Abstract: Some materials may naturally exhibit singularity phenomena such as cracks or other manifestations as a result of scale effects
and long range interactions. Peridynamic theory models such behavior introducing a new nonlocal framework for the basic equations of continuum mechanics. In this lecture we consider a nonlinear peridynamic model and discuss its qualitative properties and well-posedness
in suitable fractional Sobolev spaces.
Those results were obtained in collaboration with A. Coclite (Bari), N. Dimola (Milano), S. Dipierro (Perth), G. Fanizza (Casamassima), L. Lopez (Bari), F. Maddalena (Bari),
S. F. Pellegrino (Bari), T. Politi (Bari), and E. Valdinoci (Perth).