Deformations of an elastic, internally constrained material. I: Homogeneous deformations
type: Item
instance of: scholarly article
title: Deformations of an elastic, internally constrained material. I: Homogeneous deformations
zbMATH Open document ID: 0786.73018
DOI: 10.1007/BF00043445
published in: Journal of Elasticity
publication date: 1993-04-01T00:00:00Z
review text: Subject of this extensive research are the finite homogeneous deformations and the stresses accompanying them of an isotropic elastic material subject to Bell's constraint, i.e., the sum of the principal stretches equals three. Firstly, the authors study the kinematics of deformation. Though any small strain deformation is isochoric, large volume preserving deformations as pure shear or simple shear cannot occur. Another consequence of Bell's constraint is that pure dilatation does not exist, i.e., a cube cannot be transformed into a cube of different size. Secondly, based on ordered forces inequalities and ad hoc inequalities, the authors determine the response functions of isotropic elastic materials. Finally, they consider hyperelastic behavior, i.e., they postulate the existence of a strain energy function. It is interesting to note that James F. Bell found the above mentioned constraint experimentally by deforming samples of different annealed metals plastically. He also studied their behavior theoretically within the frame of incremental plasticity. Besides a few exceptions, the results of the present paper are in excellent agreement with Bell's. This is possible since an elastic body and an elastic-plastic body may exhibit the same material response as long as unloading does not occur. This clearly written paper contains an abundancy of results interesting to researchers in elasticity and continuum mechanics. Two additional papers on this topic are announced.
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 74A20
Mathematics Subject Classification ID: 74C99
zbMATH DE Number: 147030
zbMATH Keywords: Bell's constraint
zbMATH Keywords: kinematics of deformation
zbMATH Keywords: ordered forces inequalities
zbMATH Keywords: response functions
zbMATH Keywords: hyperelastic behavior
zbMATH Keywords: incremental plasticity
author: Millard F. Beatty
author: M. Hayes
reviewed by: U. Gamer
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00043445
OpenAlex ID: W2015867287
description: scientific article; zbMATH DE number 147030