  We propose a dynamical theory of low-temperature shear deformation in
amorphous solids. Our analysis is based on molecular-dynamics simulations of a
two-dimensional, two-component noncrystalline system. These numerical
simulations reveal behavior typical of metallic glasses and other viscoplastic
materials, specifically, reversible elastic deformation at small applied
stresses, irreversible plastic deformation at larger stresses, a stress
threshold above which unbounded plastic flow occurs, and a strong dependence of
the state of the system on the history of past deformations. Microscopic
observations suggest that a dynamically complete description of the macroscopic
state of this deforming body requires specifying, in addition to stress and
strain, certain average features of a population of two-state shear
transformation zones. Our introduction of these new state variables into the
constitutive equations for this system is an extension of earlier models of
creep in metallic glasses. In the treatment presented here, we specialize to
temperatures far below the glass transition, and postulate that irreversible
motions are governed by local entropic fluctuations in the volumes of the
transformation zones. In most respects, our theory is in good quantitative
agreement with the rich variety of phenomena seen in the simulations.
