Design and evaluation of three–dimensional axisymmetric mechanical metamaterial exhibiting negative Poisson's ratio

Mechanical metamaterials are generally two-dimensional periodic structures or three-dimensional cellular structures that exhibit mechanical properties beyond the ordinary. Due to size and boundary effects, three-dimensional mechanical metamaterials typically display anisotropic changes even if they are isotropic in construction and composition. However, in this study, the comprehensive design and fabrication of a three-dimensional axisymmetric auxetic structure that exhibits uniform and axisymmetric transverse deformation under longitudinal compression loading are proposed. Extending the concept of two-dimensional periodically perforated auxetic sheet structures to the third dimension, the design of the metamaterial was generated by revolving a two-dimensional parabolic curve along the axis of rotation and subsequently perforating the structure periodically with elliptical voids varying in size longitudinally along the curvature of the structure in order to promote the exhibition of isotropic negative Poisson's ratio. Furthermore, this study elucidates the significance of the perforations by comparing the metamaterial structure to a so-called plain structure.