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Injectivity of the Cauchy-stress tensor along rank-one connected lines under strict rank-one convexity condition

Neff, Patrizio and Mihai, Loredana Angela 2017. Injectivity of the Cauchy-stress tensor along rank-one connected lines under strict rank-one convexity condition. Journal of Elasticity 127 (2) , pp. 309-315. 10.1007/s10659-016-9609-y

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Abstract

In this note, we show that the Cauchy stress tensor σ σ in nonlinear elasticity is injective along rank-one connected lines provided that the constitutive law is strictly rank-one convex. This means that σ(F+ξ⊗η)=σ(F) σ(F+ξ⊗η)=σ(F) implies ξ⊗η=0 ξ⊗η=0 under strict rank-one convexity. As a consequence of this seemingly unnoticed observation, it follows that rank-one convexity and a homogeneous Cauchy stress imply that the left Cauchy-Green strain is homogeneous, as is shown in Mihai and Neff (Int. J. Non-Linear Mech., 2016, to appear).

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Uncontrolled Keywords: rank-one convexity, nonlinear elasticity, Cauchy stress tensor, invertible stressstrain law
Publisher: Springer Verlag
ISSN: 0374-3535
Date of First Compliant Deposit: 28 October 2016
Date of Acceptance: 28 October 2016
Last Modified: 07 Nov 2017 05:19
URI: http://orca.cf.ac.uk/id/eprint/95683

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