AI 中文总结
本文改进键关联近场动力学（BAPD）模型的修正因子，开发BAPD与经典连续介质力学（CCM）的自适应耦合模型，通过数值算例验证其精度与效率，I型裂纹问题中计算成本降低超72%。
AI 中文摘要
本文对键关联近场动力学（BAPD）模型力态中的修正因子进行了重新构建，该重新构建基于材料点处BAPD模型与经典连续介质力学（CCM）模型之间的应变能密度等效关系。以有限元法（FEM）解为参考，本文提出的修正因子提升了BAPD解的精度。此外，基于上述应变能密度等效关系开发了BAPD-CCM耦合模型，并引入“ Morphing”函数实现两种模型间的平滑过渡。时间积分方面，准静态和动态问题均采用显式格式；空间离散化方面，CCM模型采用单元离散，BAPD模型采用粒子离散。通过与FEM解对比，并评估位移误差的$L^2$范数、$H^1_{\text{semi}}$范数及能量范数，验证了耦合模型的解精度。二维和三维数值算例表明，所提模型计算效率更高：例如在I型裂纹扩展问题中，其计算成本较纯BAPD模型降低72%以上，且预测的裂纹模式与实验结果一致。
英文摘要
This paper reformulates the correction factor in the force-state of the bond-associated peridynamic (BAPD) model. The reformulation is established from the strain energy density equivalence between the BAPD model and the classical continuum mechanics (CCM) model at a material point. With the FEM solution taken as the reference, the proposed correction factor improves the accuracy of the BAPD solution in this study. Furthermore, a BAPD-CCM coupled model is developed based on the above energy density equivalence, and a ``Morphing" function is introduced to achieve a smooth transition between the two models. For time integration, explicit schemes are adopted for both quasi-static and dynamic problems. In the spatial discretization, the CCM model is discretized by elements, whereas the BAPD model is discretized by particles. The solution accuracy of the coupled model is validated by comparison with the FEM solution and by evaluating the $L^{2}$ norm, the $H^{1}_{\mathrm{semi}}$, and the energy norm of the displacement error. Two- and three-dimensional numerical examples show that the proposed model has higher computational efficiency. For example, in the Mode I crack propagation problem, its computational cost is reduced by more than 72\% compared with that of the pure BAPD model, and the predicted crack patterns agree with experimental results.
