A class of univeral relations in isotropic elasticity theory
type: Item
instance of: scholarly article
title: A class of univeral relations in isotropic elasticity theory
zbMATH Open document ID: 0603.73010
DOI: 10.1007/BF00043019
published in: Journal of Elasticity
publication date: 1987-01-01T00:00:00Z
review text: A class of universal relations for isotropic elastic materials is described by the tensor equation \(TB=BT\). This simple rule yields at most three component relations which are the generators of many known universal relations for isotropic elasticity theory, including the well- known universal rule for a simple shear. Universal relations for four families of nonhomogeneous deformations known to be controllable in every incompressible, homogeneous and isotropic elastic material are exhibited. These same universal relations may hold for special compressible materials. New universal relations for a homogeneous controllable shear, a nonhomogeneous shear, and a variable extension are derived. The general universal relation for an arbitrary isotropic tensor function of a symmetric tensor also is noted.
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 74E15
zbMATH DE Number: 3974395
zbMATH Keywords: Cauchy stress related to Cauchy-Green deformation tensor
zbMATH Keywords: universal relations
zbMATH Keywords: four families of nonhomogeneous deformations
zbMATH Keywords: incompressible
zbMATH Keywords: homogeneous and isotropic elastic material
zbMATH Keywords: homogeneous controllable shear
zbMATH Keywords: nonhomogeneous shear
zbMATH Keywords: variable extension
zbMATH Keywords: isotropic tensor function
zbMATH Keywords: symmetric tensor
author: Millard F. Beatty
MaRDI profile type: Publication
cites work: Q4023641
cites work: Q4128080
full work available at URL: https://doi.org/10.1007/bf00043019
OpenAlex ID: W2077947177
description: scientific article; zbMATH DE number 3974395