Cosserat连续体平均场理论中的Hill定理
HILL's LEMMA FOR THE AVERAGE-FIELD THEORY OF COSSERAT CONTINUUM
查看参考文献17篇
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文摘
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基于平均场理论的多尺度均匀化模拟必须满足Hill-Mandel细宏观能量等价条件,这首先需要推导Hill定理。Cosserat连续体平均场理论中,宏观平均偶应力的定义存在2种不同的方案,给Hill定理的推导带来了困难。该文构造了一个不考虑宏观平均偶应力具体表达式的Hill定理中间形式,将2种宏观偶应力定义分别代入,推导和建立了2个版本的Hill定理,并对二者做了比较和分析,为后续非均质Cosserat连续体多尺度模拟研究工作提供了理论基础。 |
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其他语种文摘
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The Hill-Mandel condition, i.e. the micro-macro energy equivalence condition, should be satisfied in the multi-scale homogenization process based on the average-field theory. It needs firstly the derivation of Hill's lemma. The macroscopic average couple stress tensor can be defined in two different ways in the average-field theory of Cosserat continuum. That leads to difficulties in deriving the Hill's lemma. This paper constructs a transition form of Hill's lemma without considering the specific expressions of macro average couple stress tensor. Substitution of the two existing definitions of average couple stresses into the transition form leads to two different versions of Hill's lemma, respectively. The comparison and analysis are also performed on the presented versions. This paper provides the theoretical basis for further research on the multi-scale modeling of heterogeneous Cosserat continuum. |
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来源
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工程力学
,2013,30(8):29-34 【核心库】
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DOI
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10.6052/j.issn.1000-4750.2012.04.0264
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关键词
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多尺度模拟
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平均场理论
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Cosserat连续体
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平均偶应力定义
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Hill定理
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地址
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1.
大连交通大学土木与安全工程学院, 辽宁, 大连, 116028
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中国科学院力学研究所, 北京, 100190
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大连交通大学交通运输工程学院, 辽宁, 大连, 116028
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语种
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中文 |
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文献类型
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研究性论文 |
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ISSN
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1000-4750 |
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学科
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力学 |
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基金
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国家自然科学基金项目
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文献收藏号
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CSCD:4907220
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参考文献 共
17
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