a b s t r a c tAn interaction (energy) integral is derived for the computation of mixed-mode stress intensity factors (SIFs) in nonhomogeneous materials with continuous or discontinuous properties. This method is based on a conservation integral that relies on two admissible mechanical states (actual and auxiliary fields). In general, the interaction energy contour integral is converted into an equivalent domain integral in numerical computations. It can be seen from the equivalent domain integral, the integrand does not involve any derivatives of material properties. Moreover, the formulation can be proved valid even when the integral domain contains material interfaces. Therefore, it is not necessary to limit the material properties to be continuous for the present method. Due to these advantages the application range of the interaction integral method can be greatly enlarged. The numerical implementation of the derived expression is combined with the extended finite element method (XFEM). Using this method, the influences of material properties on the mixed-mode SIFs are investigated for four types of material properties selected in this work. Numerical results show that the mechanical properties and their first-order derivatives can affect mode I and II SIFs greatly, while the higher-order derivatives affect the SIFs very slightly.

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A new interaction integral formulation is derived for obtaining mixed-mode stress intensity factors (SIFs) of an interface crack with the tip clo.w to complicated material interfaces. The method is a conser\'ation integral that relies on two admissible mechanical states (actual and auxiliaty fields). By a suitable selection of the auxiliary fields, the dotnain formulation does not contain any integral related to the material intetfaces, which makes it quite convenient to deal with complicated intetface problems. The numerical implementation of the derived e.xpression is cotnbitied with the e.xtended finite elemetU method (XFEM). According to the numerical calculatiotis. the interaction integral shows good accuracy for straight attd cwyed ititetface crack problems and exhibits domain-independence for material intetfaces. Finally, an ititerfacial fracture problem is investigated for the representative centrosymmetric structure formed by two con.stituent materials.

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