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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Abstract
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 |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| 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: | 1081-2865 |
| 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 |
| Related URLs: |
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