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

Saxena, Prashant and Reddy, Narravula Harshavardhan and Pradhan, Satya Prakash (2019) Magnetoelastic deformation of a circular membrane: Wrinkling and limit point instabilities. International Journal of Non-Linear Mechanics, 116 . pp. 250-261. ISSN 0020-7462.

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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 (2018, 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:Article
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URLURL TypeDescription
Saxena, Prashant0000-0001-5071-726X
Reddy, Narravula Harshavardhan0000-0003-3897-8162
Additional Information:© 2019 Elsevier Ltd. Received 31 January 2019, Revised 12 June 2019, Accepted 12 July 2019, Available online 18 July 2019. Major part of this work was conducted when PS was based at IIT Hyderabad,India. This research was financially supported by a Ramanujan fellowship awarded to PS by the Science and Engineering Research Board.
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Science and Engineering Research Board (SERB)UNSPECIFIED
Subject Keywords:Magnetoelasticity; Wrinkling; Instability; Membrane; Limit point
Record Number:CaltechAUTHORS:20190718-141844950
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Official Citation:Prashant Saxena, Narravula Harshavardhan Reddy, Satya Prakash Pradhan, Magnetoelastic deformation of a circular membrane: Wrinkling and limit point instabilities, International Journal of Non-Linear Mechanics, Volume 116, 2019, Pages 250-261, ISSN 0020-7462, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:97243
Deposited By: Tony Diaz
Deposited On:18 Jul 2019 21:25
Last Modified:22 Oct 2019 21:33

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