Plastic slip patterning driven by rate dependent non convex strain gradient plasticity

The mechanical response of many engineering materials is often influenced by an existing or emerging microstructure (martensite, dislocation sub-structures, voids, shear bands etc.). There have been various approaches to model the formation and evolution of such microstructures which involve coupled models. The difficulty in the modeling of these multi-field coupled problems is the localization of the corresponding field and strain hardening-softening elastoplastic behavior which yields numerical instabilities. In order to remedy the ill-posedness of post critical results during the formation of microstructures several models have been proposed including, methods using calculus of variations in an incremental setting, non-local methods, viscous regularization techniques and Cosserat theories. A complete understanding of models which can simulate the patterning of dislocation slip or formation of dislocation substructures (see [1]) is not at hand. In order to contribute to this, inspired by the success of phase field models, we propose an approach to illustrate the ability of non-convex field models to predict the emergence and evolution of dislocation slip microstructures in a rate dependent strain gradient plasticity framework. The framework studies the viscous relaxation of plastic slip patterning in a system with energetic hardening. Both the displacement and the plastic slip are considered as primary variables. These fields are determined on a global level by solving simultaneously the linear momentum balance and slip evolution equation which is derived from thermodynamical considerations. The slip law used in this context differs from the classical ones in the sense that it includes the non-convex free energy term leading to the patterning of this field. The format of the underlying free energy is characterized through a doublewell function. The formulation of the computational framework can be considered as dual to similar Chan-Hilliard type of phase field modeling approaches, considering the fact that there is a strong coupling between the deformation and the evolution of the plastic slip whereas in most phase field models the main fields are only weakly coupled. The derivations and implementations are done in a 1D setting which is being extended to multidimensional cases.
Citation Formats
T. YALÇINKAYA, W. A. M. BREKELMANS, and M. G. D. GEERS, “Plastic slip patterning driven by rate dependent non convex strain gradient plasticity,” presented at the 4th European Conference on Computational Mechanics (2010), Paris, Fransa, 2010, Accessed: 00, 2021. [Online]. Available: