Journal
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
Volume 160, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jmps.2021.104761
Keywords
Magnetic shape memory alloys; Dynamic response; Variant reorientation; Hamilton's principle; Constitutive modeling
Funding
- National Natural Science Foundation of China [12172133]
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The governing equation system for modeling the high-frequency dynamic magneto-mechanical response of MSMAs is formulated based on Hamilton's principle. The system includes Maxwell's equations, mechanical dynamic equations, evolution laws for internal variables, and criteria for predicting twin interface motion. This lays the foundation for future numerical simulations and mechanism analyses.
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.
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