## Appendix A
### Derivation Procedure of PD Material Parameters  
The PD strain energy density of the present two-dimensional OSB PD composite model for CFRP composite can be expressed as  
\[W_{(k)}=a\theta_{(k)}^{2}+b\sum\limits_{j=1}^{\infty}\delta\Big{|}x_{(j)}-x_{ (k)}\Big{|}s_{(k)(j)}^{2}V_{(j)}+b_{F}\sum\limits_{j=1}^{J}\delta\Big{|}x_{(j) }-x_{(k)}\Big{|}s_{(k)(j)}^{2}V_{(j)}+b_{Z}\sum\limits_{j=1}^{J}\delta\Big{|}x _{(j)}-x_{(k)}\Big{|}s_{(k)(j)}^{2}V_{(j)}. \tag{116}\]  
The PD material parameters in Equations (4), (5) and (10) can be derived by comparing the PD strain energy density and the strain energy density of continuum mechanics under simple loading conditions. Four simple loading conditions are assumed: (1) Pure shear loading on x-z plane (\(\gamma_{13}\)); (2) Uniaxial stretch in fiber direction (\(\epsilon_{11}\)); (3) Uniaxial stretch in thickness direction (\(\epsilon_{33}\)); (4) Biaxial tension on x-z plane (\(\epsilon_{11},\;\epsilon_{33}\)). (1) Pure shear loading on x-z plane (\(\gamma_{13}\))  
Under this loading condition, we assume \(\gamma_{13}=\zeta\) and all other strains equal zero. From the derivation in Appendix A.1,  
\[\theta_{(k)}^{CM}=0,\;W_{(k)}^{CM}=\frac{1}{2}Q_{55}\zeta^{2}. \tag{117}\]  
Firstly, the stretch of bonds \(s_{(k)(j)}\) should be calculated under \(\gamma_{13}=\zeta\). As shown in Figure A1, under this simple loading condition, material point M moves to M'. \[ \begin{array}{ll}OM^{\prime}&=\sqrt{{\rm OP}^{\prime 2}+M^{\prime}{\rm P}^{ \prime 2}}=\sqrt{\left(\xi\cos\theta+\xi\sin\theta\zeta\right)^{2}+\left(\xi \sin\theta\right)^{2}}\\ &=\sqrt{\xi^{2}+2\xi^{2}\cos\theta\sin\theta\zeta}+\xi^{2}\sin\theta^{2}\zeta ^{2}\\ &\approx\sqrt{\xi^{2}+2\xi^{2}\cos\theta\sin\theta\zeta}\end{array} ,\] (A23)  
\[ \begin{array}{ll}s_{(k)(j)}&=\frac{OM^{\prime}-OM}{OM}=\frac{\sqrt{\xi^{2}+ 2\xi^{2}\cos\theta\sin\theta\zeta}-\xi}{\xi}=\sqrt{1+\zeta 2\cos\theta\sin \theta}-1\\ &\approx 1+\frac{1}{2}\zeta 2\cos\theta\sin\theta-1=\zeta\sin\theta\cos\theta \end{array} .\] (A24)  
Then the PD dilatation can be derived as  
\[ \begin{array}{ll}\theta_{(k)}&=d\sum\limits_{j=1}^{\infty}\delta s_{(k)(j)} \Lambda_{(k)(j)}V_{(j)}=d\sum\limits_{j=1}^{\infty}\delta\xi\sin\theta\cos \theta\Lambda_{(k)(j)}V_{(j)}\\ &=d\int_{0}^{\delta}\int_{2^{2\pi}}\delta\xi\sin\theta\cos\theta\zeta d\theta d \xi=0\end{array} ,\] (A25)  
and the PD strain energy could be derived as  
\[ \begin{array}{ll}W_{(k)}=a\theta_{(k)}^{2}+b\sum\limits_{j=1}^{\infty}\delta \Big{|}x_{(j)}-x_{(k)}\Big{|}s_{(k)(j)}^{2}V_{(j)}+b_{\tilde{r}}\sum\limits_{ j=1}^{\tilde{l}}\delta\Big{|}x_{(j)}-x_{(k)}\Big{|}s_{(k)(j)}^{2}V_{(j)}+b_{ \tilde{r}}\sum\limits_{j=1}^{\tilde{l}}\delta\Big{|}x_{(j)}-x_{(k)}\Big{|}s_{ (k)(j)}^{2}V_{(j)}\\ &=a(0)+b\sum\limits_{\tilde{H}}\delta\zeta(\xi\sin\theta\cos\theta)^{2}dH+b_{ \tilde{r}}(0)+b_{\tilde{\rm Z}}(0)\\ &=b\int_{0}^{\delta}\int_{0}^{2\pi}\delta\xi(\zeta\sin\theta\cos\theta)^{2} \xi d\theta d\xi=\frac{\pi\delta\xi^{2}}{12}b=\frac{1}{2}Q_{55}\xi^{2}\end{array} .\] (A26)  
Comparing with Equation (A22),  
\[b=\frac{\frac{1}{2}Q_{55}\xi^{2}}{\frac{\pi\delta^{4}\xi^{2}}{12}}=\frac{6Q_ {55}}{\pi\delta^{4}}.\] (A27)  
(2) Uniaxial stretch in fiber direction (\(\epsilon_{11}\))  
Setting \(\epsilon_{11}=\zeta\), similarly,  
\[\theta_{(k)}^{CM}=\zeta,\ W_{(k)}^{CM}=\frac{1}{2}Q_{11}\xi^{2},\] (A28)  
\[s_{(k)(j)}=\zeta\cos^{2}\theta,\] (A29)  
\[\theta_{(k)}=d\sum\limits_{j=1}^{\infty}\delta s_{(k)(j)}\Lambda_{(k)(j)}V_{( j)}=d\sum\limits_{j=1}^{\infty}\delta\zeta\cos^{2}\theta\Lambda_{(k)(j)}V_{(j)} \\ =d\int_{0}^{\delta}\int_{2^{2\pi}}^{2}\delta\zeta\cos^{2}\theta d\theta d \xi=\frac{\pi}{2}d\delta^{3}\zeta=\zeta\end{array},\] (A30)  
\[