MULTISCALE MODELING OF MULTI-LAYERED STRUCTURES

A mechanical model based on a novel multiscale approach has been recently formulated in Massabo and Campi, Meccanica, 50(4), 2015, to study multi-layered plates with imperfect interfaces and delaminations loaded dynamically. The model couples an equivalent single-layer structural theory and a discrete-layer cohesive-crack model in order to efficiently and accurately describe both the global behaviour and the local perturbations of the fields generated by the inhomogeneous material structure and the presence of interfacial imperfections. The homogenized field equations depend on the global variables only so that problems characterized by a large number of layers and delaminations are conveniently treated and efficient and insightful closed-form solutions can be derived for relevant problems. The model is applied to investigate the effects of the presence of imperfect interfaces on the dynamic characteristics of the plates. Closed form solutions are derived for unidirectionally reinforced wide plates with elastic sliding interfaces. The asymptotic limits, which can be obtained through a perturbation analysis, define the free vibrations of fully-bonded and fully-debonded plates. Changes in the interfacial stiffness strongly affects natural frequencies and modes of vibration: new modes are activated and the cut-off frequency of the second flexural spectrum, which in fully bonded plates is quite large so that the spectrum is usually disregarded, decreases and vanishes for decreasing/vanishing interfacial stiffness.