A generalised three-dimensional tethered-nodule model for auxetic materials

Models for the nano/micro-structural deformation and mechanical properties of auxetic materials (i.e. materials with a negative Poisson's ratio) have been previously developed. However, most of these models have been two-dimensional, were usually designed specifically to describe some particular class of auxetic materials, and generally only described the behaviour of one particular plane whilst completely ignoring the out-of-plane behaviour of the material. A three-dimensional model has been developed which can be applied to several classes of auxetic materials, including microporous expanded polymers such as e-PTFE, e-UHMWPE and e-PA, body-centered cubic metals and foams. It is generalised that its underlying structure is not specific to a lengthscale or material as the previous list shows. The new model offers a better insight into the underlying principles behind the observed auxetic behaviour and offers a significant improvement in the agreement of the models with existing experimental data. It is shown that there are geometric limitations to the number of planes that can simultanesously display auxetic behaviour. This has ramifications on the design of ordered auxetic materials.