New universal relations for nonlinear isotropic elastic materials
type: Item
instance of: scholarly article
title: New universal relations for nonlinear isotropic elastic materials
zbMATH Open document ID: 0602.73017
DOI: 10.1007/BF00042450
published in: Journal of Elasticity
publication date: 1987-01-01T00:00:00Z
review text: A nonlinear isotropic elastic block is subjected to a homogeneous deformation consisting of simple shear superposed on triaxial extension. Two new relations are established for this deformation which are valid for all nonlinear elastic isotropic materials, and hence are universal relations. The first is a relation between the stretch ratios in the plane of shear and the amount of shear when the deformation is supported only by shear tractions. The second relation is established for a thin- walled cylinder under combined extension, inflation and torsion. Each material element of the cylinder undergoes the same local homogeneous deformation of shear superposed on triaxial extension. The properties of this deformation are used to establish a relation between pressure, twisting moment, angle of twist and current dimensions when no axial force is applied to the cylinder. It is shown that these relations also apply for a mixture of a nonlinear isotropic solid and a fluid.
Mathematics Subject Classification ID: 74B20
zbMATH DE Number: 3972301
zbMATH Keywords: nonlinear isotropic elastic block
zbMATH Keywords: homogeneous deformation
zbMATH Keywords: simple shear superposed on triaxial extension
zbMATH Keywords: relation
zbMATH Keywords: stretch ratios
zbMATH Keywords: plane of shear
zbMATH Keywords: amount of shear
zbMATH Keywords: shear tractions
zbMATH Keywords: thin-walled cylinder
zbMATH Keywords: combined extension, inflation and torsion
zbMATH Keywords: pressure
zbMATH Keywords: twisting moment
zbMATH Keywords: angle of twist
zbMATH Keywords: current dimensions
zbMATH Keywords: no axial force
zbMATH Keywords: mixture of a nonlinear isotropic solid and a fluid
author: K. R. Rajagopal
author: Alan S. Wineman
MaRDI profile type: Publication
cites work: Q4023641
cites work: On local and global universal relations in elasticity
cites work: Applications of the theory of interacting continua to the diffusion of a fluid through a nonlinear elastic media
cites work: Incompressible mixtures of Newtonian fluids
cites work: On boundary conditions for a certain class of problems in mixture theory
description: scientific article; zbMATH DE number 3972301