Elastic pantographic 2D lattices: a numerical analysis on the static response and wave propagation

In the present paper we consider a structure constituted by 'long' Euler beams forming two mutually intersecting arrays and interacting via internal pivots, which we call pantographic 2D lattices. For this structure, small deformations, but possibly large displacements, can be considered. We performed numerical simulations concerning 2D pantographic sheets of rectangular shape with two families of beam arrays cutting at 90 degrees. The set of theoretical tools needed to describe the continuous limit for such kind of structures goes beyond classical continuum mechanics. In particular, non-Cauchy contact actions can arise in the considered context. The results motivate further investigations, the first step reasonably being the determination of a generalized continuum model.