II.1.10.12 Tsai-Hill criterion (3D)

The Tsai-Hill criterion is a quadratic criterion. The 3D version of this criterion has a failure index calculated as follows:

The allowables ${\sigma }_{11}^{\text{all}}$, ${\sigma }_{22}^{\text{all}}$ and ${\sigma }_{33}^{\text{all}}$ depend on the signs of ${\sigma }_{11}$, ${\sigma }_{22}$ and ${\sigma }_{33}$ respectively. Ply passes the failure criterion if

The Tsai-Hill failure index depends quadratically on the different components of the stress tensor. The reserve factor is calculated as follows:

and the strength ratio is given by:

This criterion is referred to as “TsaiHill3D” criterion in FeResPost.