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Hyperelastic bodies under homogeneous Cauchy stress induced by three-dimensional non-homogeneous deformations

Mihai, Loredana Angela and Neff, Patrizio 2018. Hyperelastic bodies under homogeneous Cauchy stress induced by three-dimensional non-homogeneous deformations. Mathematics and Mechanics of Solids 23 (4) , pp. 606-616. 10.1177/1081286516682556

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Abstract

In isotropic finite elasticity, unlike in the linear elastic theory, a homogeneous Cauchy stress may be induced by non-homogeneous strains. To illustrate this, we identify compatible nonhomogeneous three-dimensional deformations producing a homogeneous Cauchy stress on a cuboid geometry, and provide an example of an isotropic hyperelastic material, which is not rank-one convex, and for which the homogeneous stress and the associated non-homogeneous strains on a domain similar to those analysed are given explicitly. Mathematics Subject Classification: 74B20, 74G65, 26B25.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Uncontrolled Keywords: nonlinear elasticity; invertible stress-strain law; non-homogeneous deformations; rankone connectivity; loss of ellipticity.
Publisher: SAGE Publications
ISSN: 1081-2865
Date of First Compliant Deposit: 18 November 2016
Date of Acceptance: 5 November 2016
Last Modified: 01 Sep 2018 05:00
URI: http://orca.cf.ac.uk/id/eprint/96257

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