Growth of a semi-infinite inclusion in an elastic wave metamaterial with local resonators

In this study, the dynamic response of a growing inclusion in an elastic wave metamaterial with local resonators is investigated. It is assumed that the inclusion at a constant speed is composed of particles with larger or smaller mass than the surrounding lattice is. Based on the integral transform, wave equations of the growing inclusion are derived as the Wiener–Hopf form. In order to show the effect of local resonators, stop band properties and the ratio of the tip to end displacements of the inclusion are considered. Numerical results show that the local resonators can make the displacement ratio tend to the case without inclusion. It indicates that the outstanding ability of elastic wave metamaterials inhibits structural deformation and defect growth.