EXTREMAL PROPERTIES OF ENDOCHRONIC PLASTICITY, .1. EXTREMAL PATH OF THE CONSTITUTIVE EQUATION WITHOUT A YIELD SURFACE

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.