Auxetic System Based on Rotating Hexagons and Triangles

Abstract

An auxetic metamaterial that exhibits isotropic in‐plane deformation is introduced herein in the form of rotating rigid units, consisting of regular hexagons and equilateral triangles, that are connected at their vertices. By inspection, the in‐plane Poisson's ratio is at a constant value of ν = −1. The size descriptor of this metamaterial can be expressed as a function of rotating unit sizes and their internal angle by means of geometrical construction. By energy method, the effective in‐plane Young's modulus of this metamaterial has been established and shown to be governed by the rotational stiffness at the connecting hinges in addition to the relative sizes of the rotating units and their internal angle. Results indicate that the in‐plane Young's modulus is linearly proportional to the rotational stiffness at the connecting hinges and inversely proportional to the rigid unit size. In addition, the Young's modulus is governed by the ratio of the hexagon‐to‐triangle size for small internal angle, and rapidly approaches extreme value as the internal angle approaches right angle. The characteristics of the proposed metamaterial would allow its use as a sieve that not only controls the filtering of particles by size but also by the aspect ratio of rod‐like particles.