Predictions of cyclic yielding behavior of solids based on a nonequilibrium thermodynamic theory

Abstract

A nonequilibrium thermodynamic framework for solids is proposed in this study to account for and predict the fundamental mechanical behavior of stability and yielding in solid materials. The constitutive relations are derived from the nonequlibrium thermodynamic descriptions of the mechanical system of solids, including the elastic potential, the entropy production and the excess entropy production. Based on such an approach, the yielding behavior of solids can be well interpreted by the stability of thermodynamic steady state. Thus, employing the Lyapunov theory, a general yield criterion is proposed theoretically for solids based on the evolution direction of excess entropy, which depends on the excess entropy production defined. The yielding criteria of metals and granular solids are then specified and are shown to be efficient in predicting the isotropic and kinematic hardening behavior of solids. The kinematic hardening of yield loci is attributed to the residual stress induced by the irreversible deformation. As an important application of this theory, the cyclic behavior of solids under various cyclic loads can also be well predicted from the perspective of thermodynamics.