Generalized solutions in the theory of plasticity
type: Item
instance of: scholarly article
title: Generalized solutions in the theory of plasticity
zbMATH Open document ID: 0633.73042
DOI: 10.1016/0021-8928(86)90134-6
author: B. A. Druyanov
published in: Journal of Applied Mathematics and Mechanics
publication date: 1986-01-01T00:00:00Z
review text: The present paper shows that certain generalization of the Mises principle makes it possible to impart to the inequality expressing it a divergent form and enables us to write it in integral form. From this it follows that in the incompressible plastic medium the surface of discontinuity in the tangential velocity component serves as the surface of maximum tangential stresses, with tangential stress directed along the velocity jump vector. In a compressible plastic medium the stress discontinuity is determined from the condition that the direction of the six-dimensional deformation velocity ``vector'' is continuous. The problem considered here is that of steady motion of a strip of finite thickness undergoing pure shear, in a rigid-plastic hardening medium. The emission of heat caused by plastic deformation and its effect on the functions of state and the forces of inertia are all taken into account. It is shown that under certain specified conditions the strip thickness may tend to zero, i.e. the appearance of isothermal velocity discontinuities is possible. The adiabatic and quasistatic cases are discussed.
Mathematics Subject Classification ID: 74C99
Mathematics Subject Classification ID: 74B99
Mathematics Subject Classification ID: 74D99
zbMATH DE Number: 4031130
zbMATH Keywords: generalization of the Mises principle
zbMATH Keywords: inequality
zbMATH Keywords: divergent form
zbMATH Keywords: integral form
zbMATH Keywords: incompressible plastic medium
zbMATH Keywords: surface of discontinuity
zbMATH Keywords: tangential velocity component
zbMATH Keywords: surface of maximum tangential stresses
zbMATH Keywords: stress discontinuity
zbMATH Keywords: steady motion
zbMATH Keywords: strip of finite thickness
zbMATH Keywords: pure shear
zbMATH Keywords: rigid-plastic hardening
zbMATH Keywords: isothermal velocity discontinuities
zbMATH Keywords: adiabatic
zbMATH Keywords: quasistatic cases
MaRDI profile type: Publication
full work available at URL: 0021-8928(86)90134-6
OpenAlex ID: W2010632774
cites work: Q4097611
cites work: Q3674160
cites work: Shear waves in hardening rigidly plastic bodies
cites work: Q3330637
description: scientific article; zbMATH DE number 4031130