Resolving Strain Localization in Frictional and Time-Dependent Plasticity: Two- and Three-Dimensional Numerical Modeling Study Using Graphical Processing Units (GPUs)

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. In contrast to symmetric shear bands frequently observed in the literature, we demonstrate that using sufficiently small strain or strain rate increments, a non-symmetric strain localization pattern is resolved in two- and three-dimensions, highlighting the importance of high spatial and temporal resolution. 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 1.3 billion degrees of freedom. We propose a new physics-based approach explaining spontaneous stress drops in a deforming medium. Strain localization is the accumulation of strain in narrow regions of rocks and other materials like metals, soils, and concrete, occurring at different scales. The strength of most geomaterials, particularly rocks, is strongly pressure-dependent, with strength increasing with increasing pressure. We developed efficient numerical algorithms using High-Performance Computing (HPC) and graphical processing units (GPUs) to model strain localization in 2D and 3D for applications in geodynamics and earthquake physics. Unlike previous models, our method reveals non-symmetrical patterns by using very small strain increments, highlighting the need for high-detail modeling. We found that elasto-plastic and visco-plastic models show similar strain patterns for relevant materials. Our method also achieves fast, detailed computations with over 1.3 billion variables and offers a new explanation for sudden stress drops in deforming materials. We resolve material instability during deformation resulting in a non-symmetric pattern of strain localization We demonstrate the similarity in patterns of strain localization between frictional and time-dependent plasticity models We achieve fast numerical simulations in high-resolution model setups in three dimensions involving more than 500 million degrees of freedom