Poisson's ratio

When a wire is stretched, it does not simply get longer -- it also gets thinner: its length increases (an elongation, or longitudinal strain) while its diameter simultaneously decreases (a contraction, or lateral strain). The same effect is visible when a rubber band is stretched: it visibly thins out as it elongates. This behaviour, where deformation in one direction (lengthwise) produces a coupled deformation in the perpendicular direction (sideways), was quantified by the French physicist S. D. Poisson through a ratio that now bears his name. POISSON'S RATIO $\mu$ is defined as the ratio of the relative contraction (lateral strain) to the relative expansion (longitudinal strain): for a wire of length L and diameter D, if the increase in length is l and the decrease in diameter is d, $\mu=-\dfrac{d/D}{l/L}=-\dfrac{Ld}{lD}$; the negative sign simply flags that the elongation (longitudinal) and the contraction (lateral) happen in opposite senses. Because it is the ratio of two quantities with the same dimension (both are dimensionless strains), Poisson's ratio itself has NO unit and NO dimension. Poisson's ratio varies widely between materials, from nearly 0.5 for rubber (which is nearly incompressible -- it contracts sideways almost as much as it stretches lengthwise) down to essentially 0 for cork (which barely changes its lateral dimension when compressed lengthwise -- exactly why cork makes a good, non-bulging stopper for a wine bottle). Poisson's ratio als …