Gradient Enhanced Physically Based Plasticity: Implementation and Application to a Problem Pertaining Size Effect: Implementation and application to a problem pertaining size effect

A physically based plasticity model is implemented which describes work hardening of a material as a function of the total dislocation density. The local part of the model, which involves statistically stored dislocations (SSDs) only, is based on Bergström's original model. The nonlocal part is based on geometrically necessary dislocations (GNDs) which appear and evolve due to existence of large plastic strain gradients. The evolution of GNDs with respect to strain gradients is described based on the flow theory. The gradients are computed explicitly using the converged plastic strain field and the coupling is achieved using a staggered (weak) approach. Gradient computation is carried out using an effcient algorithm that makes use of plastic strain increments at integration points whose arrangement is not necessarily regular. The algorithm is applied on a void growth problem in which high strain gradients occur around the void due to stress concentrations.