Glossary term
Poisson Ratio
The elastic material ratio that relates transverse strain to axial strain during uniaxial loading.
Definition
quantityPoisson's ratio is the negative ratio of transverse strain to axial strain for a material loaded within its linear elastic range.
Poisson's ratio quantifies lateral contraction or expansion when a material is stretched or compressed in one direction. It is a key elastic constant for isotropic solid mechanics and a direction-dependent property for anisotropic or orthotropic materials.
Poisson’s ratio is defined for uniaxial loading in the elastic range as:
Most metals have values around 0.25 to 0.35 in the linear elastic range. Rubber-like materials approach 0.5 because they are nearly incompressible. Cork and some foams can have low values. Auxetic materials have negative Poisson’s ratio, expanding laterally when stretched.
Role in elasticity
For an isotropic linear elastic material, Young’s modulus E, shear modulus G, and Poisson’s ratio are related by:
This relationship is valid only for isotropic linear elasticity. Orthotropic composites, rolled materials, wood, and layered structures need direction-specific elastic constants and cannot be reduced to one Poisson’s ratio.
Engineering importance
Poisson’s ratio affects stress states in constrained components, pressure vessels, bonded joints, seals, finite element models, thermal stress calculations, wave speeds, and indentation interpretation. Near-incompressible materials require special numerical treatment because ordinary finite elements can lock when \nu is close to 0.5.
Common mistakes
A common mistake is to use an elastic Poisson’s ratio deep into plastic deformation or large-strain rubber behavior. Another is to enter a value close to 0.5 in a finite element model without checking element formulation. A reliable material definition states test method, strain range, temperature, loading direction, isotropic or anisotropic assumption, and whether the value is secant, tangent, or small-strain elastic.