Nonlinear wave propagation analysis in architected materials with consideration of extension, shear and bending effects

Abstract

The current paper deals with the wave dispersion characteristics of two-dimensional architected materials, considering both the linear and nonlinear regimes. We study the full non-linear coupling between the shear, extension, and bending deformation modes on the inner material deformation of the square, triangular, hexagonal, and re-entrant hexagonal unit cells. The dynamical analysis is done at high and low frequencies and for two different wave amplitudes. Based on the Linstedt–Poincare perturbation method, the non-linear correction to the dispersion diagram is evaluated. The relative contribution of each non-linear energy mode on the nonlinear wave dispersion attributes is quantified. The obtained results show that both the wavenumber and lattice design play an important role in the nonlinear wave corrections of the dispersion characteristics. The shear mode is shown to have the highest effect in the non-linear correction for all considered architected materials, compared to the flexural mode, which has the lowest energy contribution. The eigenwaves vectors are used to compare the deformation of hexagonal and re-entrant hexagonal unit cells at low and high frequencies over the entire Brillouin zone. Overall, the present work provides some guideline as to the proper selection of the inner design of architected materials prone to strong nonlinear dynamical effects.