Poisson's ratio

The Poisson's ratio (also Poisson's ratio, Poisson's ratio or Poisson's ratio called, also referred to ) is a size on the mechanics and strength of materials. You used to calculate the Poisson's and is named after Siméon Denis Poisson. It belongs to the elastic constants of a material.

Definition

The Poisson's ratio is defined as negative relative change in thickness ratio of the relative change in length under the action of an external force or mechanical stress.

Thus:

The original length and the original thickness indicated. Positive values ​​indicate an increase or of this dimension, negative values ​​correspond to a reduction.

The Poisson's ratio is a dimensionless quantity. The Poisson's ratio is a material constant, ie it depends on the material of the workpiece used. The elastic constants are related mutually. So true for linear elastic, isotropic material, the following relationship between the shear modulus, Young's modulus and the bulk modulus:

The relative volume change, with a body that is charged only one-dimensional with a voltage (or power ), responds to a -axis strain (tensile test ) is calculated from using the Poisson's ratio, neglecting quadratic terms

Scope

For the assumption of constant volume, so if, but a change in length is present (eg no temperature effect ) must be in pure tension affection (for linearization of the volume changes (? V / V) to the zero point ( DELTA.l / l = 0) ) be and thus. Typical values ​​of Poisson's ratio for metals lie between 0.3 and 0.4 and in plastics between 0.4 and 0.5. They show that the volume changes and thus the density of these materials under train / pressure.

The incompressibility is maintained only for infinitesimal deformations. Moreover arise in the Cauchy constitutive poles. For the calculation of nearly or fully incompressible materials (eg, rubber materials, entropy materials, hyperelastic materials ) should Green's material models are used.

For a Poisson's ratio less than 0.5 at tensile strain increases the volume, when subjected to pressure from, for then; in this case, have the same sign.

For values ​​greater than 0.5 occurs a decrease in the volume under tensile loading. This can be observed in various porous materials. For fiber composites or wood usually occur also Poisson's ratio greater than 0.5, since differ moduli of the three axes (x, y, z). Accordingly, six different Poisson's ratio occurs, which describe the respective interaction. For example describes νxy the strain along the x axis due to the tension along the axis y. Thus at orthotrophen at any voltage / load the volume would remain constant, would all (6 in 3D) Poisson's ratio, in spite of different moduli of elasticity, equal to 0,5.

Chance of linearly elastic, isotropic materials with negative Poisson's ratio are known. Negative values ​​result in a transverse strain rather than a transverse contraction in elongation. Such materials are called auxetic. Examples are certain polymer foams, crystals or carbon fibers. Taking into account these ( rare ) auxetic materials, the range of values ​​of the Poisson's ratio increased to.

Numerical values

For metallic materials is often a value of or accepted and for thermoplastics 0.35, if no exact values ​​are known. An error in the Poisson's ratio affects the calculation of the component behavior under mechanical stress significantly less than one error in the modulus of elasticity. Therefore, the modulus of elasticity for the material used must be accurately determined (eg in the tensile test ), while often enough an approximate value for the Poisson's ratio.

The inverse of Poisson's ratio

In geotechnical engineering, and rock mechanics and the inverse of the Poisson's ratio is called " Poisson ". Often the character is used. A uniform designation has not been enforced. In order to standardize the following arrangements would be recommended, as Othmar Rescher has suggested in his book " Dam - static calculation and design of gravity dams " means from 1965 and Poisson's ratio with the Poisson constant with:

• Poisson's ratio: characters :; with numerical values ​​from 0 to < 0.5
• Poisson's constant, or " Poisson " ( Geotechnical Engineering ); with numerical values ​​> 2

Wherein: