Fracture analysis of composites by time independent moving-crack orthotropic XFEM

Abstract

Time-independent orthotropic enrichment functions are introduced for dynamic propagation analysis of moving cracks in composites by the extended finite element method (XFEM). The proposed enrichment functions are derived from the analytical solutions for a moving/propagating crack in orthotropic media, and can be considered as a new extension to the available XFEM techniques for dynamic analysis of stationary and moving cracks in orthotropic materials. They are included within the framework of partition of unity and XFEM to enhance the accuracy of basic FEM solution near a moving crack tip in orthotropic media. The method allows for analysis of the whole crack propagation pattern on an unaltered finite element mesh, which is independently defined from the existence of any predefined crack or its propagation path. A combination of dynamic crack initiation toughness and crack orientation along the maximum circumferential stress is used to design a relatively simple and efficient formulation. Dynamic stress intensity factors (DSIFs) are evaluated by means of the domain separation integral method and the dynamic energy release rate. The time dependent XFEM equations are constructed by discretizing the standard weak formulation of the governing elastodynamics equation. They are solved by the unconditionally stable Newmark time integration scheme. A number of benchmark and test problems are simulated and the results are compared with the available reference results to illustrate the accuracy and efficiency of the proposed scheme.