Dedicated to the memory of Professor Gaetano Fichera
The linear model equations of elasticity often give rise to oscillatory solutions in some vicinity of interface crack fronts. In this paper we apply the Wiener}Hopf method which yields the asymptotic behaviour of the elastic "elds and, in addition, criteria to prevent oscillatory solutions. The exponents of the asymptotic expansions are found as eigenvalues of the symbol of corresponding boundary pseudodi!erential equations. The method works for three-dimensional anisotropic bodies and we demonstrate it for the example of two anisotropic bodies, one of which is bounded and the other one is its exterior complement. The common boundary is a smooth surface. On one part of this surface, called the interface, the bodies are bonded, while on the complementary part there is a crack. By applying the potential method, the problem is reduced to an equivalent system of Boundary Pseudodi!erential Equations (BPE) on the interface with the stress vector as the unknown. The BPEs are de"ned via PoincareH }Steklov operators. We prove the unique solvability of these BPEs and obtain the full asymptotic expansion of the solution near the crack front. As a special case we consider the interface crack between two di!erent isotropic materials and derive an explicit criterion which prevents oscillatory solutions.