Diffuse bifurcations engraving diverse shear bands in granular materials

Shear bands with characteristic spatial patterns observed in an experiment for a cubic or parallelepiped specimen of dry dense sand were simulated by numerical bifurcation analysis using the Cam-clay plasticity model. By incorporating the subloading surface concept into the plasticity model, the model became capable of reproducing hardening/softening and contractive/dilative behavior observed in the experiment. The model was reformulated to be compatible with the multiplicative hyperelasto-plasticity for finite strains. This enhanced constitutive model was implemented into a finite-element code reinforced by a stress updating algorithm based on the return-mapping scheme, and by an efficient numerical procedure to compute critical eigenvectors of elastoplastic tangent stiffness matrix at bifurcation points. The emergence of diamond- and column-like diffuse bifurcation modes breaking uniformity of the materials, followed by the evolution of shear bands through strain localization, was observed in the analysis. In the bifurcation analysis of plane strain compression test, unexpected bifurcation modes, which broke out-of-plane uniformity and led to 3-dimensional diamond-like patterns, were detected. Diffuse bifurcations, which were difficult to observe by experiments, have thus been found as a catalyst creating diverse shear band patterns.