Wave propagation in pre-deformed periodic network materials based on large strains homogenization

This paper explores the influence of large deformations on the propagation of acoustic waves in repetitive network materials. The problem of elastic wave propagation in pre-deformed elastic materials and structures is highly interesting in many applications. Both theoretical and numerical methods are developed in this contribution in order to assess the influence of finite strains developing within repetitive networks on the evolution of their band diagrams. An incremental scheme for the update of frequency and phase velocity of the computed homogenized medium has been developed successively considering 1D and 2D structures; it incorporates an update of the frequency and phase velocity of the propagating waves versus the effective density and the state of finite deformation of the effective continuum used as a substitution medium for the initial repetitive network. The applied deformation is shown to have significant effects on the wave frequency and phase velocity. Especially, it is shown that the phase velocity for the hexagonal network strongly decreases under finite compressive strains. The influence of the effective density on the dispersion relation and band diagrams under the application of an incremental deformation over the lattice unit cell is shown.