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Lie symmetry and conservation laws for magneto-static magnetic shape memory alloys system
Krishnendu Haldar1, Dimitris C Lagoudas2
1Department of Aerospace Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India.
Abstract:
Magnetic shape memory alloys (MSMAs) have drawn significant research attention as potential high actuation energy multi-functional materials. Such a dissipative material system can be considered as a solid continuum interacting with a magnetic field. A continuum-based phenomenological model provides a magneto-mechanical system of equations that simulates and predicts primary MSMA behaviours. In this work, we investigate the local symmetries of the MSMA system equations through the Lie group analysis. Symmetry breaking due to stable-unstable transition is analysed. The conservation laws are derived, and their physical meaning is scrutinized.
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