A gradient plasticity theory is proposed, which includes dependence of the yield function on the Laplacian of an invariant plastic strain measure. The theory preserves well-posedness of the governing equations in the presence of strain softening and prevents the pathological mesh sensitivity of numerical results. An internal length scale incorporated in the theory determines the size of localization bands.
Adopting a weak satisfaction of the yield condition, mixed finite elements are developed, in which plastic strains are discretized in addition to the standard discretization of the displacements.
A gradient-dependent Drucker-Prager yield function is used to solve a two-dimensional problem of shear slip in a soil mass. A gradient-dependent Rankine failure function is used in continuum modelling of two concrete fracture experiments. The regularizing effect of the gradient dependence is demonstrated.
Softening, strain localization, higher-order continuum, finite element analysis, soil instability, concrete fracture.