Dual conservation integrals and energy release rates

Simple derivation of the dual conservation integrals in small strain elasticity is presented, without the aid of Noether’s theorem on invariant variational principles. The derived integrals are related to the release rates of the potential and complementary potential energy associated with the defect motion. The analysis corrects the errors in earlier derivation of the relationship between the dual integrals and the release rates of the complementary potential energy. Selected examples in plane and anti-plane strain illustrate the calculation of dual integrals and their application. It is shown that the evaluation of dual integrals is of similar complexity to that of classical integrals, so that either can be used to determine the stress intensity factors or the forces between defects, without solving the corresponding boundary value problems. An advantage of combining the two calculations is discussed.