New structures and materials exhibiting negative Poisson's ratios and negative compressibility

Abstract

Structures and materials can behave in a counterintuitive manner when subjected to a uniaxial load or a change in pressure. This thesis examined through modelling studies systems exhibiting negative Poisson's ratio (i.e. materials which get fatter when stretched) and/or materials exhibiting negative compressibility (i.e. systems which get smaller when exposed to a partial vacuum), are studied. A general analytical and finite-elements (FE) model for a system with circular, square or rectangular nodes linked through flexible ligaments having the anti-tertachiral geometry was produced. It was shown that the Poisson's ratio for such systems is always negative on-axis and is dependent on the ratio of the ligament length and thickness, while it is independent on the shape and size of the nodes, the type of glue, the position of the glue and the stiffness of the ligaments. All the latter factors were found to affect the Young' s modulus thus a manner for decoupling these two properties was discovered. Various new types auxetic systems built from chiral building blocks were proposed, one of which was analysed in detail through FE and analytical modelling, and confirmed to exhibit auxetic behaviour. A method for rectifying the large disagreements between the predictions of earlier analytical models and realistic results for finite systems was also discovered. Also, a new and cost-effective method for producing auxetics by introducing perforations in conventional sheets of materials in a pre-defined manner was proposed and examined through FE simulations, where it was shown that auxetic behaviour could be achieved if the perforated sheets could mimic well known auxetic mechanisms such as the rotating rigid units systems. The auxetic nature of cristobalite was also studied through force-field based molecular modelling techniques. It was shown that auxetic behaviour in a-cristobalite in all the planes perpendicular to the (001) plane may be explained through a rotating/deforming rectangles model which are the projections in the (100) and (010) planes of the more complex three dimensional (3D) Si02 tetrahedra model. The auxetic behaviour in the (001) plane of 13-cristobalite was explained through a rotating squares model, which behaviour was also related to the 3D arrangement of the tetrahedra. It was also shown that auxetic behaviour in natrolite is not exhibited at ambient conditions but at negative pressures (partial vacuum). Finally, a method for converting the chiral auxetic structures to ones which also exhibit negative compressibility through the use of bi-material ligaments was reported and verified through FE.