A perfect 2D auxetic sliding mechanism based on an Islamic geometric pattern

Abstract

A new auxetic microstructure is introduced herein by inspiration from an Islamic geometric pattern that consists of square array of 8-pointed rigid stars interspersed with square array of 4-pointed rigid stars. By permitting each star to slide across its adjoining neighbors through incorporation of slots and sliders in the stars, an in-plane isotropic Poisson’s ratio of −1, and hence equi-biaxial strain, is achieved upon applied uniaxial compression. Apart from the negativity of Poisson’s ratio, another counter-intuitive property is the occurrence of global rotation of the entire structure relative to the stars during compression. Results indicate that when fully compressed, the in-plane strain is −0.232 with the accompanying global rotation of 6.18 degrees. Without the 4-pointed stars, the system can achieve an in-plane strain of −0.288 with a corresponding global rotation of 7.86 degrees.