Coupling of meso-scale mechanics and dislocation dynamics for strain localization

The objective of this research is to develop a meso-scale physics-based gradient regularization method for analyzing strain localization problem. This is achieved by formulating a reproducing kernel strain regularization (RKSR) method as a generalization of gradient models in conjunction with a coupled meso-scale mechanics and dislocation dynamics formulation for characterization of length scales in the gradient models.; Firstly, a RKSR method is proposed as a mathematical generalization of gradient model for the strain localization problem. As an implicit gradient model, this approach eliminates the drawbacks of requiring non-physical boundary conditions in the conventional gradient model.; The second part of this research aims to characterize the length scales RKSR method and to identify how the continuum length scales are related to the microstructure features. This includes the development of multiple level set method for modeling grain boundary migration so as to determine the grain geometry, the multi-scale formulation for coupling of dislocation mechanics and continuum mechanics, and the characterization of material length scales in the continuum gradient model.; Modeling grain boundary migration is a challenging task in numerical simulation due to the complexity of topological changes. In this research, a multiple level set method for modeling of grain boundary migration is developed. The unique feature of this approach is its ability to naturally describe topological changes. Consideration of various driving forces and extension of this approach to multi-dimension are straightforward.; Since the classical plasticity theory has its intrinsic limitations in incorporating the mesoscale features, a multi-scale formulation for coupling dislocation dynamics and continuum mechanics in polycrystalline materials is developed. In this approach, the phenomenological hardening and flow rules in the classical plasticity theory are replaced by homogenized meso-scale material response characterized by dislocation evolution and their interactions.; Finally, an effort is devoted to bridge the properties obtained from dislocation dynamics to the length scales in the continuum gradient models. By using two coupled dislocation evolution equations, the length scales in the continuum gradient model are related to the ratio between mobile and total dislocation density, in addition to other material constants.