Inserted: 19 sep 2013
Last Updated: 16 aug 2015
Journal: SIAM J. Math. Anal.
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