The plastic rotation effect in an isotropic gradient plasticity model for applications at the meso scale

Although formulated to represent a large system of polycrystals at the macroscopic level, isotropic gradient plasticity models have routinely been adopted at the meso scale. For such purposes, it is crucial to incorporate the plastic rotation effect in order to obtain a reasonable approximation of the underlying granular mechanics. This paper focuses on the isotropic plasticity model by Gurtin(2004), which departs from most existing isotropic gradient plasticity theories by incorporating the plastic rotation into the formulation. To elucidate on the role of plastic rotation, we compare and contrast the Gurtin (2004) model with two analogous formulations: the gradient crystal plasticity model by Gurtin and Needleman (2005), which we take as a reference since it retains information on the underlying crystallography; and an isotropic, plastically irrotational gradient plasticity model by Gurtin and Anand (2005). Through a constrained shear problem, it is shown analytically that the plastic rotation is essential for an isotropic model to capture the crystallographic effect predicted by the reference crystal plasticity model with multiple slip systems. The role of plastic rotation is further illustrated numerically with a composite unit cell problem, for which the isotropic model by Gurtin and Anand (2005) predicts a hardening response that differs significantly from the reference solution. Finally, we study the grain boundary effect on a single crystal with the Gurtin (2004) model. By introducing an interfacial resistance at the grain boundaries, the model predicts a Hall–Petch effect where the flow stress scales inversely with the grain size.