New perspective on Poisson's ratios of elastic solids

A new perspective on Poisson's ratios of elastic solids is presented. We show that, by scaling the Poisson's ratios through the square root of a modulus ratio, the transformed Poisson's ratios, n₁, n₂, n₃, are bounded in a closed region, which is inside a cube centered at the origin with a range from - 1 to 1. The shape of this closed region, depicted in Fig. 1, looks like a Chinese food, "Zongzi". With this geometric interpretation, any positive definite compliance of an orthotropic solid can be easily constructed by selecting any point inside the region, together with any three positive Young's moduli and any three positive shear moduli. This provides a new insight to the admissible range of Poisson's ratios. We also provide an example that the inequality proven by Rabinovich [6], i.e. v₁₂ + v₂₃ + v₃₁ ≤ 3/2, is not generally true.