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Poisson's Ratio (Hencky Ratio)

Poisons Ratio

Poisson's ratio is the ratio of the transverse strain (contraction) ey,nom to the longitudinal strain ex,nom

unom = -ey,nom / ex,nom,

whereby the nominal elongations represent the relative change in length (DL) or in width (DB) with reference to the initial dimension of the measuring region according to

ex,nom = DL/L0 ey,nom = DB / B0.

Poisson’s ratio can also be used to determine whether a material maintains a constant volume when deformed or whether the volume increases under deformation e.g. due to the formation of microcracking and voids.

Rather than use the nominal Poisson’s ratio (see above) for this purpose, it makes sense to use the so-called Hencky ratio:

uH = -ln (1 + ey,nom) / ln (1 + ex,nom),

as this remains constant in the case of volume change with constant form, while the nominal Poisson’s ratio declines logarithmically (also e.g. at constant volume).

For small elongations, i.e. in particular in the linear-elastic deformation region, which is relevant for normal simulation calculations, the Hencky elongation and the nominal elongation have the same value, so the corresponding ratios are also identical within this region.

Determination of the Poisson’s ratio is carried out on a tensile test machine using the grey value correlation method. This involves tracking the changes of the local elongation using an arbitrary dot pattern.

The following table shows the Hencky ratios of a number of selected types of Desmopan® — whereby it should be noted that this ratio is identical to the nominal Poisson’s ratio in the linear-elastic region.

Grade 80A 80A 80A
82A
50D
58D
57D
72D
73D
Desmopan® 1080A 481 5080A 9380A 1050D 460 9855DU 3072D 9873DU
Poisson's ratio
(Hencky)
0.50 0.49 0.50 0.49 0.47 0.45 0.49 0.49 0.48

The selected grades of Desmopan® demonstrate Poisson’s ratios between 0.45 and 0.5. A Poisson’s ratio of 0.5 means that the volume remains constant under tensile or compressive stress. A Poisson’s ration slightly below 0.5 means that the material experiences a slight increase in volume when subjected to tensile stress and a slight decrease in volume when subjected to compressive stress.

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