On the virtual crack extension method for calculation of the rates of energy release rate

Abstract This paper generalizes the analytical virtual crack extension method presented by Lin and Abel by providing the higher order derivatives of energy release rate due to crack extension for multiply cracked bodies. It provides derivations and verifications of the following: extension to the general case of multiple crack systems, extension to the axisymmetric case, inclusion of crack-face and thermal loading, and evaluation of the second derivative of energy release rate. The salient feature of this method is that the energy release rate and its higher order derivatives for multiple crack systems are computed in a single analysis. It is shown that the number of rings of elements surrounding the crack tip that are involved in the mesh perturbation due to the virtual crack extension has an effect on the solution accuracy. Maximum errors for the mesh density used in the examples are about 0.2% for energy release rate, 2–3% for its first derivative, and 5–10% for its second derivative.