Skip to main content

Table 2 Damage model for yarns and matrix

From: Non-intrusive proper generalized decomposition involving space and parameters: application to the mechanical modeling of 3D woven fabrics

Fibre failure

Initial transverse damage under compression inside yarns

\(\displaystyle f_{ft}=\frac{\epsilon _a}{\epsilon _t}=1 \)

\(\displaystyle f_{mat}=\left( \frac{\tau _T}{S_T-\mu _T\sigma _n}\right) ^2 + \left( \frac{\tau _L}{S_L-\mu _L\sigma _n}\right) ^2=1\)

Initial matrix damage

Initial transverse damage under tension inside yarns

\(\displaystyle \Phi _{m}^{d}=\frac{3 J_2}{X_m^c\,X_m^t}+\frac{I_1\left( X_m^c-X_m^t\right) }{X_m^c\,X_m^t} \)

\(\displaystyle f_{mat}=\left( \frac{\sigma _n}{Y_T}\right) ^2 + \left( \frac{\tau _T}{S_T}\right) ^2 + \left( \frac{\tau _L}{S_L}\right) ^2=1\)