Table 5 Failure criteria and respective degradation adopted by Tian et al. 2016

Fibre tension failure (σ ₁₁ ≥ 0)

\( {\left(\frac{\sigma_{11}}{X_T}\right)}^2+\frac{\tau_{12}^2}{{\left({S}_f\right)}^2}+\frac{\tau_{13}^2}{{\left({S}_f\right)}^2}\ge 1 \)

E ₁₁, E ₂₂ , G ₁₂ , G ₂₃ , G ₁₃ , υ ₁₂ , υ ₂₃ , υ ₁₃degrade to 0.1 of their original value

Fibre compression failure (σ ₁₁ < 0)

\( {\left(\frac{\sigma_{11}}{X_C}\right)}^2+\frac{\tau_{12}^2}{{\left({S}_f\right)}^2}+\frac{\tau_{13}^2}{{\left({S}_f\right)}^2}\ge 1 \)

E ₁₁, E ₂₂ , G ₁₂ , G ₂₃ , G ₁₃ , υ ₁₂ , υ ₂₃ , υ ₁₃degrade to 0.18 of their original value

Matrix cracking (σ ₂₂ ≥ 0)

\( {\left(\frac{\sigma_{22}}{Y_T}\right)}^2+\frac{\tau_{12}^2}{{\left({S}_{12}\right)}^2}+\frac{\tau_{23}^2}{{\left({S}_{23}\right)}^2}\ge 1 \)

E ₂₂ , G ₁₂ , G ₂₃degrade to 0.4 of their original value

Matrix crushing (σ ₂₂ < 0)

\( \frac{1}{4}{\left(\frac{-{\sigma}_{22}}{S_{12}}\right)}^2+\frac{Y_C^2{\sigma}_{22}}{4{S}_{12}^2{Y}_C}+\frac{\sigma_{22}}{Y_C}+\frac{\tau_{12}^2}{{\left({S}_{12}\right)}^2}\ge 1 \)

E ₂₂ , G ₁₂ , G ₂₃degrade to 0.5 of their original value

Interface delamination (σ ₃₃ ≥ 0)

\( {\left(\frac{{{}{}^n\sigma}_{23}}{S_{123}}\right)}^2+{\left(\frac{{{}{}^{n+1}\sigma}_{23}}{S_{123}}\right)}^2+{\left(\frac{\sigma_{33}}{Z_T}\right)}^2+{\left(\frac{\sigma_{22}}{Y_T}\right)}^2\ge 1 \)

E ₃₃, E ₂₃ , G ₁₃ , υ ₂₃ , υ ₁₃ degrade to 0