Tsai Definition for Poisson's Ratios

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.