PoissonVerhältnis

PoissonVerhältnis, usually called Poisson's ratio, describes how a material deforms in directions perpendicular to an applied load. It is defined for small strains as ν = - εt / εl, where εt is the transverse strain and εl is the longitudinal strain in the load direction. The negative sign reflects that most materials contract laterally when stretched.

In isotropic linear-elastic materials, PoissonVerhältnis typically ranges from -1 to 0.5. A value of 0.5 indicates incompressible behavior, meaning the material preserves volume under deformation (common in rubbers). Negative values (auxetic materials) are uncommon but possible, yielding lateral expansion when stretched. Most metals have ν around 0.25–0.35, while many polymers span a broader range, often near 0.3–0.5. Cork has a notably low value near zero.

PoissonVerhältnis is connected to other elastic constants. For isotropic materials, E = 2G(1 + ν), where E is Young's modulus and G is the shear modulus. It is also related to the bulk modulus K by ν = (3K − E) / (6K). These relationships allow ν to be inferred from independent measurements of E, G, or K.

Measurement and applications: ν can be determined from axial and lateral strain data in uniaxial tests, from tests under hydrostatic pressure, or inferred from elastic constants obtained by methods such as ultrasound or resonant techniques. The value influences mechanical behavior including buckling, wave propagation, and the design of components under multi-axial loading.

Named after Siméon Poisson, who introduced the concept in the 19th century, PoissonVerhältnis remains a fundamental parameter in material science and engineering.