  A two-dimensional version of the shear-transformation-zone (STZ) theory by
Falk and Langer is explored numerically. Two different geometries are used to
simulate uniaxial tension experiments where materials are subjected to constant
strain rates. In the first setup, a rectangular specimen is given an
imperceptible indentation, allowing it to neck at the center. The dynamics are
explored systematically by varying both the straining capability of the STZs
(epsilon_0) and the external strain rate. Higher values of epsilon_0 increase
the plastic flow and result in sharper necks. Decreased values of the external
strain rate result in the formation of narrow shear bands, consistent with the
absence of thermal relaxation mechanisms in the model. In the second
configuration, the equivalent of pre-annealed materials are explored. Here, the
sample is initially square and the edges are made rough in order to encourage
the formation of shear bands. With respect to epsilon_0 and the external strain
rate, the results show trends similar to those in the necking simulations. The
pre-annealing was modeled by using a low initial density of STZs. This had most
effect when epsilon_0 was large, contributing to the localization of the strain
and making the material appear more brittle.
