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基于结构化变形驱动的非局部宏−微观损伤模型的真II型裂纹模拟

任宇东 陈建兵 卢广达

任宇东, 陈建兵, 卢广达. 基于结构化变形驱动的非局部宏−微观损伤模型的真II型裂纹模拟. 力学学报, 待出版 doi: 10.6052/0459-1879-22-280
引用本文: 任宇东, 陈建兵, 卢广达. 基于结构化变形驱动的非局部宏−微观损伤模型的真II型裂纹模拟. 力学学报, 待出版 doi: 10.6052/0459-1879-22-280
Ren Yudong, Chen Jianbing, Lu Guangda. Ture mode II crack simulation based on a structured deformation driven nonlocal macro-meso-scale consistent damage model. Chinese Journal of Theoretical and Applied Mechanics, in press doi: 10.6052/0459-1879-22-280
Citation: Ren Yudong, Chen Jianbing, Lu Guangda. Ture mode II crack simulation based on a structured deformation driven nonlocal macro-meso-scale consistent damage model. Chinese Journal of Theoretical and Applied Mechanics, in press doi: 10.6052/0459-1879-22-280

基于结构化变形驱动的非局部宏−微观损伤模型的真II型裂纹模拟

doi: 10.6052/0459-1879-22-280
基金项目: 国家杰出青年科学基金项目(No.51725804)资助
详细信息
    通讯作者:

    陈建兵, 教授, 主要研究方向: 结构非线性分析, 随机动力学与工程可靠性. E-mail: chenjb@tongji.edu.cn

  • 中图分类号: O346.5; TU313

TURE MODE II CRACK SIMULATION BASED ON A STRUCTURED DEFORMATION DRIVEN NONLOCAL MACRO-MESO-SCALE CONSISTENT DAMAGE MODEL

  • 摘要: II型荷载作用下裂纹变形模式也为II型的破坏问题称为真II型破坏. 准确定量地把握真II型破坏的全过程是具有挑战性的问题. 本文采用结构化变形驱动的非局部宏-微观损伤模型对真II型破坏问题进行了模拟. 根据结构化变形理论将点偶的非局部应变分解为弹性应变与结构化应变两部分, 进而利用Cauchy-Born准则与结构化应变计算点偶的结构化正伸长量. 在本文中, 结构化应变取为非局部应变的偏量部分. 当点偶的结构化正伸长量超过临界伸长量时, 微细观损伤开始在点偶层次发展. 将微细观损伤在作用域中进行加权求和得到拓扑损伤, 并通过能量退化函数将其嵌入到连续介质-损伤力学框架中进行数值求解. 进一步地, 本文采用Gauss-Lobatto积分格式计算点偶的非局部应变, 将积分点数目降低到4个, 显著降低了前处理和非线性分析的计算成本. 通过对II型加载下裂尖应变场的分析揭示了采用偏应变作为结构化应变的原因. 对两个典型真II型破坏问题的模拟结果表明, 本文方法不仅可以把握II型加载下的真II型裂纹扩展模式, 同时可以定量刻画加载过程中的荷载-变形曲线, 且不具有网格敏感性. 最后指出了需要进一步研究的问题.

     

  • 图  1  : II型荷载与作用下的I型裂纹与真II型裂纹

    Figure  1.  Mode I and true mode II crack under mode II loading

    图  2  物质点、物质点偶及作用域示意图

    Figure  2.  Schematic of material point, material point pair and influence domain

    图  3  : 有曲率试件上的点偶

    Figure  3.  Material point pair in specimen with curvature

    图  4  : II型荷载下的裂纹

    Figure  4.  Crack under mode II loading

    图  5  紧剪切试件及半结构示意图

    Figure  5.  Schematic of compact shear specimen and semi-structure

    图  6  紧剪切试件有限元网格剖分

    Figure  6.  Finite element meshes of the compact shear specimen

    图  7  紧剪切试件破坏时裂纹形态以及与近场动力学[23,24]的对比

    Figure  7.  The final crack pattern of the compact shear specimen and comparison with the one from peridynamics[23,24]

