Improved XFEM (IXFEM): 3D dynamic crack propagation under impact loading

Abstract

An improved XFEM (IXFEM) for three-dimensional non-planar crack propagation under impact loadings is developed. The proposed method couples the IXFEM (Tian and Wen, 2015; Wen and Tian, 2016) and the B-spline ruled surface method (BRSM) proposed previously by authors (Xiao, Wen and Tian (2021)). The issues of the standard XFEM for dynamic crack propagation, such as energy inconsistency, “null” critical time step size and optimal mass lumping at crack tip, are fundamentally avoided with an extra-DOF free PU approximation (Tian, 2013). The tip singularity enrichment is introduced to assure high accuracy through the extra-DOF free PU approximation. The BRSM, which is designed to solve the challenge about robust and efficient geometry representation of 3D non-planar surface crack growth, is applied to model the geometry of the 3D dynamic crack propagation in this paper. The interaction integral for 2D dynamic stress intensity factor (SIF) evaluation is extended to 3D. Efficiency of the proposed approach is demonstrated via numerical tests.