Poisson’s ratio

Poisson’s ratio, in mechanics, a quantity describing how a material behaves when it is stretched or compressed. It is expressed as the negative of the ratio (ν) of the transverse strain (perpendicular to an applied stress, ε_trans) on a solid to the axial strain (parallel to an applied stress, ε_axial) on it:$\nu =-\frac{{\epsilon }_{trans}}{{{\epsilon }_{axial}}_{}}$.Strain is the change in length of a solid divided by the original, unstressed length. For example, when a rubber band is stretched lengthwise (axially), it becomes thinner in the opposite (transverse) direction. In this case, the negative sign ensures that the ratio is positive. Poisson’s ratio has dimensionless units. It was named after French mathematician Siméon-Denis Poisson, who first described it in 1811.

For most common materials, the range of Poisson’s ratio is between 0 and 0.5. A ratio of 0 represents a material that does not contract transversely when stretched or expand transversely when compressed. (Cork is such a material, which, with its impermeability to liquids, makes it good for stopping wine bottles.) A value of 0.5 represents a material that maintains a constant value when deformed. The volume of materials that have Poisson’s ratios less than 0.5 increases under longitudinal tension and decreases under longitudinal compression.

Auxetic materials have a negative Poisson’s ratio; that is, they expand transversely when stretched. Such materials have potential for energy-absorbing applications, such as in car bumpers or sneaker insoles.