The auxetic behavior of a general Star-4 structure

Abstract

An analytical model for a general Star-4 system, having different ligament lengths, angles, and ligament thickness, is derived using Castigliano's second theorem. The analytical model is validated through finite element analysis and experimental work. The results obtained show that, depending on the parameters used, the general Star-4 system can show a wide range of Poisson's ratios with the potential of obtaining giant negative Poisson's ratios (in the order of −8) for certain conformations. The wide range of Poisson's ratio is explained in terms of the different geometrical conformations obtainable by the system, where the star-ligaments can also describe rhombi, irregular octagons, rectangles, and accordion-like systems, together with changes in the deformation mechanism due to variations in parameters. For example, if one set of star-ligaments is much thicker than the other, the deformation of the star would be akin to that of the hexagonal reentrant unit cell.