Deformation patterning driven by rate dependent non-convex strain gradient plasticity

A rate dependent strain gradient plasticity framework for the description of plastic slip patterning in a system with non-convex energetic hardening is presented. Both the displacement and the plastic slip fields are considered as primary variables. These fields are determined on a global level by solving simultaneously the linear momentum balance and the slip evolution equation which is postulated in a thermodynamically consistent manner. The slip law differs from classical ones in the sense that it includes a non-convex free energy term, which enables patterning of the deformation field. The formulation of the computational framework is at least partially dual to a Ginzburg–Landau type of phase field modeling approach. The essential difference resides in the fact that a strong coupling exists between the deformation and the evolution of the plastic slip, whereas in the phase field type models the governing fields are only weakly coupled. The derivations and implementations are done in a transparent 1D setting, which allows for a thorough mechanistic understanding, not excluding its extension to multidimensional cases.