The Tsai–Hill failure criterion is one of the phenomenological material failure theories, which is widely used for anisotropic composite materials which have different strengths in tension and compression. The Tsai-Hill criterion predicts failure when the failure index in a laminate reaches 1.
The Tsai-Hill criterion is based on an energy theory with interactions between stresses. Ply rupture appears when:[1][2]
Where:
The Tsai hill criterion is interactive, i.e. the stresses in different directions are not decoupled and do affect the failure simultaneously.[2] Furthermore, it is a failure mode independent criterion, as it does not predict the way in which the material will fail, as opposed to mode-dependent criteria such as the Hashin criterion, or the Puck failure criterion. This can be important as some types of failure can be more critical than others.