Tailoring Poisson’s ratio of bending-active mechanical metamaterials with periodic and nonperiodic pentagonal grids

Author

Sakai, Yusuke

Abstract

This study proposes a shape design method for a bending-active mechanical metamaterial composed of a three-dimensional pentagonal grid with a tailorable Poissons ratio. The specific shape of the proposed grid is derived from a dual geometry of rotating rigid squares. Slender flexible beams with rectangle cross-sections are used for components of structural units, and the connections between members are rigid. To explore the values of Poissons ratio for in-plane deformation of the proposed grid, we parametrically alter the shape of a structural unit and the bending stiffness of a member. Shape parameters are defined as positions of connections, cross-sectional height and width of a member, and the ratio determining the convexity and concavity of a pentagonal grid. Based on geometric frustration, a nonperiodic pentagonal grid can also be designed. In numerical examples, we investigate the mechanical properties for in-plane and out-of-plane deformations of grids by carrying out finite element analysis. A wide range of Poissons ratios ranging from 5 to 5 is observed. Moreover, we investigate the relationships between the distribution of Poissons ratio of an initial pentagonal grid and that of discrete Gaussian curvature on nodes of a curved surface obtained by out-of-plane deformation.