Comments on loss of strong ellipticity in elastoplasticity
type: Item
instance of: scholarly article
title: Comments on loss of strong ellipticity in elastoplasticity
zbMATH Open document ID: 0980.74008
DOI: 10.1016/S0020-7683(99)00062-1
author: N. Delaunay
published in: International Journal of Solids and Structures
publication date: 2000-11-22T00:00:00Z
review text: After a detailed historical introduction, the author considers a rate-independent infinitesimal model, the loss of positiveness of symmetric part of acoustic tensor corresponding to local stability. Taking into account various bifurcation criteria for multisurface plasticity, the author determines plastic hardening moduli and their critical values together with critical orientation (for single surface plasticity, non-associative flow rules, and linear isotropic elasticity). The principal axes of second-order tensors of plastic potential and yield surfaces are coaxial. It is suggested that the critical orientations are identical for all principal directions, except for the case of double eigenvalues of plastic potential and yield surfaces. Some additional expressions are obtained for solids of Raniecki type. Examples concerning the loss of strong ellipticity and classical shear localization are compared for axially-symmetric compression and tension.
reviewed by: M. Mişicu
Mathematics Subject Classification ID: 74C05
Mathematics Subject Classification ID: 74G60
zbMATH DE Number: 1488668
zbMATH Keywords: rate-independent infinitesimal model
zbMATH Keywords: symmetric part of acoustic tensor
zbMATH Keywords: local stability
zbMATH Keywords: bifurcation criteria
zbMATH Keywords: multisurface plasticity
zbMATH Keywords: plastic hardening moduli
zbMATH Keywords: critical orientation
zbMATH Keywords: tensors of plastic potential
zbMATH Keywords: yield surfaces
zbMATH Keywords: principal directions
zbMATH Keywords: double eigenvalues
zbMATH Keywords: shear localization
zbMATH Keywords: axially-symmetric compression
zbMATH Keywords: tension
describes a project that uses: Mathematica
MaRDI profile type: Publication
full work available at URL: s0020-7683(99)00062-1
OpenAlex ID: W2044174398
description: scientific article; zbMATH DE number 1488668