n次齐次屈服函数相关联流动法则失效的机理研究

胡亚元

n次齐次屈服函数相关联流动法则失效的机理研究 English Version

胡亚元

浙江大学软弱土与环境土工教育部重点实验室，滨海和城市岩土工程研究中心，浙江杭州 310027

基金项目: 国家自然科学基金项目（51178419）

详细信息

作者简介:
胡亚元(1968– )，男，副教授，从事环境土工、地基处理和土体本构关系的研究工作。E-mail: huyayuan@ccea.zju.edu.cn

中图分类号: TU47
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出版历程
- 收稿日期: 2012-04-22
- 发布日期: 2013-03-06

Failure mechanism of associated flow rule for nth homogenous yield function

HU Ya-yuan

Key Laboratory of Soft Soils and Geoenvironmental Engineering of Ministry of Education, Research Center of Coastal and Urban Geotechnical Engineering of Zhejiang University, Hangzhou 310058, China

摘要

摘要: 岩土材料一些常用的与摩擦有关的经典屈服准则，如Mohr-Coulomb屈服准则、俞茂宏广义双剪应力屈服准则、Lade-Duncan屈服准则、Matsuoka-Nakai屈服准则和沈珠江三剪应力屈服准则等，都属于n阶欧拉齐次函数。把上述屈服准则从真实空间推广到耗散空间后发现，当耗散空间中的n阶齐次屈服函数与真实应力无关时，根据耗散空间的Drucker塑性公设获得的耗散功与应力状态无关；对于砂性材料其值甚至为零，与塑性发生时熵增大于零的热力学第二定律相违背。为了克服上述缺陷，必须在耗散空间的n阶齐次屈服函数中引入与真实应力有关的函数项，然而，由此获得的真实空间屈服准则与塑性应变增量之间必须服从非相关联流动法则。由于服从相关联流动法则时耗散空间屈服准则表达式与真实空间的完全相同，故在真实空间中服从n阶齐次屈服准则的岩土摩擦材料也不适宜采用相关联流动法则。
- 屈服准则 /
- Drucker塑性公设 /
- n阶齐次函数 /
- 耗散空间 /
- 流动法则
Abstract: Some commonly-used classical yield criteria related to friction effect in geomaterials belong to nth Euler homogeneous function. Such criteria refer to Mohr-Coulomb yield criterion, generalized Yu Maohong twin shear stress yield criterion, Lade-Duncan yield criterion, Matsuoka-Nakai yield criterion and Shen Zhujiang three-shear stress yield criterion. After this type of yield criteria is extended from true space to dissipative space, it is found that if nth homogeneous yield criterion in dissipative space is independent of true stress, the dissipative work based on the Drucker's plastic postulate in dissipative space will be independent of stress state, and even equal to zero for sand materials, the latter of which does not conform to the second law of thermodynamics which demonstrates that entropy production must be larger than zero during the appearance of plastic behavior. To avoid this unconformity, a partial function related to the true stress must be added into the nth homogeneous yield function in dissipative space. Therefore, the relation between the new obtained yield criterion in true space and the increment of plastic strain must conform to the non-associated flow rule. Because the expression of the yield criteria in dissipative space is the same as that in true space on the condition of the associated flow rule, the associated flow rule is invalid for geomaterials with friction effect and nth homogeneous yield criteria in true space.
- yield criterion /
- Drucker's plastic postulate /
- nth homogeneous function /
- dissipation space /
- flow rule

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参考文献(16)

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