Stress intensity factor analysis of interface cracks using X-FEM

The extended finite element method (X-FEM) proposed by Belytschko et al. (International Journal for Numerical Methods in Engineering 1999; 45:602; 1999; 46:131; 2001; 50:993) uses interpolation functions based on the concept of partition of unity, and considers the asymptotic solution and the discontinuity of displacement fields near a crack independently of the finite element mesh. This paper describes the application of X-FEM to stress analyses of structures containing interface cracks between dissimilar materials. In X-FEM, an interface crack can be modelled by locally changing an interpolation function in the element near a crack. The energy release rate should be separated into individual stress intensity factors, K-1 and K-2, because the stress field around the interface crack has mixed modes coupled with mode-I and mode-II. For this purpose, various evaluation methods used in conjunction with numerical methods such as FEM and BEM are reviewed. These methods are examined in numerical examples of elastostatic analyses of structures containing interface cracks using X-FEM. The numerical results show that X-FEM is an effective method for performing stress analyses and evaluating stress intensity factors in problems related to bi-material fractures. Copyright (C) 2003 John Wiley Sons, Ltd.