    图  8  紧剪切试件不同网格的荷载-位移曲线

    Figure  8.  The load-displacement curves obtained from different meshes for the compact shear specimen

    图  9  紧剪切试件计算结果与PD结果[23,24]对比(网格B)

    Figure  9.  The resulting load-displacement curve for the compact shear specimen compared with the one from PD[23,24] (Mesh B)

    图  11  紧剪切试件各荷载步裂纹图(变形放大100倍)

    Figure  11.  Crack patterns of the compact shear specimen in each load step (Deformation magnified by 100 times)

    图  12  : 紧剪切试件荷载步III应力云图

    Figure  12.  Stress contour of compact shear specimen in load step III

    图  10  两种积分格式计算荷载-位移曲线对比

    Figure  10.  The load-displacement curves obtained from two integration schemes

    图  13  长剪切试件示意图

    Figure  13.  Schematic of the long shear specimen

    图  14  长剪切试件有限元网格划分

    Figure  14.  Finite element meshes of the long shear specimen

    图  15  长剪切试件破坏时的裂纹形态

    Figure  15.  The final crack pattern of the long shear specimen

    图  16  长剪切试件不同网格的荷载-位移曲线

    Figure  16.  The load-displacement curves obtained from different meshes for the long shear specimen

    图  17  长剪切试件计算结果与相场模型[18]计算结果对比(网格B)

    Figure  17.  The resulting load-displacement curve for the long shear specimen compared with the one from phase field model[18] (Mesh B)

    图  18  两种积分格式计算荷载-位移曲线对比

    Figure  18.  The load-displacement curves obtained from two integration schemes

    图  19  长剪切试件各个荷载步裂纹形态(变形放大20倍)以及与相场模型[18]结果对比

    Figure  19.  Crack patterns of the long shear specimen in each load step (Deformation magnified by 20 times) and comparison with phase field model[18]

    图  20  : 长剪切试件荷载步III应力云图

    Figure  20.  Stress contour of long shear specimen in load step III

    表  1  4点Gauss-Lobatto格式积分点与积分权重

    Table  1.   The integral points and weights of 4 point Gauss-Lobatto scheme

    Integral Points ${s_i}$Integral Weights ${\xi _i}$
    $ \pm 0.447214$$0.833333$
    $ \pm 1.0$$0.166667$
    下载: 导出CSV

    表  2  紧剪切试件模型参数取值

    Table  2.   The model parameters for the compact shear specimen

    $\ell $${\lambda _{\text{c}}}$$\gamma $$p$$q$
    $1.5{\text{mm}}$$5 \times {10^{ - 4}}{\text{mm}}$$\infty /{\text{mm}}$$11$$0$
    下载: 导出CSV

    表  3  紧剪切试件计算时间

    Table  3.   The computational time of compact shear specimen

    MeshIntegration SchemeTime
    PreprocessingNonlinear Analysis
    Mesh AGL447.872 ms50.778 s
    EQ9141.038 ms54.955 s
    Mesh BGL4150.087 ms88.100 s
    EQ9464.347 ms126.825 s
    下载: 导出CSV

    表  4  长剪切试件模型参数取值

    Table  4.   The model parameters for the long shear specimen

    $\ell $${\lambda _{\text{c}}}$$\gamma $$p$$q$
    $3{\text{mm}}$$3.5 \times {10^{ - 3}}{\text{mm}}$$7/{\text{mm}}$$7$$13$
    下载: 导出CSV

    表  5  长剪切试件计算时间

    Table  5.   The computational time of long shear specimen

    MeshIntegration SchemeTime
    PreprocessingNonlinear Analysis
    Mesh AGL4551.107 ms44.918 s
    EQ91.695 s55.940 s
    Mesh BGL41.284 s68.400 s
    EQ94.137 s84.187 s
    下载: 导出CSV
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