The constitutive equation for finite deformations of a transversely isotropic hyperelastic material with residual stress
type: Item
instance of: scholarly article
title: The constitutive equation for finite deformations of a transversely isotropic hyperelastic material with residual stress
zbMATH Open document ID: 0799.73016
DOI: 10.1007/BF00705801
author: Anne Hoger
published in: Journal of Elasticity
publication date: 1994-11-13T00:00:00Z
review text: The strain energy \(\widehat{\sigma}\) for a material described in the title is viewed as a scalar-valued function of the right stretch tensor \(U\) and a residual stress tensor \(T^ 0\) which is invariant under the set of all rotations about a single preferred axis. Thus \(\widehat{\sigma}\) can be expressed as a function of 18 basic polynomial invariants of \(U\) and \(T^ 0\). Assuming that such \(\widehat{\sigma}\) is known, the author shows how the Piola-Kirchhoff stress tensor and the Cauchy stress tensor can be computed in terms of \(\partial \widehat{\sigma}/\partial U\).
reviewed by: Józef Ignaczak
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 74A20
zbMATH DE Number: 549821
zbMATH Keywords: Cauchy stress tensor
zbMATH Keywords: Piola-Kirchhoff stress tensor
zbMATH Keywords: strain energy
zbMATH Keywords: right stretch tensor
zbMATH Keywords: residual stress tensor
zbMATH Keywords: polynomial invariants
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 549821