基于RKPM-PD方法的岩石裂纹扩展数值模拟  

Numerical simulations of crack propagation in rock based on the RKPM-PD coupling method

作　　者：崔昊 闫自海 胡建华 郑宏 CUI Hao;YAN Zihai;HU Jianhua;ZHENG Hong(Power China Huadong Engineering Co.,Ltd.,Hangzhou 311122,Zhejiang,China;Faculty of Architecture,Civil and Transportation Engineering,Beijing University of Technology,Beijing 100124,China)

机构地区：[1]中国电建集团华东勘测设计研究院有限公司,浙江杭州311122 [2]北京工业大学城市建设学部,北京100124

出　　处：《隧道与地下工程灾害防治》2021年第3期59-75,共17页Hazard Control in Tunnelling and Underground Engineering

摘　　要：基于非局部理论的近场动力学(peridynamic,PD)方法在求解岩石裂纹扩展问题时具备极大的优势,但同时也面临零能模式与边界效应等问题。为解决上述问题,证明非常规态基PD方法等价于采用节点积分的伽辽金弱形式方法,并将非常规态基PD中变形梯度F的求解方式推广为更一般的PD微分算子(peridynamic differential operator,PDDO)近似。由于该近似与重构核粒子(reproducing kernel particle method,RKPM)近似具有相同的位移近似函数,详细对比分析两方法位移导数近似间的差异性,得到PDDO近似不满足相容性条件的结论,并形成了具备更高精度的RKPM-PD耦合算法。若干数值算例证明了该耦合算法在预测岩石动态裂纹扩展中的准确性。The peridynamic method had great advantages in solving the problem of crack propagation in rock material due to its nonlocal characteristics.However,the method also faced problems such as zero-energy mode and boundary effects.In order to solve the above problems,the paper first proved that the non-ordinary state-based peridynamic(NOSB-PD)method was equivalent to the Galerkin weak form with nodal integral scheme.The equation of solving the deformation gradient F in NOSB-PD method was extended to a more general form,namely the peridynamic differential operator(PDDO)approximation.Since the PDDO had the same displacement approximation with the reconstruction kernel particle method(RKPM),this paper compared the difference between the tw o methods in the approximations of displacement derivatives in detail.The RKPM-PD coupling method with higher accuracy was proposed in the paper.Several numerical examples proved the accuracy of the new method in predicting the dynamic crack propagation in rock.

关 键 词：近场动力学 无网格方法 伽辽金法 裂纹扩展 

分 类 号：O343[理学—固体力学]