Coupled electro-elastic deformation and instabilities of a toroidal membrane

Liu, Z. , McBride, A. , Sharma, B. L., Steinmann, P. and Saxena, P. (2021) Coupled electro-elastic deformation and instabilities of a toroidal membrane. Journal of the Mechanics and Physics of Solids, 151, 104221. (doi: 10.1016/j.jmps.2020.104221)

Abstract

We analyse here the problem of large deformation of dielectric elastomeric membranes under coupled electromechanical loading. Extremely large deformations (enclosed volume changes of 100 times and greater) of a toroidal membrane are studied by the use of a variational formulation that accounts for the total energy due to mechanical and electrical fields. A modified shooting method is adopted to solve the resulting system of coupled and highly nonlinear ordinary differential equations. We demonstrate the occurrence of limit point, wrinkling, and symmetry-breaking buckling instabilities in the solution of this problem. Onset of each of these “reversible” instabilities depends significantly on the ratio of the mechanical load to the electric load, thereby providing a control mechanism for state switching.

• Item Type: Articles
• Additional Information: Basant Lal Sharma acknowledges the partial support of MATRICS grant number MTR/2017/000013 379 from the Science and Engineering Research Board. 380 Paul Steinmann also gratefully acknowledges financial support for this work by the Deutsche Forschungs381 gemeinschaft under GRK2495/B.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: McBride, Professor Andrew and Liu, Dr Zhaowei and Saxena, Dr Prashant and Steinmann, Professor Paul
• Authors: Liu, Z., McBride, A., Sharma, B. L., Steinmann, P., and Saxena, P.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: Journal of the Mechanics and Physics of Solids
• Publisher: Elsevier
• ISSN: 0022-5096
• ISSN (Online): 1873-4782
• Published Online: 11 November 2020
• Copyright Holders: Copyright © 2020 Elsevier Ltd.
• First Published: First published in Journal of the Mechanics and Physics of Solids 151: 104221
• Publisher Policy: Reproduced in accordance with the publisher copyright policy

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
300129		Strategic Support Package: Engineering of Active Materials by Multiscale/Multiphysics Computational Mechanics	Christopher Pearce	Engineering and Physical Sciences Research Council (EPSRC)	EP/R008531/1	ENG - Infrastructure & Environment