A two-step variational approach towards the modeling of high-frequency thermo-magneto-mechanical response of magnetic shape memory alloys
Fan C, Steinmann P, Wang J, Liang Y (2025)
Publication Type: Journal article
Publication year: 2025
Journal
Book Volume: 204
Article Number: 106272
DOI: 10.1016/j.jmps.2025.106272
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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APA:
Fan, C., Steinmann, P., Wang, J., & Liang, Y. (2025). A two-step variational approach towards the modeling of high-frequency thermo-magneto-mechanical response of magnetic shape memory alloys. Journal of the Mechanics and Physics of Solids, 204. https://doi.org/10.1016/j.jmps.2025.106272
MLA:
Fan, Chengkai, et al. "A two-step variational approach towards the modeling of high-frequency thermo-magneto-mechanical response of magnetic shape memory alloys." Journal of the Mechanics and Physics of Solids 204 (2025).
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