  Shear strain localization refers to the phenomenon of accumulation of
material deformation in narrow slip zones. Many materials exhibit strain
localization under different spatial and temporal scales, particularly rocks,
metals, soils, and concrete. In the Earth's crust, irreversible deformation can
occur in brittle as well as in ductile regimes. Modeling of shear zones is
essential in the geodynamic framework. Numerical modeling of strain
localization remains challenging due to the non-linearity and multi-scale
nature of the problem. We develop a numerical approach based on graphical
processing units (GPU) to resolve the strain localization in two and three
dimensions of a (visco)-hypoelastic-perfectly plastic medium. Our approach
allows modeling both the compressible and incompressible visco-elasto-plastic
flows. We demonstrate that using sufficiently small strain or strain rate
increments, a non-symmetric strain localization pattern is resolved in two- and
three-dimensions. We show that elasto-plastic and visco-plastic models yield
similar strain localization patterns for material properties relevant to
applications in geodynamics. We achieve fast computations using
three-dimensional high-resolution models involving more than $500$ million
degrees of freedom. We propose a new physics-based approach explaining
spontaneous stress drops in a deforming medium. We demonstrate by coupling the
geomechanical model with a wave propagation solver that the rapid development
of a shear zone in rocks generates seismic signal characteristics for
earthquakes.
