy in an embodiment of the present invention, and the principle of solving the problem by 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-mentioned method embodiment, and the repeated parts will not be repeated.

[0162] Example 4

[0163] In some possible implementations, various aspects of the method of the embodiment of the present invention can also be implemented in the form of a program product, which includes a program code. When the program product is run on a computer device, the program code is used to enable the computer device to execute the steps of the method for predicting the high-frequency force-heat-magnetic-electric coupling dynamic response of a magnetic shape memory alloy according to various exemplary embodiments of the present application described above in this specification. Among them, the executable computer program code or "code" for executing each embodiment can be written in a high-level programming language such as C, C++, C#, Smalltalk, Java, JavaScript, VisualBasic, structured query language (e.g., Transact-SQL), Perl, or in various other programming languages.

[0164] It should be understood that the various parts of the present invention can be implemented by hardware, software, firmware or a combination thereof. In the above-mentioned embodiments, a plurality of steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, it can be implemented by any one of the following technologies known in the art or their combination: a discrete logic circuit having a logic gate circuit for implementing a logic function for a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0165] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0166] The above embodiments are only for illustrating the technical concept and features of the present invention, and their purpose is to enable ordinary technicians in the field to understand the content of the present invention and implement it accordingly, and they cannot be used to limit the protection scope of the present invention. Any equivalent changes or modifications made based on the essence of the content of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for predicting the high-frequency mechanical-thermal-magnetic-electrical coupling dynamic response of a magnetic shape memory alloy, characterized in that: The following steps are involved: The first Hamiltonian action functional of magnetic shape memory alloy samples without considering thermal effect is established; According to the first Hamiltonian action functional, the first control equation group of the magnetic shape memory alloy sample is derived by the variational method; the second Hamiltonian action functional of the magnetic shape memory alloy sample considering the thermal effect is established, and the heat conduction equation is obtained according to the second Hamiltonian action functional; A second control equation group of the model is constructed according to the first control equation group and the heat conduction equation, and the prediction result is obtained by solving the second control equation group.

2. The method for predicting the high-frequency mechanical-thermal-magnetic-electrical coupled dynamic response of a magnetic shape memory alloy according to claim 1, characterized in that: The method of establishing a first Hamiltonian action functional of a magnetic shape memory alloy sample without considering thermal effects comprises: Assume 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 boundaries are Indicates; in the sample area Ω r Nearby, free space around Indicates that its outer boundary At infinity; at Ω r In the equation, the position vector of a material point is denoted as X; In the current model, only the redirection between two variants is considered, namely variant 1 and variant 2; at time t∈[t0,t1], variant 1 and variant 2 occupy In the sample And there is and Between is the twin interface, and is composed of several separate regions; at the infinite boundary Ω ∞ At x=X, At time t∈[t0,t1], in the entire space An electromagnetic field is applied to the a and the scalar potential φ a On the sample surface Apply mechanical load t a ; The electromagnetic field and mechanical load caused the MSMA sample to change from the reference configuration Ω r To the current configuration Ω t The deformation of the surface boundary is Indicates that; accordingly, the surrounding area becomes Ω t The position vector of a material point in is represented by x(X, t); the total deformation gradient tensor is obtained by taking the derivative of x(X, t) and velocity v; potential function A of the applied electromagnetic field a and φ a are Euler vector fields, which are in the spacetime region The inside is smooth enough to calculate the magnetic induction intensity B a , magnetic field H a 、Electric field E a and electric displacement D a ; The applied electromagnetic field can induce effective magnetization of the MSMA sample; the Euler form of the magnetization vector field is represented by M(x, t); Electromagnetic fields are also excited in the sample. The Euler forms of the vector potential and scalar potential of these excited electromagnetic fields are denoted as A s and φ s , assuming A s (x,t) and φ s In the space-time region The first and second order derivatives in are continuous. Based on these potential functions, the magnetic induction intensity B is 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 will experience the movement of magnetic domain walls and the rotation of local magnetization vectors. In order to capture these experimental characteristics, The effective magnetization vector M i The following constitutive form: In the formula, α i is the volume fraction of the two magnetic domains, is the unit vector along the local magnetization vector; the conduction current J c It will generate Joule heat and cause the temperature change of MSMA sample; Finally, the Hamiltonian action functional of the magnetic shape memory alloy sample is obtained as The subscript r indicates the reference configuration.

3. The method for predicting the high-frequency mechanical-thermal-magnetic-electrical coupled dynamic response of a magnetic shape memory alloy according to claim 2, characterized in that: Total deformation gradient tensor The calculation formula of the velocity v is: Here, the subscript ",t" indicates 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 magnetic permeability, ∈0 is the vacuum dielectric constant; 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) where ρ is the material density of the sample in the current configuration.

4. The method for predicting the high-frequency mechanical-thermal-magnetic-electrical coupled dynamic response of a magnetic shape memory alloy according to claim 2, characterized in that: In order to simulate the elastic response of MSMA samples, the following elastic strain-energy density of two martensitic variants were used: In the formula, is the Lagrangian strain tensor, is the total deformation gradient tensor, is the inverse of the deformation reorientation strain tensor, is the second-order unit tensor; is the second-order elastic modulus.

5. The method for predicting the high-frequency mechanical-thermal-magnetic-electrical coupled dynamic response of a magnetic shape memory alloy according to claim 2, characterized in that: The first control equations of the magnetic shape memory alloy sample are derived by variational method according to the first Hamiltonian action functional, including: right The Gaussian law governing equations of the electric field in Maxwell's equations are obtained by solving the variational equations; right The variational equations are used to obtain the governing equations of Ampere's circuit law in Maxwell's equations; By varying x, we can obtain the motion control equations of magnetic-mechanical coupling; To α i and The evolution equation of the internal variables is obtained by solving the variation equation; right Solving the variation gives the Ohm's law equation; The migration criterion of the twin interface is obtained by taking the variation of Π(t).

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

7. The method for predicting the high-frequency mechanical-thermal-magnetic-electrical coupled dynamic response of a magnetic shape memory alloy according to claim 6, characterized in that: The heat conduction equation is obtained according to the second Hamiltonian action functional, including: After calculating the variation of T, substitute it into R and q r and q t , we get the heat conduction equation and boundary conditions: Where ΔT is the change in temperature; J -1 represents the total deformation gradient Inverse of a determinant; is the conduction current density under the current configuration; N r is the sample area 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 of ± is the critical value of the driving force required to activate the twin interface motion during the reorientation process for both the forward and reverse variants; It represents the difference of the physical quantity on both sides of the twin interface from the negative direction to the positive direction.

8. The method for predicting the high-frequency mechanical-thermal-magnetic-electrical coupled dynamic response of a magnetic shape memory alloy according to claim 1, characterized in that: The second control equations solving step comprises: Establish the geometric model of the sample and the external air; Select elastic and magnetic constitutive models for the sample and external air model; Input boundary conditions and basic material parameters; Calculate the deformation of samples under high-frequency mechanical-thermal-magnetic-electric coupling.

9. An electronic device, characterized in that: The electronic device includes a processor and a memory, wherein the memory stores at least one instruction, at least one program, a code set or an instruction set, and the at least one instruction, the at least one program, the code set or the instruction set is loaded and executed by the processor to implement the method described in any one of claims 1 to 8.

10. A computer-readable storage medium, characterized in that: The storage medium stores at least one instruction, at least one program, a code set or an instruction set, and the at least one instruction, the at least one program, the code set or the instruction set is loaded and executed by the processor to implement the method according to any one of claims 1 to 8.

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