## Mathematical Aspects of Material Sciences

### Faculty involved

Andrej Cherkaev, Elena Cherkaev, David Dobson, Yekaterina Epshteyn, Ken Golden, Fernando Guevara Vasquez, Graeme W. Milton, Braxton Osting, Andrejs Treibergs

- Composite materials
- Metamaterials
- 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).

Examples of exact structures (courtesy of Andrej Cherkaev and Elena Cherkaev).

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).

Webmasters: Yekaterina Epshteyn and Fernando Guevara Vasquez.