Homogenization of pinning conditions on periodic networks
Laura Sigalotti · Networks and Heterogeneous Media · 2012
This paper deals with the description of the overall effect of pinning conditions in discrete systems. We study a variational problem on the discrete in which pinning sites are modeled as network subsets on which concentrated forces are imposed.We want to determine the asymptotic effect of pinning conditions on a periodic lattice as its size vanishes. Our analysis is performed in the framework of $\Gamma$-convergence and highlights the analogies and differences with the corresponding continuous problem, i.e. periodically perforated domains. We derive a functional form for the limit energies which depends on the relationship between the space dimension and the growth rate of the interaction functions.