An enriched finite element model for wave propagation in fractured media

In this paper a new numerical method has been developed in the context of enriched finite element methods (FEMs) to analyze wave propagation in fractured media. The method combines the advantages of global enrichment with harmonic functions via the Generalized FEM (GFEM) with the efficacy of the Phantom Node Method (PNM), an eXtended FEM (XFEM) variant, to model cracks independently of the mesh. The GFEM enrichment suppresses the spurious oscillation that appear in regular FEM analysis of transient wave propagations due to numerical dispersion and Gibb's phenomenon. For use in explicit simulations, a mass lumping methodology has been introduced with a critical time step size that is both similar to that of the underlining FEM and independent of the location of the fracture. Through three examples, the developed PNMGFEM is demonstrated to more accurately model wave propagation in fractured media than either the FEM or the PNM/XFEM.