| Heterogeneous materials systems hold the key to the future development of a broad range of increasingly complex technological applications. For example, multi-phase and/or multi-component materials are at the forefront research on the development of efficient energy devices, and the future generation of structural materials with optimal mechanical properties. In this dissertation, we focus on two materials systems, namely, solid oxide fuel cells (SOFCs) and bulk metallic glasses (BMGs), where we investigate, through theoretical and mesoscale computational models, the role of microstructure on the properties of these heterogeneous systems.;For the solid oxide fuel cell project, a computational framework is developed to investigate the topological evolution of Ni phase in SOFC porous anodes, and the accompanying changes to a wide range of microstructural attributes that affect electrochemical performance. Additionally, with the aid of this framework, we study the reduction-oxidation instability, mechanical deformation and damage accumulation in SOFC anodes. In particular, the SOFC project is focused on the role of anode microstructure, characterized by particle size and ratio, on the microstructural stability and mechanical durability of SOFC anodes.;For the bulk metallic glass project, a mesoscale model is introduced that accounts for the structural heterogeneity of monolithic BMGs and BMG composites, and captures the fundamental aspects of plastic deformation in such systems. We examine the effect of internal structure, characterized by rigid/soft short range order (SRO), on the deformation behavior of monolithic BMGs, while for BMG composites, we study the role of ductile phase microstructure, particle size, morphology and area fraction, on the mechanical properties and overall ductility of these systems. |