On micromechanical-statistical modeling of microscopically damaged interfaces under antiplane deformations

A microscopically damaged interface between two elastic half-spaces under anti-plane deformations is modeled using randomly distributed interfacial micro-cracks. The micro-crack length is a continuous random variable following a given probability distribution. The micromechanical-statistical model of the interface, formulated and solved in terms of hypersingular integral equations, is used to estimate the effective stiffness of the interface. The number of micro-cracks per period length of the interface required to homogenize the effective interface stiffness is examined. Also investigated are the effects of the micro-crack length and the crack-tip gap between two neighboring micro-cracks on the effective stiffness.