An analytical stiffness derivative extended finite element technique for extraction of crack tip Strain Energy Release Rates

An analytical approach combined with the extended finite element method (XFEM) is proposed to extract the Strain Energy Release Rates within the classical stiffness derivative technique. 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 with respect to the crack extension can be computed in a closed form and on the fly during the analysis. Thus the virtual crack extension, and the error inherent in the finite difference scheme of the classical stiffness derivative technique is completely avoided. Numerical results on few benchmark problems show that this method is comparable to the J-integral method.