Sikang Yan, Alexander Schlüter, Ralf Müller

• In the last decades, the phase field method has drawn much attention for its application in fracture mechanics because it offers a simple unified framework for crack propagation. The core idea of phase field models for fracture is to introduce a continuous scalar field representing the discontinuous crack. Recently, a phase field model for fatigue has been proposed along this path. The fatigue failure differs from the other fracture scenarios since cracks only occur after a considerable number of load cycles. As fracturing happens, changes of the material microstructure are involved, which causes the evolution of the structural configuration. Thus, a new mathematical description not based on traditional spatial coordinates but the material manifold is desired, which will serve as an elegant analysis tool to understand the energetic forces for crack propagation. Configurational forces are a suitable choice for this purpose, as they describe the energetic driving forces associated with phenomena changing the material itself. In this work, we present a phase field model for fatigue. Furthermore, the phase field fatigue model is analyzed within the concept of configurational forces, which provides a straightforward way to understand the phase field simulations of fatigue fracture.