中文摘要：

基于平均场理论的多尺度模拟关键问题之一是给定恰当的代表性体积单元（RVE）的边界条件,以使均匀化过程满足Hill-Mandel细宏观能量等价条件,也即Hill宏观均匀化条件.对于非均质Cosserat连续体,已有的研究工作只能得到合理的混合平动位移-偶应力表征元边界条件,常用的一致平动位移-转角以及周期边界条件等均不能使用,给计算均匀化算法推导和实施带来了困难,也阻碍了多尺度分析方法的进一步发展与应用.为此,论文在推导和建立一个新的Hill定理版本基础上,不仅成功地给定了多种强形式表征元边界条件,而且构造出了合理的弱形式周期边界条件,这些条件既满足细宏观能量等价也符合一阶平均场理论基本假定,可在均匀化方法中推广与应用.

英文摘要：

One of the key problems in multi-scale homogenization modeling based on the average-field theory is how properly prescribe the boundary conditions on the representative volume element（RVE）, with which the Hill-Mandel condition,i, e. the Hill＇s macro-homogeneity condition,can be satisfied. From the existing contribution to the heterogeneous Cosserat continuum,only mixed translational displacement- surface couple boundary condition can be prescribed, while other commonly used RVE boundary condi- tions,such as uniform translational and rotational displacement boundary conditions and periodic RVE boundary conditions, can not be used, which holds back the development and application of the corresponding homogenization method. On the basis of derivation of a new version of Hill＇s lemma, this paper gives more versatile RVE boundary conditions in the strong form. In addition,reasonable periodic boundary conditions are successfully constructed, too. The presented RVE boundary conditions satisfy the Hill-Mandel condition and basic assumptions of the average-field theory and thus can be applied in the homogenization methods for heterogeneous Cosserat continuum.