From: Modelling of Damage Evolution in Braided Composites: Recent Developments
Failure mode I | Equivalent displacement | Equivalent stress |
---|---|---|
L t, σ 1  ≥ 0 | \( {X}_{eq}^{Lt}=l\sqrt{<{\varepsilon}_{11}{>}^2+{\varepsilon}_{12}^2+{\alpha \varepsilon}_{31}^2} \) | \( l\left(<{\sigma}_{11}><{\varepsilon}_{11}>+{\sigma}_{12}{\varepsilon}_{12}+{\alpha \sigma}_{13}{\varepsilon}_{13}\right)/{X}_{eq}^{Lt} \) |
L c, σ 1  < 0 | \( {X}_{eq}^{Lc}=l<-{\varepsilon}_{11}> \) | \( l\left(<-{\sigma}_{11}><-{\varepsilon}_{11}>\right)/{X}_{eq}^{Lc} \) |
Y t, σ 2  ≥ 0 | \( {X}_{eq}^{Yt}=l\sqrt{<{\varepsilon}_{22}{>}^2+{\varepsilon}_{12}^2+{\alpha \varepsilon}_{23}^2} \) | \( l\left(<{\sigma}_{22}><{\varepsilon}_{22}>+{\sigma}_{12}{\varepsilon}_{12}+{\alpha \sigma}_{23}{\varepsilon}_{23}\right)/{X}_{eq}^{Yt} \) |
Y c, σ 2  < 0 | \( {X}_{eq}^{Yc}=l<-{\varepsilon}_{22}> \) | \( l\left(<-{\sigma}_{22}><-{\varepsilon}_{22}>\right)/{X}_{eq}^{Yc} \) |
Z t, σ 3  ≥ 0 | \( {X}_{eq}^{Zt}=l\sqrt{<{\varepsilon}_{33}{>}^2+{\varepsilon}_{23}^2+{\varepsilon}_{31}^2} \) | \( l\left(<{\sigma}_{33}><{\varepsilon}_{33}>+{\sigma}_{23}{\varepsilon}_{23}+{\sigma}_{13}{\varepsilon}_{13}\right)/{X}_{eq}^{Zt} \) |
Z c, σ 3  < 0 | \( {X}_{eq}^{Zc}=l<-{\varepsilon}_{33}> \) | \( l\left(<-{\sigma}_{33}><-{\varepsilon}_{33}>\right)/{X}_{eq}^{Zc} \) |
<x > = (x + |x|)/2 |