On the Nature of Normality of Plastic Strain Rate and Convexity of Yield Surfaces in Plasticity

[+] Author and Article Information
P. M. Naghdi

Department of Mechanical Engineering, University of California, Berkeley, Calif.

J. A. Trapp

Computer Science Center, Aerojet Nuclear Company, Idaho Falls, Idaho

J. Appl. Mech 42(1), 61-66 (Mar 01, 1975) (6 pages) doi:10.1115/1.3423555 History: Received August 01, 1974; Revised October 01, 1974; Online July 12, 2010


Within the scope of the purely mechanical theory of plasticity, in a previous paper we have derived two inequalities which place restrictions on the constitutive equation for the rate of plastic strain in a finitely deformed elastic-plastic material. Here we take up the matter further, elaborate on the nature of the previously derived restrictions and obtain some additional results pertaining to the normality of the plastic strain rate and convexity of yield surfaces. Although in the main our discussions are carried out in the context of finite deformation, the nature of the restrictions for infinitesimal deformation is also examined. A special case of an elastic-plastic material in which the stress response is characterized by the stress rate and that of a rigid-plastic material are given detailed attention.

Copyright © 1975 by ASME
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