Mathematical Aspects of Material Sciences
- Composite materials
- Inverse homogenization
- Bounds on effective properties of composite materials
- Mathematical aspects of polycrystalline materials
Examples of unimode materials (from “Complete characterization of the macroscopic deformations of periodic unimode metamaterials of rigid bars and pivots” by Graeme W. Milton).
Two dimensional computational model for a polycrystalline materials and comparison of the empirical distribution - Grain Boundary Character Distribution (GBCD) (characteristics of the texture of the boundary networks in polycrystalline materials) versus Boltzmann distribution (from “A Theory and Challenges for Coarsening in Microstructure” by K.Barmak, E.Eggeling, M.Emelianenko, Y.Epshteyn, D.Kinderlehrer, R.Sharp and S. Ta’asan).