Tsai Definition for Poisson's Ratios

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The relation between strains, (

, and so forth) and stresses (

, and the like) is written as follows:

The Material Definition dialog box represents

as Nu.

In the above expression, 1, 2, and 3 denote the three principal material directions. In a uniaxial tension test pulling in the 1 direction, the ratios of transverse normal strains,

and

, to longitudinal normal strain,

, is given by:

and

Also, since the elasticity matrix is symmetric, the following relation between Poisson's ratios and Young's moduli holds:

where i and j take on the values 1, 2, and 3.

Therefore, if

, then

and

The values you enter for Poisson's ratios must satisfy the requirement that the determinant of the 6 X 6 constitutive equation matrix above is positive.

Return to Poisson's Ratio.