An adaptive multi-level model for multi-scale ductile fracture analysis in heterogeneous aluminum alloys

This paper addresses the multi-scale modeling of ductile fracture in microstructures characterized by a dispersion of hard and brittle heterogeneities in a softer ductile matrix. An adaptive multi-level model is developed with different inter-scale transfer operators and interfaces. Micro-mechanical analysis in regions of dominant damage is performed to capture the important micro-mechanical damage modes that are responsible for deterring the overall failure properties of these alloys. Regions of macroscopic homogeneity are otherwise modeled with constitutive relations derived from homogenization of evolving variables in representative volume elements. These two length scales of analysis, in conjunction with an intermediate swing level, form a three-level coupled multi-scale model to capture ductile crack propagation. The capabilities of the proposed model are demonstrated for a cast aluminum alloy

Localization and adiabatic pumping in a generalized Aubry-Andr\'e-Harper model

A generalization of the Aubry-Andr\'e-Harper (AAH) model is developed, containing a tunable phase shift between on-site and off-diagonal modulations. A localization transition can be induced by varying just this phase, keeping all other model parameters constant. The complete localization phase diagram is obtained. Unlike the original AAH model, the generalized model can exhibit a transition between topologically trivial bandstructures and topologically non-trivial bandstructures containing protected boundary states. These boundary states can be pumped across the system by adiabatic variations in the phase shift parameter. The model can also be used to demonstrate the phenomenon of adiabatic pumping breakdown due to localization