Magnetoelastic deformation of a circular membrane: wrinkling and limit point instabilities

Saxena, P. , Reddy, N. H. and Pradhan, S. P. (2019) Magnetoelastic deformation of a circular membrane: wrinkling and limit point instabilities. International Journal of Non-Linear Mechanics, 116, pp. 250-261. (doi: 10.1016/j.ijnonlinmec.2019.07.006)

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We study the inflation of a weakly magnetizable isotropic incompressible circular membrane in the presence of magnetic field generated by a magnetic dipole. Following the approach in recent papers by Reddy and Saxena (Int. J. Sol. Struct. 136, 203–219, 2018; Int. J. Non-Lin. Mech. 95, 248–263, 2017) we start with a variational formulation, solving the resulting governing equations to determine the equilibria and checking the second variation condition for stability. Conjecture of possibility of multiple equilibria under a single coupled load, and attaining elastic and magnetic limit points made in the above two papers is confirmed in the present work for a circular membrane. Another main focus of this work is on the determination of wrinkling instability in the membrane due to magnetoelastic stresses. Wrinkles along one or both in-plane directions of membrane appear in a majority of loading scenarios due to compressive Maxwell stresses. Our computations demonstrate that wrinkles arise in the central region when dipole and inflation are in the same direction and in the annular region close to the edges when the dipole and inflation are in opposite directions.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Saxena, Dr Prashant
Authors: Saxena, P., Reddy, N. H., and Pradhan, S. P.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:International Journal of Non-Linear Mechanics
ISSN (Online):1878-5638
Published Online:18 July 2019
Copyright Holders:Copyright © 2019 Elsevier Ltd.
First Published:First published in International Journal of Non-Linear Mechanics 116:250-261
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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