| In this dissertation, a hierarchical multiple scale computational model is proposed to concurrently predict evolution of variables at the structural and microstructural scales, as well as to track the incidence and propagation of microstructural damage. The microscopic analysis is conducted with the Voronoi cell finite element model (VCFEM) while a conventional displacement based FEM code executes the macroscopic analysis. Adaptive schemes and mesh refinement strategies are developed to create a hierarchy of computational sub-domains with varying resolution. Such hierarchy allow for differentiation between non-critical and critical regions, and help in increasing the efficiency of computations through preferential ‘zoom in’ regions. Coupling between the scales for regions with periodic microstructure is accomplished through asymptotic homogenization, whereas regions of nonuniformity and non-periodicity are modeled by true microstructural analysis with VCFEM. Various numerical examples are executed for validating the effectiveness of the model for different microstructural configurations. |
