Modeling the dynamic magneto-mechanical response of magnetic shape memory alloys based on Hamilton’s principle: The governing equation system

• Published in: Journal of the mechanics and physics of solids Vol. 160; p. 104761
• Main Authors: Wang, Jiong, Fan, Chengkai, Steinmann, Paul
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 01.03.2022; Elsevier BV
• Subjects: Constitutive modeling; Criteria; Dynamic response; Gallium; Hamilton's principle; Independent variables; Magnetic shape memory alloys; Manganese; Mathematical models; Maxwell's equations; Mechanical analysis; Nickel base alloys; Shape memory alloys; Single crystals; Variant reorientation; Dynamic response; Variant reorientation; Hamilton’s principle; Magnetic shape memory alloys; Constitutive modeling
• ISSN: 0022-5096; 1873-4782
• DOI: 10.1016/j.jmps.2021.104761

The governing equation system for modeling the high-frequency dynamic magneto-mechanical response of magnetic shape memory alloys (MSMAs) is formulated based on Hamilton’s principle. First, by taking the single-crystalline Ni-Mn-Ga alloy as a representative member of MSMAs, we introduce some constitutive assumptions and material constants. Then, Hamilton’s action integral is established for a MSMA sample subject to coupled magnetic and mechanical loads. By calculating the variation of Hamilton’s action integral with respect to the independent variables, we derive the Maxwell’s equations, the mechanical dynamic equations and some evolution laws for the internal variables in the effective magnetization. Furthermore, by studying the variation of Hamilton’s action integral with respect to the path of the variant state distribution, the criteria for predicting the motion of twin interfaces in the sample are established. Combining the above equations and the twin interface motion criteria, the governing equation system for modeling the high-frequency dynamic magneto-mechanical response of the MSMA sample is formulated, which lays the foundation for future numerical simulations and underlying mechanism analyses. For convenience of practical application of the current model, we further adopt some simplifications and derive some analytical formulas from the governing equation system, which provide good predictions for the response of the MSMA sample subject to some typical loading conditions. •High-frequency dynamic magneto-mechanical response of MSMAs is studied.•The governing equation system is formulated based on Hamilton’s principle.•The criteria of twin interface motion in MSMA samples are established.•Some analytical formulas are derived under simplified conditions.•Response of a MSMA sample subject to typical loading conditions is predicted.