Designing new auxetic structures based on known 2D systems

Abstract

During the past 40 years, a large variety of mechanisms have been devised in order to create structures that are able to exhibit a negative Poisson’s ratio [1-8]. However, most of the proposed designs are two dimensional, meaning that in the third dimension the structure is either ignored or still behaves in a conventional way. While this has created a wealth of structures that can find various applications, confining auxeticity to two dimensions restricts the ability of controlling the mechanical properties in the third dimension. This trend appears to have been changing in recent years, with an increasing number of structures showing negative Poisson’s ratio in three dimensions being proposed [9-12]. In this context, this work aims at presenting some of the recent progress made in this direction. A variety of structures will be discussed showing how it is possible to use a known auxetic 2D system to build a 3D one. The work will also present a case study of the deformation of the square grid and its generalisation for large strains and it will be shown that the structures can be designed to attain an incremental Poisson’s ratio which is negative for relatively large strains.