On equilibrium equations and their perturbations using three different variational formulations of nonlinear electroelastostatics

Saxena, P. and Sharma, B. L. (2020) On equilibrium equations and their perturbations using three different variational formulations of nonlinear electroelastostatics. Mathematics and Mechanics of Solids, 25(8), pp. 1589-1609. (doi: 10.1177/1081286520911073)

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We derive the equations of nonlinear electroelastostatics using three different variational formulations involving the deformation function and an independent field variable representing the electric character - considering either one of the electric field E, electric displacement D, or electric polarization P. The first variation of the energy functional results in the set of Euler-Lagrange partial differential equations which are the equilibrium equations, boundary conditions, { and certain constitutive equations} for the electroelastic system. The partial differential equations for obtaining the bifurcation point have been also found using the second variation based bilinear functional. We show that the well-known Maxwell stress in vacuum is a natural outcome of the derivation of equations from the variational principles and does not depend on the formulation used. As a result of careful analysis it is found that there are certain terms in the bifurcation equation which appear difficult to obtain by an ordinary perturbation based analysis of the Euler-Lagrange equation. From a practical viewpoint, the formulations based on E and D result in simpler equations and are anticipated to be more suitable for analysing problems of stability as well as post-buckling behaviour.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Saxena, Dr Prashant
Authors: Saxena, P., and Sharma, B. L.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:Mathematics and Mechanics of Solids
Publisher:SAGE Publications
ISSN (Online):1741-3028
Published Online:27 April 2020
Copyright Holders:Copyright © 2020 The Authors
First Published:First published in Mathematics and Mechanics of Solids 25(8): 1589-1609
Publisher Policy:Reproduced in accordance with the publisher copyright policy
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