Yamada-Sun criterion (version b)

II.1.10.23 Yamada-Sun criterion (version b)

A second version of the Yamada-Sun criterion, better suited to fabrics, is proposed. The “tape” version of Yamada-Sun criterion is calculated in two directions, and the worst direction is considered for failure. The failure index is calculated as follows:

F I^{YamadaSun_b} = max [{(\frac{σ_{11}}{σ_{11}^{all}})}^{2} + {(\frac{τ_{12}}{τ_{12}^{all}})}^{2}; {(\frac{σ_{22}}{σ_{22}^{all}})}^{2} + {(\frac{τ_{12}}{τ_{12}^{all}})}^{2}] .

The allowables $σ_{11}^{all}$ and $σ_{22}^{all}$ depend on the signs of $σ_{11}$ and $σ_{22}$ respectively. Ply passes the failure criterion if the two following conditions are satisfied:

{(\frac{σ_{11}}{σ_{11}^{all}})}^{2} + {(\frac{τ_{12}}{τ_{12}^{all}})}^{2} \leq 1,

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

The reserve factor is calculated as follows:

R F^{YamadaSun_b} = \frac{1}{F o S \sqrt{F I^{YamadaSun_b}}},

and the strength ratio is given by:

S R^{YamadaSun_b} = F o S \sqrt{F I^{YamadaSun_b}} .

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

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