Puck “b” criterion

II.1.10.18 Puck “b” criterion

A modified version of Puck criterion is defined as follows:

F I^{Puck_b} = \max (|\frac{σ_{11}}{σ_{11}^{all}}|, \frac{σ_{22}^{2}}{σ_{22}^{c,all} σ_{22}^{t,all}} + {(\frac{τ_{12}}{τ_{12}^{all}})}^{2} + σ_{22} (\frac{1}{σ_{22}^{t,all}} - \frac{1}{σ_{22}^{c,all}})) .

Ply passes the failure criterion if the two following conditions are satisfied

|σ_{11}| \leq σ_{11}^{all},

\frac{σ_{22}^{2}}{σ_{22}^{c,all} σ_{22}^{t,all}} + {(\frac{τ_{12}}{τ_{12}^{all}})}^{2} + σ_{22} (\frac{1}{σ_{22}^{t,all}} - \frac{1}{σ_{22}^{c,all}}) \leq 1 .

The reserve factor is calculated as follows:

R F_{a} = \frac{σ_{11}^{all}}{F o S \cdot σ_{11}},

a = \frac{σ_{22}^{2}}{σ_{22}^{c,all} σ_{22}^{t,all}} + {(\frac{τ_{12}}{τ_{12}^{all}})}^{2},

b = σ_{22} (\frac{1}{σ_{22}^{t,all}} - \frac{1}{σ_{22}^{c,all}}),

c = - 1,

R F_{b} = \frac{- b + \sqrt{b^{2} - 4 a c}}{2 \cdot F o S \cdot a},

R F^{Puck_b} = \min (R F_{a}, R F_{b}) .

The calculation of failure index is based on the calculation of the reserve factor:

F I^{Puck_b} = \frac{1}{R F^{Puck_2}},

in which the safety factor used in the calculation of the RF is 1. The advantage of this new expression is that the failure index is proportional to the components of stress tensor. This criterion is referred to as “Puck_b” criterion in FeResPost.

For the strength ratio, one uses the same expression, but the safety factor is not set to 1:

S R^{Puck_b} = \frac{1}{R F^{Puck_2}} .

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