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

A micromechanical-statistical model based on hypersingular boundary integral equations for analyzing a pair of parallel interfaces weakened by antiplane micro-cracks

“…The three-phase model takes into consideration only the density of the interfacial micro-cracks. To model the interface more realistically, Wang et al [16] proposed a micromechanical-statistical approach in which the sizes and positions of the micro-cracks are randomly generated.…”

“…Thus, no post processing is needed to compute the interface displacement jumps which are required in estimating the effective stiffness of the interface. In [16], the micro-crack length is assumed to follow a normal distribution. For a more realistic distribution of the micro-crack sizes, Wang et al [17] employed a chi-square (v 2 ) distribution of a low degree of freedom to generate the micro-crack length.…”

“…The interval containing the micro-cracks is periodically reproduced on the remaining parts of the interface. The micromechanical-statistical model in [16] is formulated and solved in terms of hypersingular integral equations. In such a hypersingular integral formulation, the unknown functions are the displacement jumps over micro-cracks on the interface [3].…”

“…In [16], a selected number of micro-cracks of varying sizes are randomly generated and positioned to form a finite interval of the microscopically damaged interface between two elastic half-spaces. The interval containing the micro-cracks is periodically reproduced on the remaining parts of the interface.…”

“…elastic half-spaces. The micromechanical-statistical approach in [16,17] is used to model the two parallel planar interfaces. The resulting boundary value problem is formulated in terms of hypersingular boundary integral equations.…”