梯度增强Cosserat连续体的广义Hill定理  

A generalized Hill's lemma for gradient-enhanced Cosserat continuum

作　　者：李锡夔[1] 张俊波[1] 张雪[1] 

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室,大连116023

出　　处：《计算力学学报》2011年第6期813-820,832,共9页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(90715011;10672033);国家973(2010CB731502)资助项目

摘　　要：基于经典Cauchy连续体的Hill定理,在平均场理论的框架下导出了梯度增强Cosserat连续体细、宏观均匀化方法的广义Hill定理。在梯度增强Cosserat连续体中,不仅宏观样条点上的应变和应力张量,而且它们的梯度均作用于与该样条点相关联的细观表征元(RVE)。依据此广义Hill定理,对梯度增强Cosserat连续体表征元提出了满足Hill-Mandel能量等价条件和平均场理论的强形式及弱形式边界条件。Based on the Hill＇s lemma for classical Cauchy continuum, a generalized Hill＇s lemma for micro-macro homogenization modeling of gradient-enhanced Cosserat continuum is presented in the frame of the average-field theory. In the gradient-enhanced Cosserat continuum modeling not only the strain and stress tensors defined in classical Cosserat continuum but also their gradients at the macroscopic sampling point are attributed to associated micro-structural representative volume element （RVE）. The admissible boundary conditions required to prescribe on the RVE in strong and/or weak forms for the modeling are discussed and given to ensure the satisfaction of the enhanced Hill-Mandel energy condition and the average-field theory.

关 键 词：Hill定理 Hill—Mandel条件 梯度增强Cosserat连续体 平均场理论 RVE边界条件 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]