Nonlinear deformation behaviour of auxetic cellular materials with re-entrant lattice structure

Recent frontiers in material development are represented by a class of so-called auxetic metamaterials that, thanks to their structure rather than composition, are characterized by a negative Poisson's ratio. In the present paper a two-dimensional auxetic plate, made by structural straight elements forming a lattice periodic structure with re-entrant cells, is considered. A thorough discussion on the linear and geometrically nonlinear deformability of the auxetic plate is presented. The key geometric parameters governing the deformability of the plate are identified, and some analytical expressions for calculating the Poisson's ratio, as a function of the applied strain, are given. Numerical (finite element) analyses and experimental tests on 3D printed specimens are carried out to verify the theoretical findings. For the latter ones, full field strain maps are obtained by means of a suitable interpolation of the sampled displacement field measured by digital image techniques.