Transverse contraction

The transverse contraction is a phenomenon of the deformation of a solid body with an approximately constant volume . It describes the behavior of the solid under the influence of a tensile force or compressive force .

In the direction of the force, the body reacts with a change in length , perpendicularly with a decrease or increase in its diameter or its thickness . The change in length with uniaxial tension can be determined in the linear-elastic range by the simplified Hooke's law . However, Hooke's law in its simplified form does not make any statements about the change in thickness. ${\displaystyle \Delta l}$ ${\displaystyle d}$ ${\displaystyle \Delta d}$

Nevertheless, the more complicated application of Hooke's law can often be dispensed with, since in many cases the relative change in diameter (transverse expansion ) is proportional to the relative change in length (longitudinal expansion) that can be determined using the simplified Hooke's law : ${\displaystyle \Delta d/d}$ ${\displaystyle \Delta l/l}$

${\displaystyle {\frac {\Delta d}{d}}=-\nu {\frac {\Delta l}{l}}}$.

The proportionality factor is a dimensionless quantity and is called Poisson or Poisson's ratio . ${\displaystyle \nu }$

The negative sign in the definition equation comes from the fact that a body under tensile load usually increases its length ( ), but its diameter is reduced ( ). So then is positive. ${\displaystyle \Delta l>0}$ ${\displaystyle \Delta d<0}$ ${\displaystyle \nu }$

Limits

In general, the change in thickness with which a body reacts to an applied mechanical tension is not the same in all directions; a body can react to the forced change in length e.g. B. react with different changes in height and width. This is particularly important for crystalline solids. When these differences matter, Hooke's law must be applied in its general form.

In addition, the same restrictions apply to the treatment of transverse contraction as to Hooke's law itself: It only applies to linear elastic deformations .

Measurement method

The Poisson's ratio can be measured mechanically in a tensile test according to DIN EN ISO 527-1.

Individual evidence

1. ↑ DIN EN ISO 527-1: 1996-04 Plastics - Determination of tensile properties - Part 1, Beuth Verlag

See also

• Auxetic material
• modulus of elasticity
• Lamé constants