In-plane wave motion and resonance phenomena in periodically layered composites with a crack

This paper investigates the transmission and propagation of two-dimensional (2D) time-harmonic plane waves in periodically multilayered elastic composites with a strip-like crack. The total wave field in the composite structure is represented as a sum of the incident wave field determined by the transfer matrix method and the scattered wave field described by integral representations in terms of the Green’s matrices and the crack-opening-displacements. A numerical scheme is developed to compute the wave propagation characteristics and the crack-characterizing quantities. The effects of the crack location and size as well as the angle of wave incidence are investigated using the averaged crack-opening-displacements and the stress intensity factors. Special attention of the paper is devoted to resonance wave motion and wave localization phenomena in a stack of periodical elastic layers weakened by a single strip-like crack. Numerical results are presented and discussed to reveal the usual and the resonant wave transmission by using the power-density vector and the energy streamlines in the vicinity of the crack. Wave localization due to interior and interface cracks is analyzed by considering the energy captured by a crack, and resonance induced crack growth is also discussed.