Modeling nonlinear beams for metamaterials design in a dynamic setting

We present, in a nonlinear dynamic framework, a beam model suitable for metamaterials design. The beam model, formulated directly in a discrete way, is completely defined by means of the strain and the kinetic energies. Differently from Hencky's seminal work, which only considers flexibility for computing buckling loads for rectilinear Euler–Bernoulli beams, the proposed model considers both the extensibility and shearability strain energy contributions along with translational and rotational kinetic energy contributions. All the derivations are carried out in a three-dimensional setting and successively particularized to the two-dimensional case. After having coded the proposed discrete model into an efficient time-step analysis strategy, its performances have been assessed by means of some numerical simulations for a simple auxetic cell.