Auxetic behaviour from stretching connected squares

Systems with negative Poisson's ratio (auxetic) exhibit the unusual characteristic of getting fatter when stretched and thinner when compressed. Such behaviour is a scale-independent property and is the result of a cooperation between the internal geometry of the system and the way this deforms when uniaxially stretched. Here, we analyse the anisotropic mechanical properties for a system constructed from connected squares which can deform through changes in length of the sides of the squares (idealised 'ystretching squares' model). In particular, we show that this system may exhibit a negative Poisson's ratio which depends on the angle between the squares and the direction of loading but is independent of the size of the squares which suggests that this model may be implemented at any scale of structure including the micro- and nano-level. We also show how this model compares and complements the existing 'rotating squares' model which also works on a system with the same geometric characteristics and which has been shown to lead to auxeticity in various classes of materials.