Nonlinear Peridynamic Models

Some materials may naturally form discontinuities such as cracks as a result of scale effects and long range interactions. Peridynamic 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 well-posedness in suitable fractional Sobolev spaces.
Those results were obtained in collaboration with S. Dipierro (Perth), F. Maddalena (Bari) and E. Valdinoci (Perth).