A semi-analytical stiffness derivative method based on the extended finite element framework Haim Waisman Department of Civil Engineering & Engineering Mechanics Columbia University, New York, NY 10027 Abstract A new approach to extract the Strain Energy Release Rates within the classical stiffness derivative method is proposed. This approach is based on the extended finite element method (XFEM), and the proposed idea hinges on the following two XFEM properties: (i) the crack is mesh independent, i.e. there is no need for mesh perturbations in the vicinity of the crack; and (ii) the asymptotic crack tip field is embedded in the mathematical formulation of the stiffness matrix. By employing these properties we show that the derivative of the stiffness matrix can be computed in a semi-analytical way and on the fly during the analysis. Thus the error inherent in the finite difference scheme of the classical stiffness derivative method may partially be avoided. Numerical results on few benchmark problems show that this method is comparable to the J-integral method. Key words: Extended Finite Element Method, XFEM, stiffness derivative, J-integral, mixed mode fracture, Stress Intensity Factors, Strain Energy Release Rates 1 Introduction Several methods have been proposed in the literature to extract the Stress In- tensity Factors (SIFs) or equivalently the Strain Energy Release Rates (SERRs) in linear elastic fracture mechanics. These methods can be grouped as direct and indirect methods. Direct methods are the simplest methods to compute SIFs, which are mainly based on correlation of crack opening displacements, * Corresponding author’s email: waisman@civil.columbia.edu Preprint submitted to Elsevier Science 28 October 2010