A Perspective on Plasticity, Dissipation and the Second Law of Thermodynamics

Abstract

The requirement of a non-negative dissipation rate for all possible deformation histories is generally imposed on plastic constitutive relations. This is a constraint analogous to the Coleman–Noll [Coleman, B. D., and Noll, W., 1964, “The Thermodynamics of Elastic Materials With Heat Conduction and Viscosity,” Arch. Ration. Mech. Anal., 13, pp. 167–178. 10.1007/BF01262690] postulate that the Clausius–Duhem inequality needs to be satisfied for all possible deformation histories. The physical basis for the Clausius–Duhem inequality is as a statistical limit for a large number of discrete events for a long time and is not a fundamental physical requirement for small systems for a short time. The relation between the requirement of a non-negative dissipation rate and the Clausius–Duhem inequality is considered. The consequences of imposing a non-negative dissipation rate for all possible deformation histories are illustrated for: (i) a single crystal plasticity framework that accounts for elastic lattice curvature changes as well as elastic lattice straining and (ii) for discrete defect theories of plasticity, with attention specifically on discrete dislocation plasticity for crystalline solids and discrete shear transformation zone (STZ) plasticity for amorphous solids. Possible less restrictive conditions on the evolution of dissipation in plasticity formulations are considered as are implications for stability. The focus is on open questions and issues.