Phase field modelling of fracture: recent theoretical developments and applications

In this seminar, the fundamentals of the phase field model for brittle fracture are presented. Originally developed for multi-field image segmentation applications, this model has recently been applied to mechanics to simulate brittle and ductile fracture in materials, opening new perspectives for research. The strong and the weak forms of the differential problem, invoving two coupled nonlinear partial differential equations for the phase field variable and for the equilibrium in the continuum, are detailed, along with the proposed monolithic finite element solution scheme. Numerical applications related to crack propagation are finally discussed.