The use of a virtual configuration in formulating constitutive equations for residually stressed elastic materials
type: Item
instance of: scholarly article
title: The use of a virtual configuration in formulating constitutive equations for residually stressed elastic materials
zbMATH Open document ID: 0857.73007
DOI: 10.1007/BF00041874
author: Byron E. Johnson
author: Anne Hoger
published in: Journal of Elasticity
publication date: 1997-03-17T00:00:00Z
review text: The authors present a method by which one can utilise data obtained from standard destructive experiments to derive constitutive equations that describe the mechanical behaviour of residually stressed elastic materials. In contrast to previous methods, the one given here leads to a constitutive equation that is an explicit function of the residual stress, and includes only material parameters that are required to describe the stress free material. The authors first obtain the constitutive equation for a special class of those residually stressed bodies which can be cut up into a finite number of parts, each of which is entirely free of residual stress. Then they introduce the idea of pointwise stress free configurations to obtain the constitutive equation for a more general class of residually stressed bodies. The derivation for this latter class is based on the assumption that each infinitesimally small neighbourhood of the body has an associated stress free configuration called its `virtual configuration'. It also requires that the constitutive equation for the stress free or natural material is known and invertible. The authors go on to illustrate the use of their theory by considering two particular bodies where the undeformed configuration is a thick walled incompressible spherical shell which supports a residual stress. One is an example of the special class and the other an example of the more general class, and in both cases the natural material is a Mooney-Rivlin material. They conclude with a discussion of the relationship between appropriate virtual configurations and destructive experiments. In particular, the use of the theory in improving the design of such experiments and the use of the experiments in obtaining data required to formulate the appropriate constitutive equation are considered.
Mathematics Subject Classification ID: 74A20
Mathematics Subject Classification ID: 74B99
zbMATH DE Number: 858464
zbMATH Keywords: elastic material
zbMATH Keywords: destructive experiments
zbMATH Keywords: Mooney-Rivlin material
reviewed by: P. J. Barratt
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 858464