Rate-and-State Theory of Plastic Deformation Near
a Circular Hole
J. S. Langer(1) and Alexander E. Lobkovsky(2) (1) Physics Deprtment
(2) Institute for Theoretical Physics
Univesity of California
Santa Barbara, CA 93106
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.
