Poissonarány

Poissonarány, denoted ν (nu), is a dimensionless material property describing the coupling between longitudinal and transverse deformations under uniaxial stress. It is defined as ν = - ε_transverse / ε_axial, where ε_axial is the strain along the applied load and ε_transverse is the strain perpendicular to it, for small strains in linear elastic regime.

In an isotropic linear-elastic material, ν relates to Young's modulus E and shear modulus G by ν = E/(2G) - 1, equivalently G = E/(2(1+ν)). For isotropic materials, the constraints yield -1 ≤ ν ≤ 0.5; ν = 0.5 corresponds to incompressible materials (volume preserved during deformation), ν ≤ -1 would be unstable.

Common materials have positive ν between 0 and 0.5; typical around 0.3. Negative Poisson's ratio materials (auxetics) expand laterally when stretched, with ν < 0; known classes exist in foams, layered structures, and some crystalline materials.

In anisotropic materials, Poisson's ratio can depend on direction and the pair of axes; multiple Poisson ratios may exist, defined for different loading and measurement directions. In engineering practice, ν is used with E and G to analyze stiffness, wave speeds, and stability.

Measurement: ν can be obtained from tensile tests, bulge tests, or ultrasound, and it is considered dimensionless.

Limitations: Poisson's ratio is defined for small strains in linear elasticity; at large deformations, nonlinear effects occur and the simple ratio may not hold.