Special Session 126: Defects, Microstructures, and Failure: Multiscale Variational Models

Multiscale analysis and homogenization of nonlocal thin films
Antonio Tribuzio
University of Bonn
Germany
Co-Author(s):    
Abstract:
In this talk, we will introduce a nonlocal, variational model for thin films. We consider family of functionals of convolution-type defined on a thin domain of thickness $\gamma$ with the size of the most effective interactions between points being of order $\varepsilon$. After discussing the correct rescaling, we study the $\Gamma$-convergence of these energies as both parameters go to zero to a local integral functional defined on a lower dimensional domain. In the case of periodic homogenization, we can show that a separation of scales takes place. This is a work in collaboration with Nadia Ansini.