A reconfigurable metamaterial using trapeziums and triangles with alternative connectivity

Abstract

A category of metamaterial that can manifest a wide range of Poisson's ratio from positive to negative is presented herein. This metamaterial consists of rigid units in the shapes of right trapeziums and right triangles that are connected at their corners in the form of necks, which supply elastic restraint during relative rotation of the rigid units. The on-axes Poisson's ratio of the metamaterial was formulated by geometrical analysis. By assigning a rotational spring constant to the connecting necks, the total spring potential energy for a specific enclosure was obtained. This energy was then matched against the strain energy of deformation for the homogenized continuum of the metamaterial for the same enclosure to give the on-axes Young's moduli. Results reveal a configuration that enables the metamaterial to display sign-programmable Poisson's ratio. In addition to being able to adjust the on-axes Young's moduli relative to each other, two specific configurations have been identified that permit both on-axes Young's moduli to be equal. The ease of reconfiguration, the wide range of effective mechanical properties and the capability of the Poisson's ratio sign to be programmed, therefore, avail the metamaterial as a viable material for applications that require frequent in situ adjustment of effective properties.