New perspective on Poisson's ratios of elastic solids

A new perspective on Poisson's ratios of elastic solids is presented. We sh ow that, by scaling the Poisson's ratios through the square root of a modul us ratio, the transformed Poisson's ratios, n(1), n(2), n(3), are bounded i n a closed region, which is inside a cube centered at the origin with a ran ge 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 pos itive 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 in sight to the admissible range of Poisson's ratios. We also provide an examp le that the inequality proven by Rabinovich [6], i.e. v(12) + v(23) + v(31) less than or equal to 3/2, is not generally true.