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颗粒土中剪切带临界状态数学描述及其完全解

黄文雄 崔贤

黄文雄, 崔贤. 颗粒土中剪切带临界状态数学描述及其完全解[J]. 应用数学和力学, 2024, 45(3): 287-294. doi: 10.21656/1000-0887.440295
引用本文: 黄文雄, 崔贤. 颗粒土中剪切带临界状态数学描述及其完全解[J]. 应用数学和力学, 2024, 45(3): 287-294. doi: 10.21656/1000-0887.440295
HUANG Wenxiong, CUI Xian. Mathematical Description and Complete Solution of the Critical State in the Shear Band of Granular Soil[J]. Applied Mathematics and Mechanics, 2024, 45(3): 287-294. doi: 10.21656/1000-0887.440295
Citation: HUANG Wenxiong, CUI Xian. Mathematical Description and Complete Solution of the Critical State in the Shear Band of Granular Soil[J]. Applied Mathematics and Mechanics, 2024, 45(3): 287-294. doi: 10.21656/1000-0887.440295

颗粒土中剪切带临界状态数学描述及其完全解

doi: 10.21656/1000-0887.440295
基金项目: 

国家自然科学基金 11772117

详细信息
    通讯作者:

    黄文雄(1961—),男,教授,博士,博士生导师(通讯作者. E-mail: wh670@hhu.edu.cn)

  • 中图分类号: O302

Mathematical Description and Complete Solution of the Critical State in the Shear Band of Granular Soil

  • 摘要: 为正确模拟土体涉及剪切带演化的后失效力学响应,需采用包含细观特征长度的高阶连续介质力学模型. 笔者利用前期所建立的微极亚塑性模型,对颗粒土中剪切带的发展过程进行了分析推导,得到了剪切带临界状态条件下关键变量所满足的非线性微分方程. 该文展示了上述非线性微分方程的简要推导,重点讨论了该非线性微分方程的主要性质、主要参数变化范围和求解途径;通过对剪切带进一步的力学分析补充建立了一个能量方程,使问题具有确定解. 在此基础上,应用数值积分求出了剪切带厚度因子和剪切内应力、变形率分布及剪切速度分布的完全解. 其中剪切带厚度因子对于微极亚塑性模型细观参数的确定具有重要作用.
  • 图  1  剪切带脱离体及受力示意图及坐标系选取

    Figure  1.  Schematic diagram for the shear band with applied forces and coordinates

    图  2  平面应变条件下Cosserat介质质点自由度

    Figure  2.  Degrees of freedom of a Cosserat continuum particle in the plane strain condition

    图  3  剪切带厚度因子ξd/2对参数r0的依赖关系

    Figure  3.  Shear band thickness factor ξd/2 vs. parameter r0

    图  4  对应r0设定值参数β的先验和后验值

    Figure  4.  Priori and posteriori values of β vs. parameter r0

    图  5  半带厚内y(ξ)和z(ξ)

    Figure  5.  Variations of y(ξ)and z(ξ)in the half shear band

    图  6  半带厚内$\hat{\theta}(\xi), \hat{\theta}^{\prime}(\xi)$和$\hat{R}(\xi)$

    Figure  6.  Variations of $\hat{\theta}(\xi), \hat{\theta}^{\prime}(\xi)$ and z(ξ) in the half shear band

    图  7  剪切带内正则化应力、偶应力分布

    Figure  7.  Distributions of the normalized stress and the couple stress components in the shear band

    图  8  剪切带内正则化应变率、微曲率率和剪切速率分布

      为了解释图中的颜色,读者可以参考本文的电子网页版本.

    Figure  8.  Distributions of the normalized strain rate, the micro-curvature rate and the shear velocity in the shear band

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出版历程
  • 收稿日期:  2023-09-28
  • 修回日期:  2023-11-23
  • 刊出日期:  2024-03-01

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