A note on non-homogeneous deformations with homogeneous Cauchy stress for a strictly rank-one convex energy in isotropic hyperelasticity

Schweickert, Eva, Mihai, L. Angela ORCID: https://orcid.org/0000-0003-0863-3729, Martin, Robert J. and Neff, Patrizio 2020. A note on non-homogeneous deformations with homogeneous Cauchy stress for a strictly rank-one convex energy in isotropic hyperelasticity. International Journal of Non-Linear Mechanics 119 , 103282. 10.1016/j.ijnonlinmec.2019.103282

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Abstract

It has recently been shown that for a Cauchy stress response induced by a strictly rank-one convex hyperelastic energy potential, a homogeneous Cauchy stress tensor field cannot correspond to a non-homogeneous deformation if the deformation gradient has discrete values, i.e. if the deformation is piecewise affine linear and satisfies the Hadamard jump condition. In this note, we expand upon these results and show that they do not hold for arbitrary deformations by explicitly giving an example of a strictly rank-one convex energy and a non-homogeneous deformation such that the induced Cauchy stress tensor is constant. In the planar case, our example is related to another previous result concerning criteria for generalized convexity properties of conformally invariant energy functions, which we extend to the case of strict rank-one convexity.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Elsevier
ISSN:	0020-7462
Date of First Compliant Deposit:	16 October 2019
Date of Acceptance:	20 September 2019
Last Modified:	09 Nov 2023 23:53
URI:	https://orca.cardiff.ac.uk/id/eprint/126076

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