Fracture mechanics analysis using the wavelet Galerkin method and extended finite element method

This paper presents fracture mechanics analysis using the wavelet Galerkin method and extended finite element method. The wavelet Galerkin method is a new methodology to solve partial differential equations where scaling/wavelet functions are used as basis functions. In solid/structural analyses, the analysis domain is divided into equally spaced structured cells and scaling functions are periodically placed throughout the domain. To improve accuracy, wavelet functions are superposed on the scaling functions within a region having a high stress concentration, such as near a hole or notch. Thus, the method can be considered a refinement technique in fixed-grid approaches. However, because the basis functions are assumed to be continuous in applications of the wavelet Galerkin method, there are difficulties in treating displacement discontinuities across the crack surface. In the present research, we introduce enrichment functions in the wavelet Galerkin formulation to take into account the discontinuous displacements and high stress concentration around the crack tip by applying the concept of the extended finite element method. This paper presents the mathematical formulation and numerical implementation of the proposed technique. As numerical examples, stress intensity factor evaluations and crack propagation analyses for two-dimensional cracks are presented. Copyright (c) 2012 John Wiley & Sons, Ltd.