岩石类材料拉裂过程模拟的三维可开裂拉格朗日元方法

A three-dimensional crackable Lagrangian element method formodelling tensile cracking processes of rock-like materials

本研究提出了适于模拟岩石类材料变形-拉裂过程的三维可开裂拉格朗日元方法,其实质是三维拉格朗日元方法与断裂力学中虚拟裂缝模型的耦合方法,主要适用于立方体单元。以三维拉格朗日元方法为基础,引入虚拟裂缝模型的具体过程主要包括3个关键步骤:首先,通过节点周围单元的应力获取节点的应力,进而利用节点的最大主应力和岩石单轴抗拉强度进行节点分离判断;然后,选择与节点最大主应力垂直平面最接近的单元边界作为裂缝扩展方向;最后,引入虚拟裂缝模型模拟裂缝的萌生和扩展过程。利用该方法模拟了单轴拉伸岩样和三点弯曲岩梁的变形-拉裂过程,并初步分析了Ⅰ型断裂能、岩样高度和单元尺寸的影响。同时,通过将本研究结果与单轴拉伸岩样峰值应力、临界位移的理论解和前人位移控制加载条件下三点弯曲岩梁的载荷-位移曲线的数值解进行对比,验证了本研究方法的正确性,这为将来的工作奠定了良好的基础。

A three-dimensional crackable continuous-discontinuous method mainly suitable for cube elements is proposed to simulate deformation and tensile cracking processes of rocks.Its essence is a hybrid method of the three-dimensional Lagrangian element method and the fictitious crack model in fracture mechanics.Introduction of the fictitious crack model into the three-dimensional Lagrangian element method consists of three key steps.First,the nodal stress is obtained by averaging stresses of elements around the node,and the nodal separation is assessed according to the maximum principal stress of the node and the uniaxial tensile strength.Then,the element boundary closest to the plane perpendicular to the maximum principal stress of the node is selected.Finally,the fictitious fracture model is introduced to simulate the processes of crack initiation and propagation.Deformation and tensile cracking processes of specimens in uniaxial tension and three-point bending are simulated by using the present method.The effects of I-type fracture energy,rock specimen height and elements size on the direct tension processes are analyzed.Meanwhile,through comparing the present results with the theoretical peak stress and critical displacement of the specimen in direct tension and the numerical load-displacement curve of the specimen in three-point bending,the correctness of the proposed method is verified,laying a good foundation for future work.