Rate-and-state theory of plastic deformation near a circular hole

We show that a simple rate-and-state theory accounts for most features of both time-independent and time-dependent plasticity in a spatially inhomogeneous situation, specifically, a circular hole in a large stressed plate. Those features include linear viscoelastic flow at small applied stresses, strain hardening at larger stresses, and a dynamic transition to viscoplasticity at a yield stress. In the static limit, this theory predicts the existence of a plastic zone near the hole for some but not all ranges of parameters. The rate-and-state theory also predicts dynamic failure modes that we believe may be relevant to fracture mechanics.