Novel weight function approach for plane elasticity crack problems (Q1388257)

In the case of boundary traction in equilibrium, we obtain a weight function for evaluating the stress intensity factors which does not depend on elastic constants. To complete derivation, a singular field called the \(\beta_1\)-field is introduced, which has an order of \(O(r^{-1/2})\) for the displacements and \(O(r^{-3/2})\) for the stresses at the vicinity of the crack tip. We also introduce a complementary regular field, called the \(\beta_2\)-field, in which the applied boundary tractions are opposite to those derived from the \(\beta_1\)-field. Numerical examples demonstrate the efficiency of the approach.