Auxetic Behaviour of Rigid Connected Squares

Abstract

The paper presents an analysis of rotating rigid unit (RRU) auxetic structures, the special property of which is negative Poisson’s ratio. The crucial features of such modified structures are the well-functioning linkages of the square units at their pivot points. This ensures the stable functioning of such structures in tension or compression. The presented geometrical analysis of these auxetic structures may facilitate their adequate construction and allow one to determine the expected values of their expansion as well as the desired porosity. The results are confirmed based on the behaviour of physical models produced by the assembly of square units. The change in the dimensions of the physical models when moving from a closed to an open position is consistent with the predictions of the geometric models. By modifying the well-known ‘rotating squares’ model, physical structures with auxetic properties are obtained that can be utilised in industrial conditions, where a simultaneous change of linear dimensions is needed—either in compression or in tension. The assembly method may prove efficient in building such structures, given the abilities of assembly robots to regularly arrange the unit cells in lines and rows and to connect them with rings at the designated positions (evenly spaced perforations). The presented auxetic structures might find their potential application in, e.g., expansion joints or structures in which the porosity is mechanically changed, such as mesoscale structures. The tested structures subjected to high compressive forces buckle when the yield strength of the rigid unit material is exceeded.