Vol. 11, No. 3, 2016

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An Eulerian formulation for large deformations of elastically isotropic elastic-viscoplastic membranes

M. B. Rubin and Ben Nadler

Vol. 11 (2016), No. 3, 197–216

Typical models of membrane-like structures use a Lagrangian formulation of a hyperelastic membrane with a specified reference configuration. Here, an Eulerian formulation is proposed for modeling elastically isotropic, elastic-viscoplastic membranes. The membrane is modeled as a composite of an elastic and an inelastic component with evolution equations for elastic deformation tensors for each component. The model includes hyperelastic response as a special case and has a smooth elastic-inelastic transition capable of modeling both rate-independent and rate-dependent inelastic response. Strongly objective numerical algorithms are developed for integrating the proposed evolution equations. Also, an example of an initially flat circular membrane loaded by a follower pressure is considered to examine: rate-independent elastic and elastic-plastic responses, as well as rate-dependent inelastic relaxation effects.

Eulerian formulation, elastic-viscoplastic, membranes, large deformations, smooth elastic-inelastic transition
Received: 8 July 2015
Revised: 29 November 2015
Accepted: 4 December 2015
Published: 25 February 2016
M. B. Rubin
Faculty of Mechanical Engineering
Technion – Israel Institute of Technology
32000 Haifa
Ben Nadler
Department of Mechanical Engineering
University of Victoria
Victoria, BC V8W 3P6