An isogeometric analysis approach to gradient-dependent plasticity

Gradient-dependent plasticity can be used to achieve mesh-objective results upon loss of well-posedness of the initial/boundary value problem because of the introduction of strain softening, non-associated flow, and geometric nonlinearity. A prominent class of gradient plasticity models considers a dependence of the yield strength on the Laplacian of the hardening parameter, usually an invariant of the plastic strain tensor. This inclusion causes the consistency condition to become a partial differential equation, in addition to the momentum balance. At the internal moving boundary, one has to impose appropriate boundary conditions on the hardening parameter or, equivalently, on the plastic multiplier. This internal boundary condition can be enforced without tracking the elastic-plastic boundary by requiring math formula-continuity with respect to the plastic multiplier. In this contribution, this continuity has been achieved by using nonuniform rational B-splines as shape functions both for the plastic multiplier and for the displacements. One advantage of this isogeometric analysis approach is that the displacements can be interpolated one order higher, making it consistent with the interpolation of the plastic multiplier. This is different from previous approaches, which have been exploited. The regularising effect of gradient plasticity is shown for 1- and 2-dimensional boundary value problems.