On constitutive inequalities and bifurcation in elastic-plastic solids with a yield-surface vertex
type: Item
instance of: scholarly article
title: On constitutive inequalities and bifurcation in elastic-plastic solids with a yield-surface vertex
zbMATH Open document ID: 0668.73004
DOI: 10.1016/0022-5096(89)90012-4
author: H. Petryk
published in: Journal of the Mechanics and Physics of Solids
publication date: 1989-01-01T00:00:00Z
review text: A constitutive inequality for time-independent elastic-plastic models of polycrystalline metals at finite strain is derived from the known constitutive framework for single metal crystals obeying the normality and symmetry postulates. Consequences of the inequality are examined for a general class of nonlinear constitutive rate equations at a yield- surface vertex. It is demonstrated that existence of a strain-rate potential and the normality flow rule can be inferred from the inequality alone. With the help of the constitutive inequality, it is proved that bifurcation in velocities is ruled out by positive definiteness of the quadratic functional based on the tangent moduli. Micromechanically-based justification for linearization of the bifurcation problem along a regular deformation path is obtained in that way, without the need of specifying the full constitutive law. As another example of application of the constitutive inequality, explicit restrictions on phenomenological models of material behaviour at a yield-surface vertex are derived.
Mathematics Subject Classification ID: 74A20
Mathematics Subject Classification ID: 74B99
Mathematics Subject Classification ID: 74C99
Mathematics Subject Classification ID: 74D99
zbMATH DE Number: 4094914
zbMATH Keywords: time-independent elastic-plastic models
zbMATH Keywords: polycrystalline metals
zbMATH Keywords: finite strain
zbMATH Keywords: nonlinear constitutive rate equations
zbMATH Keywords: yield-surface vertex
zbMATH Keywords: linearization
zbMATH Keywords: regular deformation path
MaRDI profile type: Publication
full work available at URL: 0022-5096(89)90012-4
OpenAlex ID: W2065414131
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description: scientific article; zbMATH DE number 4094914