Interface cracks in anisotropic composites

The linear model equations of elasticity often give rise to oscillatory sol utions in some vicinity of interface crack fronts. In this paper we apply t he Wiener-Hopf method which yields the asymptotic behaviour of the elastic fields and, in addition, criteria to prevent oscillatory solutions. The exp onents of the asymptotic expansions are found as eigenvalues of the symbol of corresponding boundary pseudodifferential equations. The method works fo r three-dimensional anisotropic bodies and we demonstrate it for the exampl e of two anisotropic bodies, one of which is bounded and the other one is i ts exterior complement. The common boundary is a smooth surface. On one par t of this surface, called the interface, the bodies are bonded, while on th e complementary part there is a crack. By applying the potential method, th e problem is reduced to an equivalent system of Boundary Pseudodifferential Equations (BPE) on the interface with the stress vector as the unknown. Th e BPEs are defined via Poincare-Steklov operators. We prove the unique solv ability of these BPEs and obtain the full asymptotic expansion of the solut ion near the crack front. As a special case we consider the interface crack between two different isotropic materials and derive an explicit criterion which prevents oscillatory solutions. Copyright (C) 1999 John Whey & Sons, Ltd.