Shear Band Formation in Simple Shear: Softening and Alignment of Shear Bands in 2D and 3D Numerical Experiments

Simple shear experiments in 2D and 3D numerical models of strain-softening, pressure-sensitive viscoelastic plastic materials display a cascade of shear-banding instabilities. The models are done in a periodic domain with sidewalls driven by a fixed-velocity boundary condition. The propagation of shear bands across the periodic boundary is mildly discouraged by including a plug of viscous material with no strain-softening characteristics. 3D experiments introduce layered domains with the additional effects such as the thickness of the sample layer, the properties of the substrate, and the width of the imposed basal shear relative to the total width of the experiment. We examine the influence of strain-softening on the models - in particular we are interested in the orientation of early and late shear bands relative to the sense of shear, the evolution of the shear band pattern as a function of depth in the 3D case, and the extent to which we can determine the basal boundary condition from the near-surface deformation pattern. Our experiments run to strains of between 50 and 100%. In 2D we see a clear sequence of shear bands initially forming slightly sub-parallel to the Mohr-Coulomb orientation to the shear stress, and then further generations of shear bands linking each earlier generation. Through-going structures only seem to develop when the friction coefficient softens strongly. 3D models are considerably more challenging to resolve numerically but show similar results to the 2D in "deep" layers. These are better shown than described in an abstract.