Gradient Enhanced Plasticity and Damage Models ¿ addressing the limitations of classical models in softening and hardening.

Abstract

The thesis considers two limitations of classical continuum models. The first two chapters focus on the mesh dependency issues during strain softening. It is shown that the ¿over-nonlocal¿ gradient enhancement is able to fully regularize softening models when standard nonlocal gradient formulations fail to do so. The next three chapters discuss on the size effect phenomena in metals. An implicit scalar gradient model, capable of predicting size dependent behavior, is problematic when the effective plastic strains do not have smooth profiles. An implicit tensorial gradient model is thus formulated in Chapter 4 to address this limitation. Chapter 5 discusses on the influence of the interfacial resistance on material behavior. A homogenization theory for a crystal plasticity model with one slip system is proposed such that the fine-scale properties propagate into the (coarse) macro-scale. Chapter 6 extend this theory to a plane strain bending problem, where the homogenized micro-force balance has the same form as the implicit gradient equation.