Auxeticity of monoclinic tetrachiral honeycombs

Chiral honeycombs of different types have been found to display auxetic behavior (a negative Poisson's ratio). This paper investigates the constitutive relations and the auxetic properties of tetrachiral honeycombs. It is found that coupling between shearing and stretching exists in tetrachiral honeycombs and this causes some ambiguity when calculating the Poisson's ratio. An effective Poisson's ratio is proposed, as opposed to the traditional definition of Poisson's ratio. This proposed parameter correctly describes the auxeticity of tetrachiral and other honeycombs. An analytical expression for this effective Poisson's ratio is derived, which describes the relationship between the geometric dimensions and auxeticity of the tetrachiral honeycombs.