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Dielectric elastomers: Asymptotically-correct three-dimensional displacement field

Gupta, Ramesh and Harursampath, Dineshkumar (2015) Dielectric elastomers: Asymptotically-correct three-dimensional displacement field. In: INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 87 . pp. 1-12.

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Official URL: http://dx.doi.org/ 10.1016/j.ijengsci.2014.10.006

Abstract

Asymptotically-accurate dimensional reduction from three to two dimensions and recovery of 3-D displacement field of non-prestretched dielectric hyperelastic membranes are carried out using the Variational Asymptotic Method (VAM) with moderate strains and very small ratio of the membrane thickness to its shortest wavelength of the deformation along the plate reference surface chosen as the small parameters for asymptotic expansion. Present work incorporates large deformations (displacements and rotations), material nonlinearity (hyperelasticity), and electrical effects. It begins with 3-D nonlinear electroelastic energy and mathematically splits the analysis into a one-dimensional (1-D) through-the-thickness analysis and a 2-D nonlinear plate analysis. Major contribution of this paper is a comprehensive nonlinear through-the-thickness analysis which provides a 2-D energy asymptotically equivalent of the 3-D energy, a 2-D constitutive relation between the 2-D generalized strain and stress tensors for the plate analysis and a set of recovery relations to express the 3-D displacement field. Analytical expressions are derived for warping functions and stiffness coefficients. This is the first attempt to integrate an analytical work on asymptotically-accurate nonlinear electro-elastic constitutive relation for compressible dielectric hyperelastic model with a generalized finite element analysis of plates to provide 3-D displacement fields using VAM. A unified software package `VAMNLM' (Variational Asymptotic Method applied to Non-Linear Material models) was developed to carry out 1-D non-linear analysis (analytical), 2-D non-linear finite element analysis and 3-D recovery analysis. The applicability of the current theory is demonstrated through an actuation test case, for which distribution of 3-D displacements are provided. (C) 2014 Elsevier Ltd. All rights reserved.

Item Type: Journal Article
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Additional Information: Copy right for this article belongs to the PERGAMON-ELSEVIER SCIENCE LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND
Keywords: VAM; Dielectric; Elastomer; Hyperelastic; Membrane; Actuators; VAMNLM
Department/Centre: Division of Mechanical Sciences > Aerospace Engineering (Formerly, Aeronautical Engineering)
Date Deposited: 19 Mar 2015 12:07
Last Modified: 19 Mar 2015 12:07
URI: http://eprints.iisc.ernet.in/id/eprint/51041

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