基于有限断裂法和比例边界有限元法的裂纹扩展模拟

基于有限断裂法和比例边界有限元法提出了一种裂缝开裂过程模拟的数值模型。采用基于有限断裂法的混合断裂准则作为起裂及扩展的判断标准,当最大环向应力和能量释放率同时达到其临界值时,裂缝扩展。结合多边形比例边界有限元法,可以半解析地求解裂尖区域附近的应力场和位移场,在裂尖附近无需富集即可获得高精度的解。计算能量释放率时,只需将裂尖多边形内的裂尖位置局部调整,无需改变整体网格的分布,网格重剖分的工作量降至最少。裂缝扩展步长通过混合断裂准则确定,避免了人为假设的随意性,并可以实现裂缝变步长扩展的模拟,更符合实际情况。通过对四点剪切梁的复合型裂缝扩展过程的模拟,对本文模型进行了验证,并应用于重力坝模型的裂缝扩展模拟,计算结果表明,本文提出的模型简单易行且精度较高。

Modelling of crack propagation by finite fracture mechanics and scaled boundary finite element method

A numerical model of crack propagation is proposed based on Finite Fracture Mechanics and Scaled Boundary Finite Element Method (SBFEM). With hybrid fracture criterion based on Finite Fracture Mechanics as the criterion of crack initiation, the crack is assumed to be initiated and to grow if and only if both the energy release rate and the maximum circumferential stress simultaneously reach critical values. By introducing polygon SBFEM, the stress field and displacement field in the vicinity of a crack tip are obtained semi-analytically without any enrichment. When energy release rate is calculated, the required changes in the mesh are easily accommodated by shifting the crack tip within the cracked polygon without changing the global mesh structure, hence the workload of remeshing is minimized. Confirming the crack propagation length on hybrid fracture criterion can avoid arbitrary assumptions and it is more realistic to simulate crack propagation of variable length. By analysing the mixed mode crack propagation of four-point shear beam, the effectiveness of the proposed model is verified. Finally, the model is applied to simulate the crack propagation of a gravity dam model, which indicates that the proposed model is not only simple in form and application but also has high precision.