Analysis of Modern Materials with Periodic Microstructure

The study of periodic homogenization is a fundamental application of calculus of variations to material sciences. While there are many extensive and general results to cover energies for classical materials with periodic microstructure, it is only in the last 10 years that the periodic homogenization of modern materials have been considered. These materials are characterized by some non-classical behavior, and so the energies which model them do not fall under any classical framework. We will specifically present results on the homogenization limit for thin metamaterials (joint work with Elisa Davoli (TU Wien)) and a result on phase transitions of heterogenous temperature-responsive materials (joint work with Riccardo Cristoferi (Radboud University) and Irene Fonseca (Carnegie Mellon University).