## 5 Conclusions  
In this study, a two-dimensional ordinary state-based peridynamic (OSB PD) modeling of mode-I delamination growth in double cantilever composite beam (DCB) test is conducted. The two-dimensional OSB PD composite model for DCB modeling is obtained by reformulating the previous OSB PD lamina model in x-z direction. Additionally, revised energy-based failure criteria are proposed for modeling delamination initiation and growth.  
In order to investigate the reliability of current modeling, loading increment convergence analysis and grid spacing influence study are conducted. It is shown that the PD modeling load-displacement curve converges with the decrease of loading increment. The linear loading part of PD modeling load-displacement curve converges with the decrease of grid spacing. However, the delamination growth initial point of PD modeling load-displacement curve seems sensitive to grid spacing, similar to the previous literature work.  
The standard DCB test was performed with five composite DCB specimens to measure the mode-I delamination fracture toughness \(G_{\text{IC}}\). The load-displacement variation and delamination growths were also measured. The modeling load-displacement curve and delamination growth process using the present PD model are then compared with experimental results. The results show that the PD-based load-displacement curve agrees well with experimental results. The zigzag load-displacement curve for delamination growth was observed both in experimental results and the present PD modeling results. Well agreement of the PD modeling delamination growth progress with experimental results is achieved. In particular, the maximum difference between PD and experimental average results in displacement is \(-14.10\%\), and in load is \(11.78\%\). Besides, the PD modeling delamination growth process damage contours are illustrated.  
To demonstrate the influence of the revised energy-based failure criteria, a comparison study using the revised and original energy-based failure criteria in the PD modeling is conducted. It is shown that the modeling delamination initiation was delayed using the revised energy-based failure criteria, which agrees more closely with the experimental results. In particular, by using the revised energy-based failure criteria, the differences with experimental results in the maximum load of the modeling load-displacement curve was reduced from \(-12.93\%\) to \(-6.96\%\), which show significant improvement in the accuracy of delamination modeling of DCB test.  
**Author Contributions:** Supervision, S.G. and H.W.; Writing--original draft preparation, X.-WJ.; Writing--review and editing, H.L.  
**Funding:** This research was funded by China Scholarship Council (CSC NO. 201706230169).  
**Acknowledgments:** The authors acknowledge the financial support from China Scholarship Council (CSC NO. 201706230169).  
**Conflicts of Interest:** The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Comparison** & **Experimental Avg.** & **PD\_original** & **PD\_revised** \\ \hline Max load & \(95.29\) & \(82.97\) & \(88.66\) \\ Difference & / & \(-12.93\%\) & \(-6.96\%\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Influence of the revised bond energy-based failure criteria on maximum load.