Non-elliptic elastic materials and the modelling of elastic-plastic behavior for finite deformation
type: Item
instance of: scholarly article
title: Non-elliptic elastic materials and the modelling of elastic-plastic behavior for finite deformation
zbMATH Open document ID: 0608.73044
DOI: 10.1016/0022-5096(87)90012-3
author: James K. Knowles
author: Rohan Abeyaratne
published in: Journal of the Mechanics and Physics of Solids
publication date: 1987-01-01T00:00:00Z
review text: For illustrative purposes this paper treats a special problem in the theory of finite deformations of elastic materials whose associated displacement equations of equilibrium do not remain elliptic at all strains. The typical deformation arising in this problem possesses a discontinuous gradient, so that quasi-static motions involving such equilibrium states may be dissipative. For a special class of such ''non- elliptic'' elastic materials, it is shown that the macroscopic response in the problem treated may be precisely of the form associated with elastic- perfectly plastic behavior. The counterparts of yield, plastic strain and plastic strain rate are determined by the underlying the elastic strain energy function.
Mathematics Subject Classification ID: 74B20
zbMATH DE Number: 3984697
zbMATH Keywords: twist problem
zbMATH Keywords: torque-twist relations
zbMATH Keywords: set of equilibrium states
zbMATH Keywords: medium with cavity
zbMATH Keywords: attractor for quasi-static motions
zbMATH Keywords: unobservable equilibrium states
zbMATH Keywords: internal variable formalism
zbMATH Keywords: maximum-dissipation
zbMATH Keywords: discontinuous gradient
zbMATH Keywords: dissipative
zbMATH Keywords: ''non-elliptic'' elastic materials
zbMATH Keywords: macroscopic response
zbMATH Keywords: elastic-perfectly plastic behavior
MaRDI profile type: Publication
full work available at URL: 0022-5096(87)90012-3
OpenAlex ID: W2000506952
cites work: Discontinuous deformation gradients in plane finite elastostatics of incompressible materials
cites work: Q3240173
cites work: The elastic energy-momentum tensor
cites work: Finite deformation by mechanical twinning
cites work: Displacive phase transformations in solids
cites work: On the dissipation associated with equilibrium shocks in finite elasticity
cites work: On the failure of ellipticity and the emergence of discontinuous deformation gradients in plane finite elastostatics
cites work: Inelastic constitutive relations for solids: An internal-variable theory and its application to metal plasticity
description: scientific article; zbMATH DE number 3984697