基于间接热力学方法的变换应力方法推导

姚仰平; 何冠; 崔文杰

doi:10.11779/CJGE20230332

基于间接热力学方法的变换应力方法推导 English Version

1.
北京航空航天大学交通科学与工程学院, 北京 100191
2.
中国五冶集团, 四川成都 610063

基金项目:

国家自然科学基金项目 52238007

国家自然科学基金项目 51979001

详细信息

作者简介:
姚仰平(1960—)，男，博士，教授，主要从事土体本构理论方面的教学和科研工作。E-mail: yaoyp@buaa.edu.cn

中图分类号: TU43
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出版历程
- 收稿日期: 2023-04-16
- 网络出版日期: 2023-11-21
- 刊出日期: 2024-06-30

Derivation of transformed stress method based on indirect thermodynamic method

1.
School of Transportation Science and Engineering, Beihang University, Beijing 100191, China
2.
China MCC5 Group Corp. Ltd., Chengdu 610063, China

摘要

摘要: 金属等没有剪胀性的连续材料在根据试验结果建立屈服函数后，可以由Drucker公设及其相关联流动法则推论直接唯一地确定出与屈服函数一致的塑性势函数。但大量试验结果与理论分析都表明Drucker公设对于土材料这种有剪胀性的颗粒材料并不适用，所以更具普适性的热力学成了正确描述土材料塑性流动方向的必要条件。然而塑性流动方向无法只由热力学这一描述材料特性的必要条件唯一地确定，因此便出现了先由试验确定屈服面与塑性流动方向再对其进行热力学验证的间接热力学方法。此外，由于土材料在三维应力空间中不同洛德角对应子午面上的应力应变规律并不一致，因此一般会通过三维化方法来描述土材料在三维应力空间中的力学特性。三维化方法会使得不同子午面上的屈服面及塑性流动方向与三轴压缩状态下所建立的本构模型有所不同，导致三维化后的本构模型是否符合热力学原理成为新的问题。所以本文利用间接热力学方法推导了符合热力学原理的三维化方法，并通过构建变换应力空间将其整理为更有实用性的变换应力方法。
- 塑性流动 /
- 剪胀性 /
- 间接热力学方法 /
- 三维化 /
- 变换应力方法
Abstract: The unique plastic potential function consistent with the yield function can be directly determined by the Drucker's postulate and its associated flow law deduction after the yield function is established for the continuous materials without dilatancy, such as metals. However, a large number of test results and theoretical analyses show that the Drucker's postulate is not applicable to soils, which is a type of granular material with dilatancy, then the more universal thermodynamics is selected as a new necessary condition for correctly describing the plastic flow direction of soils. Nevertheless, the plastic flow direction cannot be determined solely by thermodynamics, which is only a necessary condition to describe the properties of materials. Therefore, the indirect thermodynamic method is developed in which the yield surface and the plastic flow direction are firstly determined with tests and then verified by thermodynamics. In addition, since the stress-strain relationships on the meridional planes corresponding to different Lode angles in the three-dimensional stress space of soils are not consistent to each other, the generalized methods are generally used to describe such mechanical characteristics of soils. Meanwhile, the generalized yield surface and plastic flow direction on different meridional planes will be different from those in the constitutive models established under triaxial compression state, so whether the generalized constitutive model conforms to the thermodynamics becomes a new problem. Therefore, the indirect thermodynamic method is used to derive a generalized method conforming to the principles of thermodynamics, which is then organized into a more practical transformed stress method by constructing the transformation stress space.
- plastic flow /
- dilatancy /
- indirect thermodynamic method /
- generalization /
- transformed stress method

HTML全文

图 1 耗散应力空间中的塑性流动方向分布范围

Figure 1. Distribution ranges of plastic flow direction in dissipative stress space

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图 2 耗散应力空间中的椭圆塑性势面

Figure 2. Elliptical plastic potential surface in dissipative stress space

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图 3 水滴形屈服面

Figure 3. Drop-shaped yield surfaces

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图 4 水滴形屈服面与椭圆塑性势面

Figure 4. Drop-shaped yield surface and elliptical plastic potential surface

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图 5 屈服面与两个应力空间中的塑性势面

Figure 5. Plastic potential surfaces in two stress spaces and yield surface

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$\pi$ 平面上三维化后的屈服线

Generalized yield envelope on $\pi$ plane

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图 7 三轴压缩与三轴伸长应力状态下的屈服面

Figure 7. Yield surfaces under triaxial compression and triaxial extension stress states

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图 8 三维化后的屈服面与塑性流动方向

Figure 8. Yield surfaces and plastic flow direction after generalization

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图 9 三轴伸长应力状态下不同应力空间中的屈服面与塑性势面

Figure 9. Yield surfaces and plastic potential surface in different stress spaces under triaxial extension stress state

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图 10 三轴伸长应力状态下变换应力空间与真实应力空间中的屈服面

Figure 10. Yield surfaces in transformed stress space and true stress space under triaxial extension stress state

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图 11 变换应力方法示意图

Figure 11. Schematic diagram of transformed stress method

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