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土的各向同性化变换应力方法

姚仰平 唐科松

姚仰平, 唐科松. 土的各向同性化变换应力方法. 力学学报, 2022, 54(6): 1651-1659 doi: 10.6052/0459-1879-21-651
引用本文: 姚仰平, 唐科松. 土的各向同性化变换应力方法. 力学学报, 2022, 54(6): 1651-1659 doi: 10.6052/0459-1879-21-651
Yao Yangping, Tang Kesong. Isotropically transformed stress method for the anisotropy of soils. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(6): 1651-1659 doi: 10.6052/0459-1879-21-651
Citation: Yao Yangping, Tang Kesong. Isotropically transformed stress method for the anisotropy of soils. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(6): 1651-1659 doi: 10.6052/0459-1879-21-651

土的各向同性化变换应力方法

doi: 10.6052/0459-1879-21-651
基金项目: 国家自然科学基金(51979001)和国家重点研发计划(2018YFE0207100)资助项目
详细信息
    作者简介:

    姚仰平, 教授, 主要研究方向: 土的本构关系. E-mail: ypyao@buaa.edu.cn

  • 中图分类号: TU43

ISOTROPICALLY TRANSFORMED STRESS METHOD FOR THE ANISOTROPY OF SOILS

  • 摘要: 在不同方向的力学参数、结构特性及应力应变关系的不同为材料的各向异性, 建立能够反映这种复杂特性的强度准则、本构模型, 对于材料本构关系的研究具有重要的理论意义. 但材料的各向异性一直是其力学特性描述的难点, 对此, 郑泉水院士提出了各向同性化定理, 为后续研究解决材料的各向异性问题提供了方向及思路. 作者等针对土的应力诱导各向异性提出了变换应力方法, 这种方法同样遵循对材料进行各向异性问题各向同性化处理的思路, 与郑泉水院士的各向同性化定理是一脉相承的, 也是对各向同性化定理的发展. 本文旨在通过分析各向同性化定理与变换应力方法明确两者间的内在联系, 并以土材料的应力诱导各向异性处理为例, 说明在具体材料的各向异性处理过程中面临的现实问题以及变换应力方法是如何解决这些问题的. 分析并给出了变换应力方法应用时的三个合理假设, 推导出了具体的变换应力数学公式, 阐明了在考虑土的应力诱导各向异性的具体函数已经给出的情况下, 在构造土的弹塑性本构模型中采用变换应力方法的必要性.

     

  • 图  1  SMP准则在π平面上的屈服线/破坏线(真应力空间)

    Figure  1.  Yield locus/failure loci of SMP criterion in π-plane (original stress space)

    图  2  SMP准则在$ {{\tilde {\text{π}} }} $平面上的屈服线/破坏线(变换应力空间)

    Figure  2.  Yield locus/failure loci of SMP criterion in $ {{\tilde {\text{π}} }} $-plane (transformed stress space)

    图  3  天然地基中的土单元的受力状态

    Figure  3.  The stress state of unit from natural foundation soil

    图  4  SMP准则在真应力空间和变换应力空间中在π平面上的对应关系

    Figure  4.  The relation of original stress space and transformed space of SMP criterion in π-plane

    图  5  部分屈服面及其对应塑性应变增量方向[33]

    Figure  5.  Plastic strain increment directions and associated yield envelope segments[33]

    图  6  MCC模型在$p \text{-} \left( {{\sigma _{\text{a}}} - {\sigma _{\text{r}}}} \right)$面上的屈服线及正交方向

    Figure  6.  Yield locus of generalized MCC model and the orthogonal directions in $p \text{-} \left( {{\sigma _{\text{a}}} - {\sigma _{\text{r}}}} \right)$ plane

    图  7  MCC模型在$\tilde p \text{-} \left( {{{\tilde \sigma }_{\text{a}}} - {{\tilde \sigma }_{\text{r}}}} \right)$面上的屈服线及其对应的正交方向

    Figure  7.  Yield locus of generalized MCC model and the orthogonal directions in $\tilde p \text{-} \left( {{{\tilde \sigma }_{\text{a}}} - {{\tilde \sigma }_{\text{r}}}} \right)$ plane

    图  8  变换应力三维化的MCC模型在$p \text{-} \left( {{\sigma _{\text{a}}} - {\sigma _{\text{r}}}} \right)$面上的屈服线及流动方向

    Figure  8.  Yield locus and plastic strain flow directions of generalized MCC model using TS method in $p \text{-} \left( {{\sigma _{\text{a}}} - {\sigma _{\text{r}}}} \right)$ plane

    图  9  三维化MCC模型在变换应力空间内屈服面

    Figure  9.  Yield surface of generalized MCC model in transformed stress space

    图  10  三维化MCC模型在真应力空间内屈服面

    Figure  10.  Yield surface of generalized MCC model in real stress space

    图  11  三维化MCC模型的屈服面及其相应的塑性应变流动方向

    Figure  11.  Yield surface of generalized MCC model with corresponding plastic strain directions

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出版历程
  • 收稿日期:  2021-12-09
  • 录用日期:  2022-04-12
  • 网络出版日期:  2022-04-18
  • 刊出日期:  2022-06-18

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