Auxetic Metamaterial Model Made from Rotating Rectangles, Hexagons, and Triangles

Abstract

A perfectly auxetic 2D metamaterial model is described herein by means of interconnected rotating rigid units of three different shapes: hexagons, triangles, and rectangles. The in‐plane Young's modulus is obtained by matching the discrete elastic energy stored at the hinges during relative rotation of the rigid units with the overall elastic energy stored in the metamaterial's continuum equivalence. Results indicate that, in addition to the trivial effects from the rotational spring constant at the hinges, the in‐plane Young's modulus is highly influenced by the internal angle, followed by the relative size of the triangle with reference to the sizes of other rigid units. The effect from the rectangle aspect ratio presents the least influence. As such, there are several parameters to control the Young's modulus, from the coarse tuning by adjusting the internal angle to fine tuning by controlling the rectangle aspect ratio. The capability of the metamaterial's Young's modulus to be tuned from a spectrum of parameters that range from coarse to fine tuning permits this metamaterial's mechanical property to be precisely designed and manufactured in a cost‐effective manner.