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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:

FITsaiHill3D = σ11 σ11all 2 + σ22 σ22all 2 + σ33 σ33all 2 + τ12 τ12all 2 + τ23 τ23all 2 + τ31 τ31all 2 - 1 σ11all 2 + 1 σ22all 2 - 1 σ33all 2 σ11σ22 - 1 σ22all 2 + 1 σ33all 2 - 1 σ11all 2 σ22σ33 - 1 σ33all 2 + 1 σ11all 2 - 1 σ22all 2 σ33σ11.(II.1.121)

The allowables σ11all, σ22all and σ33all depend on the signs of σ11, σ22 and σ33 respectively. Ply passes the failure criterion if

FITsaiHill3D 1.

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

RFTsaiHill3D = 1 FoSF ITsaiHill3D, (II.1.122)

and the strength ratio is given by:

SRTsaiHill3D = FoSF ITsaiHill3D. (II.1.123)

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