On the response and symmetry of elastic materials with internal constraints
type: Item
instance of: scholarly article
title: On the response and symmetry of elastic materials with internal constraints
zbMATH Open document ID: 0629.73003
DOI: 10.1007/BF00251389
author: B. George
published in: Archive for Rational Mechanics and Analysis
publication date: 1987-01-01T00:00:00Z
review text: Elastic material is one where the Cauchy stress T is a function of the deformation gradient. The material is constrained if the accessible values of F are only those which belong to a submanifold \({\mathcal M}\) of the set of tensors with positive determinant. The constraint is internal if QF\(\in {\mathcal M}\) for all \(F\in {\mathcal M}\) and for all proper orthogonal tensors Q. Notice that the authors do not request that the identity tensor belong to \({\mathcal M}\); this fact renders certain points of the analysis subtler and certain assertions perhaps less palatable to some readers. A concept of group of symmetry k for the constraint is introduced and explored; examples are provided. A separate concept of group of material symmetry is successively introduced and studied as a subgroup of k; it includes transformations under which the constraint and the space of admissible active stresses are both invariant. Delicate questions arise due to the `interaction' between the two conditions of invariance and to the indeterminancy of active stress. Ample space is finally given to the response of some special types of materials and the corresponding representation formulae.
reviewed by: Gianfranco Capriz
Mathematics Subject Classification ID: 74A99
Mathematics Subject Classification ID: 74B20
zbMATH DE Number: 4024862
zbMATH Keywords: internal constraint
zbMATH Keywords: group of symmetry
zbMATH Keywords: conditions of invariance
zbMATH Keywords: indeterminancy of active stress
MaRDI profile type: Publication
cites work: Thermodynamics of a continuum with internal constraints
cites work: The thermodynamics of constrained materials
cites work: Q4066685
cites work: On the response functions of elastic materials
cites work: On representations for isotropic functions. I: Isotropic functions of symmetric tensors and vectors. II: Isotropic functions of skew-symmetric tensors, symmetric tensors, and vectors
description: scientific article; zbMATH DE number 4024862