II.1.10.9 Tsai-Hill criterion

The Tsai-Hill criterion is a quadratic criterion. The 2D version of this criterion has a failure index calculated as follows:

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

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

and the strength ratio is given by:

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