Design and analysis for large magnitudes of programmable Poisson's ratio in a series of lightweight cylindrical metastructures

Abstract Cylindrical metastructures, which have the exclusive programmability in Poisson's ratio, are widely used in engineering. Herein, a series of cylindrical metastructures with programmable Poisson's ratio were devised via the curling of the planar metamaterials. The relationships of the deformation characteristics and Poisson's ratio between the cylindrical metastructures and planar metamaterials were systematically analyzed. It is originally identified that the number of the circumferential unit cell N remarkably affects the deformation modes. When N is small, the warp effect, induced by the curved members, is remarkable. The cylindrical metastructures present the petal- and polygon-like deformation modes. Consequently, the Poisson's ratios deviate notably from those of the planar metamaterials. Further, the quantitative analysis figures out that when N is larger than specific critical values, the Poisson's ratios approach to those of the planar metamaterials. Thus this work identifies a design strategy, i.e. once the circumferential unit cells are sufficiently dense, the Poisson's ratios of the cylindrical metastructures can be predicted by the theory of the corresponding planar metamaterials. Moreover, through modulating the geometric parameters, large magnitudes of both positive and negative Poisson's ratio are obtained. This extraordinary feature of the large radial expansion and shrinkage, actuated through a slight axial stretching, can be used in shape morphing and deployable devices. The design and analysis provide a perspective on the multifunctional metastructures with programmable Poisson's ratio.