岩石三维裂纹扩展问题的近场动力学数值模拟

Numerical Simulation of 3D Crack Propagation in Rock by Peridynamics Approach

摘要:

近场动力学（PD）方法基于键的形式处理断裂问题，对裂纹尖端可自动追踪，因而在求解三维裂纹扩展问题时具备极大的优势，但该方法中也存在数值震荡与边界误差等问题。为解决上述问题，首先应用无网格伽辽金弱形式框架对非常规态基近场动力学方法进行了探讨；随后引入近场动力学微分算子（PDDO）近似，并对比分析了该近似与重构核粒子（RKPM）近似间的差异，提出了具备更高数值精度的RKPM-PD耦合算法，并给出了该算法的隐式迭代流程。最后，通过若干数值算例验证了该算法在求解三维裂纹扩展问题上的有效性。

Abstract:

The peridynamics method has great advantages in solving crack propagation problems due to its automatic tracking of crack tips by breaking bonds， but it also faces the problems such as numerical oscillations and boundary errors. In order to solve the above defects， this paper first discussed the NOSB-PD method with the meshless Galerkin weak-form framework. Next， it introduced the peridynamics differential operator approximation and fully compared and analyzed the difference between the PDDO approximation and the reproducing kernel particle method （RKPM） approximation. Then， it proposed the RKPM-PD coupling algorithm with a higher numerical accuracy and gave the implicit iterative process of the RKPM-PD method. Finally， it verified the effectiveness of the algorithm in solving three-dimensional crack propagation problems by using several numerical examples.