Communications in Mathematical Sciences

Volume 10 (2012)

Number 1

Special Issue on the Occasion of C. David Levermore’s Sixtieth Birthday

A variational approximation scheme for radial polyconvex elasticity that preserves the positivity of Jacobians

Pages: 87 – 115

DOI: https://dx.doi.org/10.4310/CMS.2012.v10.n1.a5

Authors

Alexey Miroshnikov (Department of Mathematics, University of Maryland, College Park)

Athanasios E. Tzavaras (Department of Applied Mathematics, University of Crete, Heraklion, Greece)

Abstract

We consider the equations describing the dynamics of radial motions for isotropic elastic materials; these form a system of non-homogeneous conservation laws. We construct a variational approximation scheme that decreases the total mechanical energy and at the same time leads to physically realizable motions that avoid interpenetration of matter.

Keywords

elasticity, polyconvex, variational approximation

2010 Mathematics Subject Classification

35L70, 49J45, 74B20, 74H20

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Published 14 October 2011