The structure of rank-one-convex quadratic forms on linear elastic strains

Zhang, Kewei (2002) The structure of rank-one-convex quadratic forms on linear elastic strains. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 133 (1). pp. 213-224. ISSN 0308-2105

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Abstract

We classify the Morse indices for rank-convex quadratic forms defined on the space of linear elastic strains in two- and three-dimensional linear elasticity. For the higher-dimensional case n > 3, we give a universal lower bound of the largest possible Morse index and various upper bound of this index. We show in the three-dimensional case that the Morse index is at most 1, and in this case the nullity cannot exceed 2. Examples are given that show that the estimates can be reached. We apply the results to study the critical points for smooth rank-one convex functions defined on the space of linear strains. We also examine an example and construct a quasiconvex function that vanishes in a finite set in the direct sum of the null subspace and the negative subspace of the rank-one quadratic form.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Kewei Zhang
Date Deposited: 06 Feb 2012 20:16
Last Modified: 10 Jul 2012 09:10
URI: http://sro.sussex.ac.uk/id/eprint/25041
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