Stefan Loehnert

Fatigue fracture simulations with the phase‐field method (PFM) lack efficiency due to the fine meshes required, especially when each load cycle is simulated explicitly. Recent developments in combining the phase‐field method for brittle fracture with the extended/generalised finite element method (XFEM/GFEM) show a remarkable reduction of the number of degrees of freedom and thus a reduction of computational effort while retaining or even improving accuracy. In this paper, the combined extended phase‐field method (XPFM) is expanded to fatigue processes in a two‐dimensional setting. A new stabilisation of the phase‐field transformation function is proposed and a convergence criterion for the nested staggered solution process and enrichment scheme update procedure as well as an adaptive integration technique for the non‐polynomial ansatz functions is incorporated. Several numerical examples emphasise the benefits and the efficiency of the newly developed method.