An isotropic zero Poisson's ratio metamaterial based on the aperiodic ‘hat’ monotile

Abstract

Metamaterials are synthetic materials, engineered to have desirable mechanical properties. This paper is concerned with a class of cellular metamaterials that minimise the Poisson's ratio, a metric that characterises the deformation behaviour of materials according to their orthogonal response to applied force. This secondary deformation is usually visually apparent as a sideways “bulge”, and can limit the longevity of multi-material components, from aircraft parts to medical implants, because of the interference shear stresses that arise between different materials due to deformations in different directions by different amounts. As a result, low Poisson's ratio can be a desirable mechanical property and the challenge of producing cellular metamaterials that have reduced Poisson's ratio has received significant research attention. However, solutions that have been proposed tend to be limited in their applicability, either because they are anisotropic, so behaviour varies greatly according to direction of the applied force, or because they are very low in relative density, so have low stiffness. Here we introduce a new cellular metamaterial, a honeycomb based on the recently discovered aperiodic ‘hat’ monotile, which offers nominally zero Poisson's ratio. Results from compression testing and computational modelling show that the behaviour of this metamaterial is isotropic, and is consistent across a range of relative densities, leading to the exciting conclusion that zero Poisson's ratio is possible for different stiffnesses. We envisage that this metamaterial will facilitate otherwise unfeasible technologies, such as morphing wing structures and medical devices that better mimic the behaviour of tissues such as cartilage.