On the properties of auxetic rotating stretching squares

Abstract

Auxeticity (i.e. negative Poisson's ratios) is associated with particular geometrical features and deformation mechanisms occurring within a system. Among the models which have been shown to exhibit such behaviour are the ‘rotating rigid unit’ models, in particular two-dimensional systems constructed from connected squares. In this work, we consider such a system which deforms through simultaneous stretching and rotation of the squares. We derive the analytical model describing its mechanical behaviour to show that the mechanical properties depend on the relative magnitude of the stretching and hinging constants, the square dimensions and the angle between the squares. In particular we show that the mechanical properties of the combined model are dependent on the relative contribution of the individual mechanisms and that by changing the relative magnitude of the force constants and/or the geometric parameters describing the system, the contribution from each of the two mechanisms, and thus the Poisson's ratio, can be set to predesired values.