Positive definiteness of the elasticity tensor of a residually stressed material
type: Item
instance of: scholarly article
title: Positive definiteness of the elasticity tensor of a residually stressed material
zbMATH Open document ID: 0824.73008
DOI: 10.1007/BF00040848
author: Anne Hoger
published in: Journal of Elasticity
publication date: 1995-05-11T00:00:00Z
review text: This paper is concerned with the linear theory of hyperelastic materials that support a residual stress. The term residual stress is used to refer to an equilibrated stress field in the reference configuration with vanishing associated tractions. In general, the residual stress is not uniform. This fact generates mathematical difficulties in the study of boundary value problems. The author derives conditions on the elasticity tensors that assure that the total work to deform the body will be positive. The relationships of these conditions to the positive definiteness of the elasticity tensors are established. It is shown that in some cases the elasticity tensors associated with the first and second Piola-Kirchhoff stress tensors fail to be positive definite. This is an interesting paper.
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 74G99
Mathematics Subject Classification ID: 74H99
zbMATH DE Number: 753718
zbMATH Keywords: linear theory
zbMATH Keywords: hyperelastic materials
zbMATH Keywords: first and second Piola-Kirchhoff stress tensors
reviewed by: D. Ieşan
MaRDI profile type: Publication
cites work: Q4079139
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full work available at URL: https://doi.org/10.1007/bf00040848
OpenAlex ID: W2014060377
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description: scientific article; zbMATH DE number 753718