  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 [1] 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.
