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The Quarterly Journal of Mechanics and Applied Mathematics 1975 28(1):25-46; doi:10.1093/qjmam/28.1.25
© 1975 by Oxford University Press
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RESTRICTIONS ON CONSTITUTIVE EQUATIONS OF FINITELY DEFORMED ELASTIC-PLASTIC MATERIALS

P. M. NAGHDI and J. A. TRAPP

( University of California Berkeley
Aerojet Nuclear Company Idaho Falls, Idaho )

This paper is concerned with restrictions on the constitutive equations of elastic-plastic materials in the presence of large deformation. Our development is confined to the purely mechanical theory in which the response of the medium is characterized by nonlinear constitutive equations of rate-type. Starting with a physically plausible assumption concerning non-negative work in a closed cycle of deformation, we derive two local inequalities which hold in all motions and which place restrictions on the general constitutive equations of elastic-plastic materials. An implication of one of the inequalities is then used to express the constitutive equation for the plastic strain rate in terms of the yield (or loading) function, as well as the stress response and a measure of work-hardening.


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