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Haldar K, Lagoudas DC. Lie symmetry and conservation laws for magneto-static magnetic shape memory alloys system. Proc Math Phys Eng Sci. 2020;476(2240):20200168doi: 10.1098/rspa.2020.0168.
Haldar, K., & Lagoudas, D. C. (2020). Lie symmetry and conservation laws for magneto-static magnetic shape memory alloys system. Proceedings. Mathematical, physical, and engineering sciences, 476(2240), 20200168. https://doi.org/10.1098/rspa.2020.0168
Haldar, Krishnendu, and Lagoudas, Dimitris C. "Lie symmetry and conservation laws for magneto-static magnetic shape memory alloys system." Proceedings. Mathematical, physical, and engineering sciences vol. 476,2240 (2020): 20200168. doi: https://doi.org/10.1098/rspa.2020.0168
Haldar K, Lagoudas DC. Lie symmetry and conservation laws for magneto-static magnetic shape memory alloys system. Proc Math Phys Eng Sci. 2020 Aug;476(2240):20200168. doi: 10.1098/rspa.2020.0168. Epub 2020 Aug 05. PMID: 32922153; PMCID: PMC7482205.
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Proc Math Phys Eng Sci. 2020 Aug;476(2240):20200168. doi: 10.1098/rspa.2020.0168. Epub 2020 Aug 05.

Lie symmetry and conservation laws for magneto-static magnetic shape memory alloys system.

Proceedings. Mathematical, physical, and engineering sciences

Krishnendu Haldar, Dimitris C Lagoudas

Affiliations

  1. Department of Aerospace Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India.
  2. Department of Aerospace Engineering and Department of Materials Science and Engineering, Texas A&M University, College Station, TX 77843, USA.

PMID: 32922153 PMCID: PMC7482205 DOI: 10.1098/rspa.2020.0168

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.

© 2020 The Author(s).

Keywords: conservation laws; lie symmetry; magnetic shape memory alloys; symmetry breaking

Conflict of interest statement

We do not have any competing interests.

References

  1. Philos Trans A Math Phys Eng Sci. 2013 Nov 18;371(2005):20120344 - PubMed
  2. Proc Math Phys Eng Sci. 2014 Sep 8;470(2169):20140216 - PubMed

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