An extended phase-field approach for the efficient simulation of fatigue fracture processes

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.