Tsai Definition for Poisson's Ratios
The relation between strains, (
![](../../../../../simulate/simulate/images/i_tsai_def_1.gif)
, and so forth) and stresses (
![](../../../../../simulate/simulate/images/i_tsai_def_2.gif)
, and the like) is written as follows:
| The Material Definition dialog box represents ![](../../../../../simulate/simulate/images/nu2k.gif) 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,
![](../../../../../simulate/simulate/images/i_tsai_def_4.gif)
and
![](../../../../../simulate/simulate/images/i_tsai_def_5.gif)
, to longitudinal normal strain,
![](../../../../../simulate/simulate/images/i_tsai_def_6.gif)
, is given by:
![](../../../../../simulate/simulate/images/i_tsai_def_7.gif)
and
![](../../../../../simulate/simulate/images/i_tsai_def_8.gif)
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
![](../../../../../simulate/simulate/images/i_tsai_def_10.gif)
, then
![](../../../../../simulate/simulate/images/i_tsai_def_11.gif)
,
![](../../../../../simulate/simulate/images/i_tsai_def_12.gif)
and
![](../../../../../simulate/simulate/images/i_tsai_def_13.gif)
.
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.