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

Nonlocal aproximation of a Griffith-type energy
Stefano Almi
University of Naples Federico II
Italy
Co-Author(s):    Elisa Davoli, Anna Kubin, Emanuele Tasso
Abstract:
We prove that De Giorgi's conjecture for nonlocal approximation of free discontinuity problems extends to the case of functionals defined in terms of the symmetric gradient of the admissible field. For a suitable class of continuous finite difference functionals, we show the compactness of deformations with equibounded energies, as well as their Gamma convergence. The compactness (and closure) analysis builds on a Fr\`echet-Kolmogorov approach and a novel characterization of GSBD.