In contrast to the traditional interpretation of shear bands in sand as a bifurcation problem in continuum mechanics, shear bands in sand are considered as high-strain phase (plastic phase) of sand and the materials outside the bands are still in low-strain phase (elastic phase), namely, the two phases of sand can coexist under certain condition. As a one-dimensional example, the results show that, for materials with strain-softening behavior, the two-phase solution is a stable branch of solutions, but the method to find two-phase solutions is very different from the one for bifurcation analys...
