An elastic-viscoplastic model exhibiting continuity of solid and fluid states
type: Item
instance of: scholarly article
title: An elastic-viscoplastic model exhibiting continuity of solid and fluid states
zbMATH Open document ID: 0616.73006
DOI: 10.1016/0020-7225(87)90081-4
author: M. B. Rubin
published in: International Journal of Engineering Science
publication date: 1987-01-01T00:00:00Z
review text: In this paper specific unified consitutive equations for an elastic- viscoplastic material are developed which in the limit of infinite resistance to plastic flow become those of a general hyperelastic isotropic material; and in the limit of zero resistance to plastic flow become those of a general Reiner-Rivlin fluid. The constitutive equations satisfy the restrictions imposed by continuum thermodynamics and are hyperelastic in the sense that the symmetric Piola-Kirchhoff stress is related to a derivative of the Helmholtz free energy. In this formulation the Helmholtz free energy depends on five scalar invariants: two new scalars which are pure measures of ''elastic'' distortional deformation, a measure of total dilatation, a measure of plastic dilatation, and temperature. Specifically, the stress is not characterized by a hypoelastic equation so no special rates of stress need be considered. Both isotropic hardening and a measure of directional hardening which models the Bauschinger effect are included. Finally, examples of simple shear are considered to examine the solid-like and fluid-like response to large deformations including cycles of loading, unloading and reloading.
Mathematics Subject Classification ID: 74A20
Mathematics Subject Classification ID: 76A10
Mathematics Subject Classification ID: 74C99
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 74C10
zbMATH DE Number: 3999367
zbMATH Keywords: unified consitutive equations
zbMATH Keywords: elastic-viscoplastic material
zbMATH Keywords: infinite resistance to plastic flow
zbMATH Keywords: general hyperelastic isotropic material
zbMATH Keywords: limit of zero resistance
zbMATH Keywords: general Reiner-Rivlin fluid
zbMATH Keywords: continuum thermodynamics
zbMATH Keywords: symmetric Piola-Kirchhoff stress
zbMATH Keywords: Helmholtz free energy
zbMATH Keywords: five scalar invariants
zbMATH Keywords: isotropic hardening
zbMATH Keywords: measure of directional hardening
zbMATH Keywords: Bauschinger effect
zbMATH Keywords: simple shear
MaRDI profile type: Publication
full work available at URL: 0020-7225(87)90081-4
OpenAlex ID: W2012733218
cites work: An elastic-viscoplastic model for large deformation
cites work: An Elastic-Viscoplastic Model for Metals Subjected to High Compression
cites work: The visco-plastic approach to problems of plasticity and creep involving geometric non-linear effects
description: scientific article; zbMATH DE number 3999367