Xh. Peng et Ars. Ponter, EXTREMAL PROPERTIES OF ENDOCHRONIC PLASTICITY, .1. EXTREMAL PATH OF THE CONSTITUTIVE EQUATION WITHOUT A YIELD SURFACE, International journal of plasticity, 9(5), 1993, pp. 551-566
Based on the general extremal properties of time-independent inelastic
materials proposed by Ponter and Martin, some extremal properties of
endochronic theory of plasticity are investigated. The extremal path o
f an endochronic constitutive equation without using a yield surface i
s found, which makes plastic work act as a potential such that the dev
iatoric stress can be derived from its derivative with respect to plas
tic strain. These properties are important because they provide the po
ssibility for the irreversible thermodynamically based constitutive eq
uation, which is strongly history-dependent, to be applied to simplifi
ed analysis in engineering problems. Using the derived extremal proper
ties, the principle of minimum potential energy is extended to endochr
onic theory of plasticity. As an example, the stress and strain fields
of a hinge-joint three-bar truss are analyzed.