A Drucker-Prager gradient plasticity theory is applied in finite element simulation of two-dimensional localization problems in geomaterials. The gradient-dependent theory preserves well-posedness of the governing equations in presence of material instability and prevents a spurious mesh sensitivity of numerical results. An internal length scale incorporated in the theory determines the width of shear bands.
Assuming weak satisfaction of the yield condition a family of mixed finite elements is developed, in which plastic strains are interpolated with C1-continuity in addition to the standard discretization of the displacements. Instabilities in a biaxially compressed specimen and in a slope under an increasing gravity load are simulated.