Strain gradient crystal plasticity: thermodynamics and implementation

This chapter studies the thermodynamical consistency and the finite element implementation aspects of a rate-dependent nonlocal (strain gradient) crystal plasticity model, which is used to address the modeling of the size-dependent behavior of polycrystalline metallic materials. The possibilities and required updates for the simulation of dislocation microstructure evolution, grain boundary-dislocation interaction mechanisms, and localization leading to necking and fracture phenomena are shortly discussed as well. The development of the model is conducted in terms of the displacement and the plastic slip, where the coupled fields are updated incrementally through finite element method. Numerical examples illustrate the size effect predictions in polycrystalline materials through Voronoi tessellation