The Tsai-Hill criterion is a quadratic, interactive stress-based criterion that identifies failure, but does not distinguish between different modes of failure. Failure occurs whenever the following condition is satisfied:
The coefficients Sij of the Tsai-Hill criterion are computed as follows:
= Value of σ11 at longitudinal tensile failure
= Value of σ11 at longitudinal compressive failure
= Value of σ22 at transverse tensile failure
= Value of σ22 at transverse compressive failure
= Absolute value of σ12 at longitudinal shear failure
If 
, then 
If 
, then 
If 
, then 
If 
, then 
The failure index reported for the Tsai-Hill criterion is
