On the convexity of nonlinear elastic energies in the right Cauchy-Green tensor

Title: On the convexity of nonlinear elastic energies in the right Cauchy-Green tensor
Creator: Gao, David; Neff, Patrizio; Roventa, Ionel; Thiel, Christian
Date: 2017
Type: Text; Journal article
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/159312
Identifier: vital:11948
Identifier: https://doi.org/10.1007/s10659-016-9601-6
Identifier: ISSN:0374-3535
Abstract: We present a sufficient condition under which a weak solution of the Euler-Lagrange equations in nonlinear elasticity is already a global minimizer of the corresponding elastic energy functional. This criterion is applicable to energies which are convex with respect to the right Cauchy-Green tensor , where denotes the gradient of deformation. Examples of such energies exhibiting a blow up for are given.
Publisher: Springer
Relation: Journal of Elasticity Vol. 127, no. 2 (2017), p. 303-308
Rights: Open Access
Rights: This metadata is freely available under a CCO license
Subject: 0102 Applied Mathematics; 0905 Civil Engineering; 0912 Materials Engineering; Nonlinear elasticity; Convexity; Global minimizers; Second Piola-Kirchhoff stress tensor
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