Energy release rates near the interface between two anisotropic solids

If a crack starts from an interface between two dissimilar anisotropic materials, or is approaching the interface, various scenarios can happen. The question whether the crack will reach or even penetrate the interface depends on the mismatch of elastic moduli in the two materials. This contribution is devoted to the question how to calculate the change of the potential energy if the crack starts with its tip is on the interface or approaching it from a small distance. The energy release is calculated using the method of matched asymptotic expansions. Other than for the energy release rate in homogeneous materials it may happen here that the ERR is zero or infinity. The method is universal in the sense that it does not depend on the particular geometry and is even applicable if the crack tip meets a junction of several materials, or an angular point of the material interface e.g.

► The change of the potential energy is calculated by using matched asymptotic expansions.
► It is expressed with coefficients of the near field expansion of the displacement field u around the crack tip.
► We provide asymptotic formulae for the energy release.