Abstract
In the present study frequency-dependent effective spring boundary conditions are introduced to describe wave propagation through an interface between two elastic isotropic media with a distribution of rectangular aligned micro-cracks. The explicit analytic formulae are obtained for stiffnesses in effective spring boundary conditions modelling the distribution of rectangular cracks employing the boundary integral equation method, the ensemble averaging technique and Boström–Wickham approach. Three diagonal components of the introduced stiffness matrix are expressed in terms of the elastic properties of materials, the frequency, and dimensions of rectangular cracks. The analysis of the derived relations for stiffnesses shows the low influence of density on stiffnesses. If the area of rectangular cracks is constant, but the elongation of rectangular cracks increases then stiffnesses become larger. On the other hand, stiffnesses get smaller if one side is constant and the second side of rectangular crack increases. Examples demonstrating the influence of material properties and the elongation of rectangular cracks on three components of the stiffness matrix are provided. Effective stiffnesses for the distribution of square cracks are nearly proportional to the corresponding stiffnesses obtained for the distribution of circular cracks.
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