Inspired by the pioneering work of Professor T.J.R. Hughes on the variational multi-scale method, this document summarizes recent developments in multiple-scale modeling using a newly developed technique called the bridging scale. The bridging scale consists of a two-scale decomposition in which the coarse scale is simulated using continuum methods, while the fine scale is simulated using atomi...

725 Abstract With the ability to locate and identify atoms in three dimensions, atom-probe tomography (APT) has revolutionized our understanding of structure-property relationships in materials used for structural applications. The atomic-scale details of clusters, second phases, and microstructural defects that control alloy properties have been investigated, providing an unprecedented level o...

This article presents new probabilistic models for generating microstructures and multi-scale fracture analysis of a random heterogeneous material. The microstructure model involves a level-cut, inhomogeneous, filtered Poisson field comprising a sum of deterministic kernel functions that are scaled by random variables and centred at Poisson points. The fracture model involves stochastic descrip...