Spontaneous localization of inelastic deformation of geomaterials as a consequence of structural pressure drop in localized shear bands

Abstract

According to plate tectonics, the Earth's crust is made up of relatively rigid blocks - lithospheric plates. Lithospheric plates that are in constant motion relative to each other. The plates on the Earth's surface are separated by faults, which separate the non-deformable blocks in the form of shear bands. Instead of a smooth distribution, the deformation is localized into slip bands.  Standard and simplest rheological models of brittle deformation and dry friction are used in study. Plasticity is realized using the Coulomb-Mohr theory with the corresponding flow law. The main parameter controlling strain localization is the yield strength.  What is different about the evolution of stresses inside the localization zone compared to outside? Outside the zone there is unloading. As will be seen in the diagram of Mohr's circles, inside the zone the circle is small but touches the limit of strength. Instead of cutting off equally at high pressure, nature makes a band where there is less pressure and the yield strength depends on the pressure. Strain localization is due to the pressure drop in the localization zone. Mathematical models require high resolution in space and time, since strain localization occurs at a location and time unknown in advance. To achieve high resolution, the initially developed prototype of the computational algorithm in a high-level language like Matlab is translated into the CUDA extension of C. The CUDA extension allows the use of the latest computer hardware characterized by high speed processing (read/write) of memory. The numerical solution is realized on the basis of combinations of finite difference and finite volume methods on rectangular structured meshes.