Viscoplastic relaxation in granular flow

The equations governing the non-associative elastic-plastic deformation of granular materials are prone to violent instability at moderate strain. This instability signals the onset of strain localization and shearband formation. Commonly used constitutive models do not contain a regularization mechanism, and additional, often ad-hoc, modeling of the shearband is required to follow subsequent deformation. These regularizing mechanisms may include crack-smearing or high-order gradient additions; here we present a viscoplastic regularization and consider the anti-plane shearing of a granular material. We discuss stability, energy bounds, and how these estimates affect numerical computations. We mention that the results we derive have analogous formulations in the mechanics of softening materials.