Evolving shear bands in a nonlinear micropolar continuum

Shear bands in inelastic solids are often treated as stationary failure zones whose orientation is fixed at bifurcation, a view reinforced by classical Cauchy continua with softening and no internal length scale, where loss of ellipticity drives deformation into a single planar band. Experiments in granular media, however, increasingly show curved, branching and migrating shear zones. Here, we study finite-strain localization in a geometrically nonlinear micropolar (Cosserat) continuum implemented in an implicit material point method, using a non-associative Drucker–Prager model with a unified yield surface based on a generalized measure of stresses and couple stresses to introduce an intrinsic length scale. Two-dimensional boundary-value problems show that localization need not remain rectilinear or stationary: the active zone can curve, reorient and migrate as the stress state evolves, without ad hoc parameter tuning. Viewed through the microrotation field, the evolving centreline is consistently traced by a near-zero ridge of the band-normal microrotation gradient, which we propose as a natural band-selection rule in the nonlinear micropolar continuum.