Dynamics of viscoplastic deformation in amorphous solids

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