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工程力学  2013 

Cosserat连续体平均场理论中的Hill定理

DOI: 10.6052/j.issn.1000-4750.2012.04.0264, PP. 29-34

Keywords: 多尺度模拟,平均场理论,Cosserat连续体,平均偶应力定义,Hill定理

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Abstract:

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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