A consistent finite element approach for dynamic crack propagation with explicit time integration

Abstract

The concept of the partition of unity (PU) enabled the development of nodal enrichment strategies, such as the Extended Finite Element Method (XFEM) and Generalised Finite Element Method (GFEM), for realistic simulations of structural behaviour with applications to both static and dynamic problems. Nonetheless, the majority of existing methodologies still inherit instability issues for arbitrary discontinuity geometries when using an explicit time integration scheme. To address this, the discrete strong discontinuity approach is herein developed for the simulation of dynamic crack propagation. The formulation is fully variationally consistent and a new mapping approach is introduced to embed the rigid body movements associated with discontinuities while keeping the critical time step bounded. Multiple discontinuities within a single element are also considered for the accurate modelling of crack branching. The stability of the new technique is first verified in one- and two-dimensional elements. Next, the accuracy and efficiency are validated with structural examples including tensile and mixed-mode loadings. A concrete L-specimen, where different loading rates produce significant variations in failure patterns and strength, is also considered. Results show the good overall agreement with experimental data and other numerical studies available in the literature. The new formulation, however, is able to capture complex crack propagation phenomena, such as crack branching, without any specific additional criterion (e.g. based on crack tip velocity). The formulation presented in this paper is, to the best of the authors’ knowledge, the first PU-based consistent finite element with intrinsically bounded critical time step for explicit time integration.