Field-enriched finite element method for numerical simulation of initiation, propagation and coalescence of multiple cracks
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摘要: 研究含多裂纹岩石的力学响应和裂纹行为对岩体结构的设计与稳定性分析具有重要的指导意义。提出了场富集有限元方法研究脆性岩石材料中多裂纹的演化规律，包括裂纹的起裂、扩展和连接过程。提出了多裂纹在扩展过程中出现的各种交汇情况的解决方案。场富集有限元方法可以直接处理复杂的交叉裂纹，而不需要像扩展有限元一样引入额外的富集函数。通过数值算例，充分说明了场富集有限元方法在处理各种复杂裂纹系统扩展演化方面的能力。Abstract: The study on the mechanical response and cracking behaviors of brittle rock materials with multiple cracks is of vital significance for the design and stability analysis of rock engineering structures. A field-enriched finite element method (FE-FEM) is proposed to study the evolution behaviors of multiple cracks in rock materials, including crack initiation, propagation and coalescence. The solutions to the crack coalescence problem during simulation are proposed. The field-enriched finite element method can directly deal with the complex multiple crack problem, while the extra enriched function needs to be introduced in the extended finite element method (XFEM). The analytical results of the present numerical examples demonstrate that the proposed numerical method has the capability to handle complex multiple crack propagation and coalescence.
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图 4 裂尖与裂纹段交汇方式
Figure 4. Intersection strategy of crack tip of a crack with crack segment of another crack
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图 6 含3条平行裂纹的3点弯曲梁几何尺寸与加载条件
Figure 6. Geometry and loading condition of three-point bending beam containing three flaws
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图 7 无量纲应力强度因子K*的数值解和理论解[27]对比
Figure 7. Comparison of analytical and numerical normalized stress intensity factors at different B/W
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图 8 B=0.2W条件下的Von Mises云图和损伤图
Figure 8. Von Mises contour and damage field contour at B=0.2W
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图 9 B=2W条件下的Von Mises云图和损伤图
Figure 9. Von Mises contour and damage field contour at B=2W
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图 10 三点弯曲梁的载荷–位移曲线图
Figure 10. Load-displacement curves of three-point bending beam containing three flaws
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图 17 裂纹分布和几何加载条件
Figure 17. Distribution of multiple cracks and geometry and loading conditions
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图 19 含复杂多裂纹板的载荷–位移曲线
Figure 19. Load-displacement curves of plate containing complex cracks
表 1 裂纹扩展和交汇顺序
Table 1 Sequence of periodic crack propagation and coalescence
标记点 裂纹交汇顺序 点a 裂纹开始起裂 点b C2的裂尖与C4的T2和C5的T1相互吸引，C17的裂尖与C14的T2和C15的T1相互吸引 点c C1的T1，C3的T2，C16的T1，C18的T2同时扩展到模型边界 点d 裂纹贯穿整个模型试样 
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表 2 裂纹扩展和交汇顺序
Table 2 Sequence of random crack propagation and coalescence
标记点 裂纹交汇顺序 点a 裂纹开始起裂 点b C11的T2扩展到数值模型边界 点c C11的T1和C10的T2交汇 点d C10的T1与C14的T1交汇 点e C9的T1与C8交汇 点f C8的T1与C7交汇 点g C7的T1扩展到数值模型边界 点h C9的T2与C10的T1交汇
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