基于SBFEM的剪切型裂纹动态开裂模拟

DYNAMIC CRACKING SIMULATION OF SHEAR-BASED FRACTURE BY USING SBFEM

剪切型断裂是岩土工程中常见的破坏模式,了解剪切破坏机理并准确预测剪切型裂纹的萌生、扩展过程对保障工程结构的安全性与稳定性具有重要意义.文章建立了基于比例边界有限元法(scaled boundary finite element methods,SBFEM)和非局部宏-微观损伤模型的剪切型裂纹动态开裂模拟方法,定义了基于偏应变概念的物质点对的正伸长量,可作为预测剪切型裂纹扩展行为的动态开裂准则,一点的损伤定义为该点影响域范围内连接的物质键损伤的加权平均值,而物质键的损伤则与基于偏应变概念的物质点对的正伸长量相关联,并引入能量退化函数建立结构域几何拓扑损伤与能量损失之间的关系,将拓扑损伤与应力应变联系起来,通过能量退化函数修正了SBFEM的刚度系数矩阵,得到了子域在损伤状态下的刚度矩阵,推导了考虑结构损伤的SBFEM动力控制方程,采用Newmark隐式算法对控制方程进行时间离散.最后,通过3个典型算例验证了建议的模型可较好地模拟剪切型断裂问题,能够很好地捕捉剪切型裂纹的扩展路径,并得到较为准确的载荷-位移曲线.

Shear failure is a common failure mode in geotechnical engineering.Understanding the shear failure mechanism and accurately predicting the initiation and propagation process of shear fractures is of great significance for ensuring the safety and stability of engineering structures.This paper establishes a dynamic cracking simulation method for shear-based fractures based on the scaled boundary finite element methods(SBFEM)and a non-local macro-micro damage model.It defines the positive elongation of material point pairs based on deviator strain concept,which can serve as a dynamic cracking criterion for predicting the propagation behaviour of shear-based fractures.The damage at a point is defined as the weighted average of material bond damage within the influence domain of that point,where material bond damage is related to the positive elongation of material point pairs based on deviator strain concept.An energy degradation function is introduced to establish the relationship between geometric topological damage in the structural domain and energy loss,linking topological damage with stress and strain.The energy degradation function is used to modify the stiffness matrix of SBFEM,resulting in the stiffness matrix of the subdomain in the damaged state.The dynamic governing equation of SBFEM considering structural damage is derived,and the Newmark implicit algorithm is used for time discretization of the governing equation.Finally,through three typical numerical examples,it is verified that the proposed model can effectively simulate shear failure problems,accurately capture the crack path of shear fractures,and obtain relatively accurate load-displacement curves.