Two-temperature continuum model for viscoplasticity in metals based on   fluctuation relation
  A continuum plasticity model for metals is presented from considerations of non-equilibrium thermodynamics. Of specific interest is the application of a fluctuation relation that subsumes the second law of thermodynamics en route to deriving the evolution equations for the internal state variables. The modeling itself is accomplished in a two-temperature framework that appears naturally by considering the thermodynamic system to be composed of two weakly interacting subsystems, viz. a kinetic vibrational subsystem corresponding to the atomic lattice vibrations and a configurational subsystem of the slower degrees of freedom describing the motion of defects in a plastically deforming metal. When externally driven, the two subsystems, identified with their own temperatures, fall out of equilibrium. An apparently physical nature of the present model derives upon considering the dislocation density, which characterizes the configurational subsystem, as a state variable. The continuum model accommodates finite deformation and describes plastic deformation in a yield-free setup via the so-called microscopic force balance along with the more conventional macroscopic force balance. Though the theory here is essentially limited to face-centered cubic metals modelled with a single dislocation density as the internal variable, an extension to body-centered cubic metals and modelling with two internal variables with dislocation densities of two non-overlapping types are briefly touched upon. 
S Roy Chowdhury, D Roy and J N Reddy
cond-mat.mtrl-sci