On the feasibility of introducing auxetic behavior into thin-walled structures

Classical elasticity theory indicates that the existence of negative Poisson’s ratios (NPRs), i.e. auxetic behavior in materials, will result in an increase in shear stiffness. Motivated by the assumption of gaining potential structural benefits, this study undertook to examine two main issues: (i) the feasibility of inducing auxetic behavior into thin-walled structures; and (ii) in cases where it is possible, whether it leads to shear stiffness enhancement. In the present study, the geometry of a membrane was chosen as a geometric model to address these issues. The results obtained in this study reveal that on the one hand the model effective elastic properties, E∗ and G∗, are lower than those of the material the surface is fabricated from, E∗ ∼ 1% of the material elastic modulus and G∗ ∼ 80% of its shear modulus. On the other hand, the obtained properties are much higher than those observed for other available auxetics like honeycombs, foams and polymers.