On the adjustable auxeticity of rotating rhombi and parallelograms

Abstract

Auxetic behaviour, i.e. the property of expanding laterally when stretched, is an unusual property which in recent years has been discovered in a number of materials and structures, and which may be explained through a number of geometries and deformation mechanisms (e.g. ‘rotating rigid units’ mechanisms such as the ‘rotating triangles’ and ‘rotating squares’ mechanisms). Recent studies suggest that the ‘rotating squares’ model can be generalised by changing the length of adjacent sides in such a way that the squares become rectangles. Furthermore it was also suggested that ‘rotating rectangles’ may be constructed in such a way that two different non-equivalent forms, the so called Type I and Type II, may be constructed (either with adjacent side having the same length or with adjacent sides having different lengths).