Improved XFEM: Accurate and robust dynamic crack growth simulation

The extended finite element method (XFEM) is widely accepted in academy as the major technique for crack analysis. Starting from 2009, commercial codes started to use this technique for crack analysis, singling the mature and acceptance of the technique in industries. However, the direct extension of the singular tip enrichment of XFEM, the core of the method, to dynamic crack growth simulation has long been a difficulty due to: (a) elevated bad conditioning as crack propagating, (b) extra-dof dynamics and energy inconsistency, and (c) “null” critical time step size and optimal mass lumping at crack tip. Based on an extra-dof-free partition of unity enrichment technique (Tian, 2013), we have improved XFEM through a crack tip enrichment without extra dof (Tian and Wen, 2015). This paper is to answer the question whether the improved XFEM can also be easily extended to dynamic problems. Numerical tests show that the new XFEM is not only straightforward in implementation in dynamic problems, also provides the most accurate dynamic SIF in the benchmark problems and is orders of magnitude faster with an iterative solver.