Field Dislocation Mechanics with Applications in Atomic, Mesoscopic and Tectonic Scale Problems

This thesis consists of two parts. The first part explores a 2-d edge dislocation model to demonstrate characteristics of Field Dislocation Mechanics (FDM) in modeling single and collective behavior of individual dislocations. The second work explores the possibility of modelling adiabatic shear bands propagation within the timespace averaged framework of Mesoscopic Field Dislocation Mechanics (MFDM). It is demonstrated that FDM reduces the study of a significant class of problems of discrete dislocation dynamics to questions of the modern theory of continuum plasticity. The explored questions include the existence of a Peierls stress in translationally-invariant media, dislocation annihilation, dislocation dissociation, finite-speed-of-propagation effects of elastic waves vis-a-vis dynamic dislocation fields, supersonic dislocation motion, and short-slip duration in rupture dynamics. A variety of dislocation pile-up problems are studied, primarily complementary to what can be dealt by existing classical pile-up models. In addition, the model suggests the possibility that the tip of a shear band can be modelled as a localized spatial gradient of elastic distortion with the dislocation density tensor in continuum dislocation mechanics; It is demonstrated that the localization can be moved by its theoretical driving force and forms a diffuse traveling band tip, thereby extending the thin layer of the deformation band. A 3-d, parallel finite element framework of MFDM is developed in a geometrically nonlinear context for the purpose of modelling shear bands. The numerical formulations and algorithm are presented in detail. Constitutive models appropriate for single crystal plasticity response and J2 plasticity with thermal softening are implemented.