Calculus of Variations and Geometric Measure Theory

A. Braides - V. Chiadò Piat - A. Piatnitski

Homogenization of Discrete High-Contrast Energies

created by braidesa on 19 Sep 2013
modified on 16 Aug 2015


Published Paper

Inserted: 19 sep 2013
Last Updated: 16 aug 2015

Journal: SIAM J. Math. Anal.
Volume: 47
Number: 4
Pages: 3064-3091
Year: 2015
Doi: 10.1137/140975668


We consider a periodic array of points in a discrete setting linked by (long-range, nonlinear) elastic interactions of two types, weak and strong. By scaling the lattice and the interactions (differently if weak or strong) we obtain as a Gamma-limit a multi-phase energy analogous to the one obtained in double-porosity continuous models. While in the continuous case such models are obtained as a result of complex micro-geometries, here they are a simple consequence of natural assumptions on the discrete interactions. We also treat a dynamical case using a minimizing-movement approach, obtaining a non-local evolution equation.

The preprint version of the paper had the title Discrete Double Porosity Models

Keywords: discrete systems, minimizing movements, double porosity