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考虑混凝土塑性耗散的CDM-XFEM裂缝计算方法

金浩 余朔

金浩, 余朔. 考虑混凝土塑性耗散的CDM-XFEM裂缝计算方法. 力学学报, 2021, 53(10): 2790-2799 doi: 10.6052/0459-1879-21-272
引用本文: 金浩, 余朔. 考虑混凝土塑性耗散的CDM-XFEM裂缝计算方法. 力学学报, 2021, 53(10): 2790-2799 doi: 10.6052/0459-1879-21-272
Jin Hao, Yu Shuo. CDM-XFEM method for crack calculation considered plastic dissipation of concrete. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(10): 2790-2799 doi: 10.6052/0459-1879-21-272
Citation: Jin Hao, Yu Shuo. CDM-XFEM method for crack calculation considered plastic dissipation of concrete. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(10): 2790-2799 doi: 10.6052/0459-1879-21-272

考虑混凝土塑性耗散的CDM-XFEM裂缝计算方法

doi: 10.6052/0459-1879-21-272
基金项目: 国家自然科学基金(51908428)和江苏省自然科学基金(BK20211173)资助项目
详细信息
    作者简介:

    金浩, 副研究员, 研究方向: (城市)轨道交通振动工程. E-mail: jinhao@seu.edu.cn

  • 中图分类号: TU311.4

CDM-XFEM METHOD FOR CRACK CALCULATION CONSIDERED PLASTIC DISSIPATION OF CONCRETE

  • 摘要: 混凝土结构在服役期间受外界载荷的影响容易产生裂缝, 导致结构刚度降低、构件承载性能衰退, 而采用准确的计算方法预测混凝土裂缝的发展是治理裂缝的基本前提, 也是保障结构安全的重要手段. 连续损伤力学方法(continuou damage method, CDM)能够描述微裂缝的扩展过程, 但不能表示离散的开裂面, 且存在网格诱导偏差及虚假应力传递的弊端, 扩展有限单元法(mechanics-extended finite element method, XFEM)能够描述宏观裂纹的扩展过程, 但不能反映微裂缝的动态扩展, 两者计算出的裂纹分布与实际差异均较大. 现有的CDM-XFEM方法已经能够模拟混凝土微裂缝及宏观裂缝发展的整个过程, 但忽略了宏观裂缝出现时混凝土产生的塑性应变, CDM与XFEM的能量转化过程欠缺平衡性. 因此, 本文重点考虑能量转化时的塑性耗散, 选取指数型函数为粘结裂缝的牵引-分离模式, 基于能量及应力等效的条件重新构建了CDM与XFEM之间的能量转化方程. 采用广义逆最小二乘法求解能量转化系数, 确定能量转化时的临界位移, 并给出了裂缝面水平集的更新算法及整体计算方法的程序流程. 以双切口混凝土受剪拉开裂试验为例, 采用多种裂缝计算方法与试验进行了对比. 结果表明, 采用考虑混凝土塑性耗散的CDM-XFEM方法算出的裂缝分布及拉力-张开位移曲线与试验结果差异最小, 说明采用考虑混凝土塑性耗散的CDM-XFEM计算方法能够更好地计算混凝土裂缝.

     

  • 图  1  CDM-XFEM方法计算过程示意图

    Figure  1.  Calculation process CDM-XFEM method

    图  2  CDM的应力-应变曲线

    Figure  2.  Stress-strain curve of CDM

    图  3  XFEM粘结裂缝的牵引-分离曲线

    Figure  3.  Traction-separation curve of XFEM cohesive crack

    图  4  考虑混凝土塑性耗散的CDM-XFEM方法计算流程

    Figure  4.  Calculation flow of CDM-XFEM method considered concrete plastic dissipation

    图  5  裂缝水平集函数速度分量示意图

    Figure  5.  Velocity component of crack level set function

    图  6  双切口混凝土受剪拉开裂试验[45]

    Figure  6.  Shear tensile cracking test of concrete contained double notched[45]

    图  7  试验与各种方法算出的裂缝分布对比

    Figure  7.  Comparison of crack distribution calculated by various methods and experiment

    图  8  考虑塑性耗散的CDM-XFEM计算出的三维裂缝分布云图

    Figure  8.  3D crack distribution calculated by CDM-XFEM considered plastic dissipation

    图  9  试验与各种方法算出的拉力-张开位移曲线对比

    Figure  9.  Comparison of the tension-open displacement curves obtained by experiment and various calculation methods

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出版历程
  • 收稿日期:  2021-06-16
  • 录用日期:  2021-09-24
  • 网络出版日期:  2021-09-25
  • 刊出日期:  2021-10-26

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