Stepwise analysis of pantographic beams subjected to impulsive loads

Abstract

Materials based on pantographic unit cells have very interesting mechanical peculiarities. For these reasons they are largely studied from a theoretical, experimental, and numerical point of view. Numerical simulations furnish an important contribution for the the design and optimization of such materials and, more generally, for metamaterials. Here, we consider the influence of inertial forces, removing the hypothesis of quasistatic loading. By using an intrinsically discrete model, inspired by Hencky’s ideas, already tested in a series of published works, here we add the contribution of inertial forces and, in the framework of stepwise schemes, we re-experience an adaptive integration scheme capable of reconstructing the best structural response corresponding to a prefixed time step. Several numerical simulations, although preparatory, inspire some remarks on materials based on pantographic cells and outline the way for future challenges.