颗粒材料的组构–应力关系与等效应力法

doi:10.13722/j.cnki.jrme.2017.1623

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摘要对已有各向异性本构模型的建模思想进行系统地回顾，指出组构方向性的刻画大都归结为组构–应力坐标变换问题。对于各向异性材料而言，沿不同方向的土骨架的有效承载面积不同，总应力需要以各组分实际承载面积为权重进行分配。通过引入变换张量，提出等效应力张量，使之可以综合地描述颗粒材料的各向异性水平、材料内部真实应力的大小以及组构–应力的方向关系。将颗粒材料的宏观各向异性视为细观尺度上各向异性应力作用在各向同性材料上的结果，以等效应力张量描述细观尺度上的各向异性应力，以已有本构模型来刻画等效各向同性材料的力学特性，提出对现有的各向同性破坏准则与本构模型进行“各向异性化”改造的一般性方法——等效应力法。以SMP准则为例进行“各向异性化”改造，通过与已有试验结果对比，验证了这种“各向异性化”改造的合理性和有效性。

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	董彤1
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	孔亮2
	郑颖人1
	王兴2
	刘云3

关键词 ：土力学, 各向异性, 等效应力张量, 组构张量, 应力方向, 等效应力法

Abstract：The methods in establishing the existing anisotropic constitutive models are reviewed systematically. It is pointed out that the description of the fabric direction should be attributed to the coordinate transformation of fabric and stress. For anisotropic materials，the total stress needs to be allocated according to the actual bearing area of each component，because the effective bearing areas of soil skeleton in different directions are different. Therefore，by introducing the transformation matrix，the equivalent stress tensor is proposed to describe the anisotropy of granular materials，the true stress inside the material and the relationship between the fabric direction and the stress direction. Therefore，the material anisotropy in macro-scale can be regarded as the result of the application of anisotropic stress on an equivalent isotropic material in micro-scale. The equivalent stress tensor is used to describe the anisotropic stress and the existing isotropic model is used to describe the mechanical property of the equivalent isotropic material. A general method of transforming the existing isotropic failure criterion and constitutive model into anisotropic ones，named“Equivalent Stress Method”，is put forward from the perspective of stress. Finally，the SMP criterion is transformed into anisotropic one as an example. The comparison with the existing experimental results proves the rationality and validity of the anisotropic transformation.

Key words： soil mechanics anisotropy equivalent stress tensor fabric tensor stress direction equivalent stress method

引用本文:

董彤1，2，孔亮2，郑颖人1，王兴2，刘云3. 颗粒材料的组构–应力关系与等效应力法[J]. 岩石力学与工程学报, 2018, 37(7): 1741-1747.
DONG Tong1，2，KONG Liang2，ZHENG Yingren1，WANG Xing2，LIU Yun3. The fabric-stress relationship and the equivalent stress method of granular materials. , 2018, 37(7): 1741-1747.

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http://www.rockmech.org/CN/10.13722/j.cnki.jrme.2017.1623 或 http://www.rockmech.org/CN/Y2018/V37/I7/1741

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