模拟岩石中裂纹扩展连接的近场动力学方法

脆性岩石材料在压应力作用下常出现两类裂纹：翼型张拉裂纹和次生剪切裂纹。近场动力学是一种新型的无网格数值计算方法。在近场动力学理论中，采用积分形式的控制方程代替微分形式的控制方程使得该数值算法在断裂问题上具有独特的优势。将Mohr-Coulomb准则和最大主应力准则引入非普通“态”基近场动力学理论中，分别用于模拟材料常见的压剪和张拉破坏。这种扩展的非普通“态”基近场动力学可以有效地模拟脆性岩石材料在多种受力状态下的裂纹起裂、扩展和连接问题。通过5个不同的数值算例说明该数值算法在处理脆性岩石材料断裂问题的有效性和准确性。首先，通过模拟含圆孔的弹性板拉伸数值试验说明该数值算法的有效性和准确性。其次，数值模拟了简单三点弯曲试验以及不使用其他外部准则条件下动荷载作用下裂纹的分叉试验，所得结果与其他试验结果或数值结果相吻合，从而验证了该理论的有效性。然后，模拟了包含斜裂纹的巴西圆盘试验，裂纹扩展路径和计算所得的断裂韧度同样吻合于试验结果。最后，模拟了单轴压缩状态下，预制裂纹试样的裂纹扩展和连接问题。将该数值算法与试验结果对比表明，所提出的数值方法可以模拟和预测岩石类材料的张拉和压剪裂纹的起裂、扩展和连接行为。

Numerical simulation of crack propagation and coalescence using peridynamics

In the rock-like materials, two types of cracks can be observed when the specimens are subjected to compressive loads: tensile cracks and shear cracks. Peridynamics is a novel meshfree method used to solve the fracture problems. To simulate crack propagation of rock specimens under compression, Mohr-Coulomb criterion and maximum principal stress criterion are implemented into the non-ordinary state-based peridynamics, which are used respectively to simulate the shear failure and tensile failure of materials. The extended non-ordinary state-based peridynamics (ENSPD) is efficient for modelling the crack propagation and coalescence under complex loads. The program codes of ENSPD are compiled using Fortran 90. Firstly, the numerical simulation of a three-point bending test is regarded as a benchmark example to prove the accuracy of proposed method. The crack branching phenomenon under dynamic loads is modeled using ENSPD without any additional branching criterion and the present results are in good agreement with the previous experimental and other numerical results. A Brazilian disk of rock-like materials containing an inclined pre-exiting crack is then simulated. The predicted crack growth paths and the estimated fracture toughness well coincide with the previous experimental results. Finally, a rock-like specimen containing two coplanar pre-existing cracks under uniaxial compression is modeled using ENSPD. Compared with the experimental results, it can be found that the proposed numerical method has the ability to simulate and predict the initiation, propagation and coalescence of cracks in rock-like materials.