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

• The estimation of the effective stiffness of a pair of micro-damaged interfaces is considered.
• The micro-damaged interfaces are modeled as containing micro-cracks.
• Micro-models based on hypersingular integral boundary formulations are proposed.
• In one of the micro-models, the micro-cracks are generated randomly.
• Factors influencing the effective stiffness are investigated.

The estimation of the effective stiffness coefficients of a pair of microscopically damaged interfaces in a trimaterial under antiplane deformations is considered here. The trimaterial is made of a thin elastic layer sandwiched between two elastic half-spaces. The parallel planar interfaces are modeled as containing periodic arrays of randomly generated micro-cracks. The micromechanical-statistical model of the interfaces is formulated and numerically solved in terms of hypersingular boundary integral equations in which the displacement jumps across the micro-cracks are unknown functions. The numerical results obtained from the model demonstrate that the effective stiffness coefficients are influenced by the elastic moduli of the trimaterial, the thickness of the elastic layer and the densities of the micro-cracks.