Tresca criterion (2D)

Using the stress tensor components a scalar equivalent shear stress is given by:

τ_{eq}^{Tresca2D} = max (\frac{1}{2} | σ_{I} - σ_{II} |, \frac{1}{2} | σ_{I} |, \frac{1}{2} | σ_{II} |) .

Ply passes the failure criterion if

τ_{eq}^{Tresca2D} \leq σ_{t}^{all} .

This equivalent shear stress allows definition of a Tresca failure index as follows:

F I^{Tresca2D} = \frac{2 \cdot τ_{eq}^{Tresca2D}}{σ_{t}^{all}},

The reserve factor is given by:

R F^{Tresca2D} = \frac{1}{F o S \cdot F I^{Tresca2D}} = \frac{σ_{t}^{all}}{F o S \cdot 2 \cdot τ_{eq}^{Tresca2D}},

and the strength ratio by:

S R^{Tresca2D} = F o S \cdot F I^{Tresca2D} = \frac{F o S \cdot 2 \cdot τ_{eq}^{Tresca2D}}{σ_{t}^{all}} .

This criterion is referred to as “Tresca2D” criterion in FeResPost.