›› 2017, Vol. 38 ›› Issue (12): 3462-3468.doi: 10.16285/j.rsm.2017.12.009

• 基础理论与实验研究 • 上一篇    下一篇

准脆性材料断裂模拟方法研究

燕秀发1, 2 ,钱七虎1 ,赵跃堂1 , 周寅智1   

  1. 1. 陆军工程大学 爆炸冲击防灾减灾国家重点试验室,江苏 南京 210007;2. 解放军91550部队,辽宁 大连 116023
  • 收稿日期:2015-12-16 出版日期:2017-12-11 发布日期:2018-06-05
  • 作者简介:燕秀发,男,1972年生,博士后,主要从事防护工程数值仿真方面的工作。
  • 基金资助:

    中国博士后科学基金特别资助项目(No.201003768);国家自然科学基金创新研究群体科学基金(No.51321064);爆炸冲击防灾减灾国家重点试验室开放课题资助项目(No.DPMEIKF201308)。

A method for simulating fracture in quasi-brittle materials

YAN Xiu-fa1, 2, QIAN Qi-hu1, ZHAO Yue-tang1, ZHOU Yin-zhi1   

  1. 1. State Key Laboratory of Disaster Prevention & Mitigation of Explosion & Impact, Army Engineering University of PLA, Nanjing, Jiangsu 210007, China; 2. PLA 91550 Unit, Dalian, Liaoning 116023, China
  • Received:2015-12-16 Online:2017-12-11 Published:2018-06-05
  • Supported by:

    This work was supported by the China Postdoctoral Science Foundation (201003768), the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (51321064) and the Fund of the State Key Laboratory of Disaster Prevention & Mitigation of Explosion & Impact (Army Engineering University of PLA) (DPMEIKF201308).

摘要: 针对岩石、混凝土类准脆性材料的断裂过程模拟,发展了基于黏聚裂纹模型的虚节点扩展有限元法,并给出了该法的数值原理和控制方程。通过三点弯曲梁拉伸断裂、单边缺口试件Ⅰ-Ⅱ复合型断裂和Nooru-Mohammed试验多裂纹断裂等典型算例,并与已有解或试验结果对比,表明该法适合于模拟准脆性材料由张开型裂纹支配的断裂过程。相对于节点分离有限元法,该法无需预设开裂路径;相对于塑性损伤有限元法,该法能够可靠模拟多裂纹曲线扩展;相对于标准扩展有限元法,该法无需引入裂尖单元,避免了应力强度因子的计算;相对于高阶富集扩展有限元法,该法具有良好的适用性,便于得到收敛的计算结果。此外,基于单元的位移场描述使其更易于嵌入常用有限元软件,从而利用后者良好的非线性计算功能求解复杂问题。

关键词: 扩展有限元法, 虚节点, 黏聚裂纹模型, 准脆性材料, 裂纹扩展

Abstract: Based on the cohesive crack model, a virtual node extended finite element method (XFEM) was developed to simulate the fracturing process of quasi-brittle materials, such as rock and concrete. Numerical principles and governing equations of this method were also proposed. Typical numerical examples were presented, including tension fracture of the three-point bending beam, I–II mixed mode fracture of a single edge notched specimen and fracture of multiple cracks in the Nooru-Mohammed experiment. Moreover, these results were compared with existing solutions or experimental results. It is found that this method is suitable to simulate fracturing process of quasi-brittle materials dominated by opening-mode cracks. Pre-assignment of crack-growth paths is not necessary for the proposed method, in comparison with the node-separation finite element method (FEM). Contrary to the plastic-damage FEM, this method also can reliably simulate the propagation of multiple cracks. Meanwhile, it is not necessary to introduce crack-tip elements and calculate stress intensity factors in comparison with the normal XFEM. Lastly, it is particularly applicable to the acquirement of convergent computational results by contrast with the XFEM with higher-order enriched elements. Moreover, the developed method can be easily embedded into conventional finite element software to solve complex problems by applying powerful nonlinear computational functions of the latter for its displacement description based on elements.

Key words: extended finite element method (XFEM), virtual node, cohesive crack model, quasi-brittle materials, crack propagation

中图分类号: 

  • TU 457
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