Effective spring boundary conditions for modelling wave transmission through a composite with a random distribution of interface circular cracks

[Display omitted] In the present study frequency dependent effective spring boundary conditions are formulated to simulate wave propagation through an interface with distributions of micro-cracks of various sizes. The frequency dependent formulae for spring stiffnesses are obtained for circular cracks employing the boundary integral equation method, the ensemble averaging technique and Betti’s reciprocity theorem. The frequency dependent analytical relations for normal and tangential spring stiffnesses are expressed in terms of the elastic properties of contacting materials and properties of distributed cracks. In the case of equally sized cracks, the formulae for stiffnesses have an analytical form. The provided analysis of the influence of frequency on spring stiffnesses shows that for each crack size a number of sharp and narrow peaks can be observed in certain frequency ranges. The novelty of this study also lies in the consideration of different sized interface cracks. The influence of the standard deviation of radii of circular cracks on spring stiffnesses is analysed using the lognormal distribution. It is shown that there is a relatively low influence of size variation on spring stiffnesses, if the standard deviation in the distribution is not extremely large.