# Poisson's Ratio

on . Posted in Classical Mechanics Poisson's ratio, abbreviated as Po, $$\mu$$ or $$\nu$$, a dimensionless number, relates the lateral and axial strains of an elastic material when it is subjected to an external stress.

Poisson's ratio is a measure of the degree of deformation that a material undergoes when subjected to an external stress.  It is always negative or between 0 and 0.5 for most materials, indicating that when a material is compressed or stretched, it will contract or expand laterally.  The value of Poisson's ratio depends on the type of material and its structure, and it is an important parameter in engineering and materials science, especially in the design of structures that require elasticity and resilience, such as buildings, bridges, and aircraft.

See this link for Poisson's Ratio of an Element

## Poisson's Ratio formula

$$\large{ \mu = \frac { \varepsilon_t } { \varepsilon_a } }$$
Symbol English Metric
$$\large{ \mu }$$  (Greek symbol mu) = Poisson's Ratio $$\large{ dimensionless }$$
$$\large{ \epsilon_t }$$  (Greek symbol epsilon) = lateral or transverse strain (direction of load) $$\large{\frac{in}{in}}$$ $$\large{\frac{mm}{mm}}$$
$$\large{ \epsilon_a }$$  (Greek symbol epsilon) = axial or longitudinal strain (right angle to load) $$\large{\frac{in}{in}}$$ $$\large{\frac{mm}{mm}}$$ 