Abstract

The classical theory of fracture mechanics developed in the last century is very successful in stating the non-propagation conditions for pre-existing cracks, or to study their propagation along pre-assigned paths. However, the theoretical modelling and the predictive numerical simulation of crack nucleation and the emergence of complex crack patterns is still an open research subject. In the last years, variational approaches to fracture opened new perspectives, by formulating fracture mechanics as an energy minimisation problem where the crack path is treated as genuine unknown. In this talk I will discuss about the use of gradient damage models as a phase-field regularised formulation of brittle fracture. Reporting the results of theoretical analyses and numerical experiments, I will show how similar models can retrieve crack nucleation, crack propagation, and the morphogenesis of complex crack patterns in 2D or 3D. Examples will include thermal shock fracture in ceramics and thin-film cracks.