Finite strain solutions in compressible isotropic elasticity
type: Item
instance of: scholarly article
title: Finite strain solutions in compressible isotropic elasticity
zbMATH Open document ID: 0654.73030
DOI: 10.1007/BF00042141
author: M. M. Carroll
published in: Journal of Elasticity
publication date: 1988-01-01T00:00:00Z
review text: Three classes of compressible isotropic elastic solids are introduced, for each of which the strain energy, expressed as a function of the three principal invariants of the stretch tensors, is linear in two of its arguments and nonlinear in the third argument. One of these is the class of harmonic materials. Several deformation fields are examined, for which the governing equations, for general compressible isotropic elastic response, reduce to a nonlinear ordinary differential equation. For the three special classes of materials this differential equation may be solved in closed form, giving a deformation field which is independent of the material response function, or its solution may be reduced to a single quadrature, involving the nonlinear material response function.
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 74S30
zbMATH DE Number: 4068399
zbMATH Keywords: strain energy
zbMATH Keywords: function of the three principal invariants of the stretch tensors
zbMATH Keywords: nonlinear in the third argument
zbMATH Keywords: harmonic materials
zbMATH Keywords: deformation fields
zbMATH Keywords: governing equations
zbMATH Keywords: general compressible isotropic elastic response
zbMATH Keywords: nonlinear ordinary differential equation
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00042141
OpenAlex ID: W2003369863
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description: scientific article; zbMATH DE number 4068399