On elastic waves and related phenomena in lattice materials and structures

Lattice materials possessing a spatially periodic microstructure are suitable in weight sensitive multifunctional structural applications such as sandwich panels. They not only possess high specific stiffness but also provide opportunities to tailor acoustic and thermal properties through designing their unit cell topology. This paper seeks to understand their mechanical response under static and dynamic loads from a structural mechanics perspective combining Bloch wave theory with Finite Element Method (FEM). Bringing together results from earlier works, it is shown that three eigenvalue problems, containing the frequency and wave vector as the unknowns, can be used to analyze bulk and surface wave phenomena. The application of eigenvalue problems to band-gaps (spatially extended response), edge effects of Saint Venant type (spatially localised response), and buckling of long cellular structures is shown.