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

Neff, Patrizio and Mihai, Loredana Angela ORCID: https://orcid.org/0000-0003-0863-3729 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:	23 Nov 2024 05:15
URI:	https://orca.cardiff.ac.uk/id/eprint/95683

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