Variational principles of nonlinear magnetoelastostatics and their correspondences

Sharma, B. L. and Saxena, P. (2020) Variational principles of nonlinear magnetoelastostatics and their correspondences. Mathematics and Mechanics of Solids, (doi: 10.1177/1081286520975808) (Early Online Publication)

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Abstract

We derive the equations of nonlinear magnetoelastostatics using several variational formulations involving the mechanical deformation and an inde- pendent field representing the magnetic component. An equivalence is also discussed, modulo certain boundary integrals or constant integrals, between these formulations using the Legendre transform and properties of Maxwell’s equations. The second variation based bifurcation equations are stated for the incremental fields as well for all five variational principles. When the to- tal potential energy is defined over the infinite space surrounding the body, we find that the inclusion of certain term in the energy principle, associated with the externally applied magnetic field, leads to slight changes in the Maxwell stress tensor and associated boundary conditions. On the other hand, when the energy contained in the magnetic field is restricted to fi- nite volumes, we find that there is a correspondence between the discussed formulations and associated expressions of physical entities. In view of a diverse set of boundary data and nature of externally applied controls in the problems studied in the literature, along with a equally diverse list of variational principles employed in modelling, our analysis emphasises care in the choice of variational principle and unknown fields so that consistency with other choices is also satisfied.

Item Type:Articles
Additional Information:Basant Lal Sharma acknowledges the support of SERB MATRICS grant MTR/2017/ 000013. Prashant Saxena acknowledges the support of startup funds from the James Watt School of Engineering at the University of Glasgow.
Status:Early Online Publication
Refereed:Yes
Glasgow Author(s) Enlighten ID:Saxena, Dr Prashant
Authors: Sharma, B. L., and Saxena, P.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:Mathematics and Mechanics of Solids
Publisher:SAGE Publications
ISSN:1081-2865
ISSN (Online):1741-3028
Published Online:22 December 2020
Copyright Holders:Copyright © 2020 The Authors
First Published:First published in Mathematics and Mechanics of Solids 2020
Publisher Policy:Reproduced in accordance with the publisher copyright policy
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