A two-step variational approach towards the modeling of high-frequency thermo-magneto-mechanical response of magnetic shape memory alloys

IF 6 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids Pub Date : 2025-07-16 DOI:10.1016/j.jmps.2025.106272

Chengkai Fan , Paul Steinmann , Jiong Wang , Yongtao Liang

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Abstract

In this paper, a two-step variational approach is proposed to study the high-frequency thermo-magneto-mechanical response of magnetic shape memory alloy (MSMA) samples. In the first step, a Hamilton’s action integral is formulated for an MSMA sample under dynamic magneto-mechanical loads, accounting for twin interface motions and the eddy current effect. Constitutive assumptions are introduced by selecting the single-crystalline Ni–Mn–Ga alloy as a representative member of MSMA. Based on Hamilton’s action integral and through variational calculations, Maxwell’s equations, Ohm’s law, the mechanical dynamic equation, the evolution equations for internal variables and the twin interface motion criteria are derived. In the second step, the temperature change and heat transfer in the MSMA sample during the dynamic loading process are analyzed. For that purpose, a second Hamilton’s action integral is formulated, with the temperature field as the state variable. Also through variational calculations, the heat conduction equation is derived. By combining the results of the variational method, the governing equation system of the model is established. To solve the governing equation system, a numerical scheme is developed based on the software COMSOL Multiphysics. The efficiency of the current model is validated by studying the thermo-magneto-mechanical response of an MSMA sample in stress-assisted cyclic field-loading tests, with different cooling airflow convective velocities considered. From the obtained numerical results, the evolution curves of axial strain and average temperature of the MSMA sample are plotted, which show good consistency with the experimental data. Furthermore, the distribution of the temperature field and the eddy current density in the sample can be simulated, which provide a comprehensive description of the response of the MSMA sample under high-frequency dynamic loads.

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磁性形状记忆合金高频热-磁-力响应建模的两步变分方法

本文提出了一种两步变分方法来研究磁性形状记忆合金（MSMA）样品的高频热-磁-力响应。首先，考虑双界面运动和涡流效应，对动态磁机械载荷下的MSMA样品建立了Hamilton作用积分。选取单晶Ni-Mn-Ga合金作为MSMA的代表成员，介绍了本构假设。在Hamilton作用积分的基础上，通过变分计算，导出了麦克斯韦方程、欧姆定律、力学动力学方程、内变量演化方程和双界面运动准则。第二步，分析了动态加载过程中MSMA试样的温度变化和传热特性。为此，以温度场为状态变量，建立了第二个哈密顿作用积分。通过变分计算，导出了热传导方程。结合变分方法的结果，建立了模型的控制方程组。为了求解控制方程组，基于COMSOL Multiphysics软件开发了一个数值格式。在考虑不同冷却气流对流速度的应力辅助循环现场加载试验中，研究了MSMA试样的热-磁-力响应，验证了当前模型的有效性。根据得到的数值结果，绘制了MSMA试样的轴向应变和平均温度的演化曲线，与实验数据具有较好的一致性。此外，还可以模拟样品中的温度场和涡流密度分布，全面描述高频动载荷作用下MSMA样品的响应。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of The Mechanics and Physics of Solids 物理-材料科学：综合

CiteScore

9.80

自引率

9.40%

发文量

276

审稿时长

52 days

期刊介绍： The aim of Journal of The Mechanics and Physics of Solids is to publish research of the highest quality and of lasting significance on the mechanics of solids. The scope is broad, from fundamental concepts in mechanics to the analysis of novel phenomena and applications. Solids are interpreted broadly to include both hard and soft materials as well as natural and synthetic structures. The approach can be theoretical, experimental or computational.This research activity sits within engineering science and the allied areas of applied mathematics, materials science, bio-mechanics, applied physics, and geophysics. The Journal was founded in 1952 by Rodney Hill, who was its Editor-in-Chief until 1968. The topics of interest to the Journal evolve with developments in the subject but its basic ethos remains the same: to publish research of the highest quality relating to the mechanics of solids. Thus, emphasis is placed on the development of fundamental concepts of mechanics and novel applications of these concepts based on theoretical, experimental or computational approaches, drawing upon the various branches of engineering science and the allied areas within applied mathematics, materials science, structural engineering, applied physics, and geophysics. The main purpose of the Journal is to foster scientific understanding of the processes of deformation and mechanical failure of all solid materials, both technological and natural, and the connections between these processes and their underlying physical mechanisms. In this sense, the content of the Journal should reflect the current state of the discipline in analysis, experimental observation, and numerical simulation. In the interest of achieving this goal, authors are encouraged to consider the significance of their contributions for the field of mechanics and the implications of their results, in addition to describing the details of their work.