Micro-mechanics models for an imperfect interface under anti-plane shear load: Hypersingular integral formulations

Two micro-mechanics models are proposed for an imperfect (weak) interface between two anisotropic elastic half-spaces under anti-plane shear load. The imperfect interface in the first model contains an array of periodically distributed micro-cracks with random lengths and positions. The second model, a simplified version of the first, is a three-phase model in which a period length of the interface contains a single representative micro-crack, perfectly bonded parts and an effective region. Both models are formulated in terms of hypersingular integral equations which may be solved by boundary element procedures to calculate the effective interface stiffness and the critical failure load of the interface.