A three-dimensional rotating rigid units network exhibiting negative Poisson's ratios

Materials exhibiting auxetic behaviour get fatter when stretched (i.e. possess a negative Poisson's ratio). This property has been closely related to particular geometrical features of a system and how it deforms. One of the mechanisms which is known to have a potential to generate such behaviour is that of rotating rigid units. Several models based on this concept have been developed, including two-dimensional as well as three-dimensional (3D) models. In this work, we propose a new 3D structure constructed from rigid cuboids which also deform through relative rotation of the units. In particular, analytical models for the mechanical properties, namely the Poisson's ratio and the Young's moduli, are derived and it is shown that for loading on-axis, these systems have the potential to exhibit negative values for all the six on-axis Poisson's ratios.