Nonlocal continuum models for plasticity and damage

Abstract

Nonlocal interactions of material points play a vital role in modelling certain important aspects of inelastic phenomena such as plasticity and damage in solids. For plasticity problems, nonlocal interactions allow characterizations of size-dependence and energetic hardening. In the case of damage, nonlocality describes energetically favourable conditions for propagation as well as branching of cracks. The nonlocal description of inelastic phenomenon introduces certain internal length scales representative of the material micro-structure. A geometric perspective of the kinematics of inelastic deformation induces certain interesting attributes in the form of a non-trivial metric, curvature, etc. to the mathematical model. Towards realizing a unified and rational modelling setup, it is important to trace the geometric origins of the kinematics underlying nonlocal interactions. The first part of the thesis dwells on modelling of visco-plasticity and damage in metals by introducing gradients of plasticity and damage variables to capture the size-dependent plastic response and the nonlocal aspects of damage. We also try to account for dislocation inertia affecting the yield strength at high strain rates. In addition, the nonlocal flow rule also encapsulates energetic hardening. We describe temperature evolution, which is thermodynamically consistent and accounts for the heat dissipated. The coupled visco-plastic damage model is numerically implemented through peridynamics (PD) and validated via the simulations of adiabatic shear band propagation and shear plugging failure. The nonlocal terms can be accorded a geometric meaning using the concepts of gauge theory and differential geometry. We therefore focus on a geometric characterization of brittle damage via the gauge theory of solids. The local configurational changes in the manifold are captured using a non-trivial affine connection, called gauge connection. The resulting manifold is equipped with the gauge covariant quantities like gauge torsion and gauge...