Strain localization, or shear banding, is the spontaneous development of coexisting flowing and stationary regions in a sheared material. Strain localization has been identified and studied experimentally in granular materials, bubble rafts, complex fluids, and bulk metallic glasses. Shear banding may play an important role in the failure modes of structural materials and earthquake faults. Localization is a precursor to fracture in bulk metallic glasses and has been cited as a mechanism for material weakening in granular fault gouge on faults.

We model amorphous solids with a set of partial differential equations that describe Shear Transformation Zones (STZs) (Falk and Langer, 1998) with an effective temperature. We find small perturbations in the effective temperature can lead to localized regions of higher strain, or shear bands, in our numerically integrated solution, and show that the system is linearly unstable with repect to perturbations to a time-varying trajectory.

Manuscript: Localization in an STZ model for amorphous materials

We have also shown that an STZ model with a rate-dependent effective temperature predicts differet types of localization behavior as a function of two important parameters: applied strain rate and quench rate for initializing the sample. For quickly strained or slowly quenched systems, thin diffusion limited shear bands are predicted. In contrast, slowly sheared or quickly quneched samples undergo homogeneous deformation, and in between there is a regime of thick shear bands where the length scale is determined by the steady state density of STZs.

Manuscript: Rate dependent shear bands in an STZ model for amorphous solids