A class of aperiodic honeycombs with tuneable mechanical properties

Metamaterials are a promising area of research, offering the potential to customise the mechanical properties of designed components to address specific engineering problems. These synthetic materials are engineered structures, the behaviour of which is derived from internal geometry as well as the properties of the basematerial. It has been shown that designing such structures to give rise to a single desired property is relatively simple, however designing structures that give rise to combinations of desirable properties remains a challenge. This paper is concerned with a class of honeycomb metamaterials that offer the potential to independently and isotropically modify two fundamental mechanical properties, the Poisson's ratio and the Elastic modulus. The recently discovered 'hat' monotile introduced a new aperiodic pattern to investigate as the basis of honeycomb structures, and it has been reported that such structures have zero Poisson's ratio at a range of relative densities and, consequently, at a range of relative stiffnesses. Unlike most other aperiodic tilings, the 'hat' is part of a continuous family of aperiodic tilings, which gives the opportunity to tune combinations of mechanical properties by modifying the geometric properties of the tiling, all while maintaining isotropy. Here we present the full family of tilings and assess their mechanical behaviour both through testing and simulation. Results from computational modelling show that the behaviour of this family of metamaterials is isotropic and they offer a Poisson's ratio from 0.01 to 0.49 at a range of relative densities, leading to the exciting conclusion that Poisson's ratio and Elastic modulus can be tuned independently. We envisage that this finding will benefit the design of engineering components, for example by offering the possibility to match mechanical properties of metamaterial components with those of surrounding components or materials to reduce interference stresses.