Mathematical Approaches for Contemporary Materials Science: Addressing Defects in the Microstructure

Abstract

We overview a series of mathematical works that introduce new modeling and computational approaches for non-periodic materials and media. The approaches consider various types of defects embedded in a periodic structure, which can be either deterministic or random in nature. A portfolio of possible computational techniques addressing the identification of the homogenized properties of the material or the determination of the actual multi-scale solution is presented.