Coupling XFEM and Peridynamics for brittle fracture simulation: part II—adaptive relocation strategy

Abstract

An adaptive relocation strategy for a coupled XFEM-Peridynamic (PD) model is introduced. The motivation is to enhance the efficiency of the coupled model and demonstrate its applicability to complex brittle fracture problems. The XFEM and PD approximation domains can be redefined during the simulation, to ensure that the computationally expensive PD model is applied only where needed. To this end a two-step expansion/contraction process, allowing the PD patch to adaptively change its shape, size and location, following the propagation of the crack, is employed. No a priori knowledge of the crack path or re-meshing is required, and the methodology can automatically switch between PD and XFEM. Three 2D fracture examples are presented to highlight the performance of the methodology and the ability to follow multiple crack tips. Results indicate significant computational savings. Furthermore, the characteristic length scale of PD theory bestows a nonlocal and multiscale component to the methodology.

Review of Peridynamics: Theory, Applications, and Future Perspectives

“…The peridynamics are very accurate, but the speed and efficiency in "industrial problems" are lower than the concurrent methods, such as Extended-FEM or meshless methods. Coupling of PD with these methods is very efficient [16] and [88] to [90] and, as an alternative solution the parallel computing (e.g. supercomputers or GPGPU), seems natively applicable in peridynamics, which could increase the speed and efficiency of the method [91] to [93].…”