A numerical implementation of the eXtended Finite Element Method (X-FEM) to analyze crack propagation in a structure under dynamic loading is presented in this paper. The arbitrary crack is treated by the X-FEM method without re-meshing but using an enrichment of the classical displacement-based finite element approximation in the framework of the partition of unity method. Several algorithms h...

The accuracy of the Extended Finite Element Method (XFEM) in solving problems of straining plate with central crack is analyzed. Numerical solutions for displacements and stresses are compared with analytical solutions, while numerical solutions for stress intensity factor are compared with empirical solutions. The impact of the mesh density and near tip (NT) enrichment function are investigate...

The cracked Brazilian disc (CBD) specimen is widely used in order to determine mode-I/II and mixed-mode fracture toughness of a rock medium. In this study, the stress intensity factor (SIF) on the crack-tip in this specimen is calculated for various geometrical crack conditions using the extended-finite element method (X-FEM). This method is based upon the finite element method (FEM). In this m...

In this paper, and its companion Part 2 [Dong and Atluri (2013b)], the Symmetric Galerkin Boundary Element Method (SGBEM), and the SGBEMFEM alternating/coupling methods, are compared with the recently popularized Extended Finite Element Method (XFEM), for analyzing fracture and fatigue crack propagation in complex structural geometries. The historical development, and the theoretical/algorithmi...

The extended finite element method (X-FEM) is a numerical method for modeling strong (displacement) as well as weak (strain) discontinuities within a standard finite element framework. In the X-FEM, special functions are added to the finite element approximation using the framework of partition of unity. For crack modeling in isotropic linear elasticity, a discontinuous function and the two-dim...

Using crystal plasticity, finite element analyses were carried out to model cyclic deformation for a low solvus high refractory (LSHR) nickel superalloy at elevated temperature. The analyses were implemented using a representative volume element (RVE), consisting of realistic microstructure obtained from SEM images of the material. Monotonic, stress-relaxation and cyclic test data at 725 C were...