# Poisson’s Ratio

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## Definition - What does Poisson’s Ratio mean?

Poisson's ratio or Poisson coefficient can be defined as the ratio of the relative lateral strain (normal to the applied load) to the relative axial strain (in the direction of applied load). It is measured with a minus sign so that normal materials have a positive ratio. It is represented by ν and is given by:

ν = - εtransverse / εlongitudinal ,

where ε is the change in length divided by original length.

ε = ΔL/L, where ΔL - change in length and L - original length.

## Trenchlesspedia explains Poisson’s Ratio

Compressive deformation of a material is considered negative while tensile deformation is considered positive. When tensile force is applied to a material, it develops a stress corresponding to the applied force (P), contracting the cross section and elongating the length (ΔL). The tensile strain ε is expresses as ε = ΔL/L. If compressive force is applied, the compressive strain is expressed as ε = -ΔL/L. Based on Hooke's law, the relation between stress and strain is expressed as σ = Eε, where σ - stress, E - Young's modulus and ε - strain.

On receiving tensile force, the material expands in the axial direction (longitudinal strain) while contracting in the transverse direction (transverse strain). The ratio between the longitudinal and transverse strains is known as Poisson's ratio.