Laura De Lorenzis (Technische Universität Braunschweig, Allemagne). Phase-field modeling and computation of fatigue.

The phase-field framework for modeling systems with sharp interfaces consists in incorporating a continuous field variable which differentiates between multiple physical phases through a smooth transition. In the context of fracture, the so-called crack phase-field describes the transition between the fully broken and intact material phases, thus approximating the sharp crack discontinuity. The evolution of this field models the fracture process. With respect to classical techniques with discrete fracture description, the phase-field approach to fracture has the main advantage of enabling the straightforward description of complicated processes, including crack initiation, propagation, coalescence, and branching with arbitrarily complex topology in 3D.

In this talk, after a general introduction to the framework, a recent extension to model fatigue in brittle materials is discussed. The standard regularized free energy functional is modified introducing a fatigue degradation function that effectively reduces the fracture toughness as a proper history variable accumulates. Numerical experiments show that this macroscopic approach is able to reproduce the main known features of fatigue crack growth in brittle materials: the Wöhler curve, the crack growth rate curve and the Paris law are naturally recovered, while the approximate Palmgren-Miner criterion and monotonic failure are obtained as special cases. Also, the approach is able to naturally handle complex geometries, loading conditions and fracture patterns including multiple cracks with arbitrary topology also in 3D.