  There is an ever-growing need for predictive models for the
elasto-viscoplastic deformation of solids. Our goal in this paper is to
incorporate recently developed out-of-equilibrium statistical concepts into a
thermodynamically consistent, finite-deformation, continuum framework for
deforming amorphous solids. The basic premise is that the configurational
degrees of freedom of the material --- the part of the internal energy/entropy
that corresponds to mechanically stable microscopic configurations --- are
characterized by a configurational temperature that might differ from that of
the vibrational degrees of freedom, which equilibrate rapidly with an external
heat bath. This results in an approximate internal energy decomposition into
weakly interacting configurational and vibrational subsystems, which exchange
energy following a Fourier-like law, leading to a thermomechanical framework
permitting two well-defined temperatures. In this framework, internal variables
that carry information about the state of the material equilibrate with the
configurational subsystem, are explicitly associated with energy and entropy of
their own, and couple to a viscoplastic flow rule. The coefficients that
determine the rate of flow of entropy and heat between different internal
systems are proposed to explicitly depend on the rate of irreversible
deformation. As an application of this framework, we discuss two constitutive
models for the response of glassy materials, a simple phenomenological model
and a model related to the concept of Shear-Transformation-Zones as the basis
for internal variables. The models account for several salient features of
glassy deformation phenomenology. Directions for future investigation are
briefly discussed.
