Abstract: The widely used phase-field approach for modeling fracture is based on the Griffith criterion, which says that the elastic energy released is proportional to the length of the crack formed. Mathematically, this is posed as the minimization of the Griffith energy that penalizes both bulk (elastic) and surface (crack) contributions. The goal of this talk is to understand the existence and structure of minimizers of this energy. We will discuss existence of strong solutions, which have concentrated cracks that cannot "pulverize" the material. Further, in dimension 2, we dramatically improve our understanding of the minimal cracks: We show that the crack is given by a regular surface outside of a singular set of points with dimension strictly less than 1.

Contact: Ian Tobasco