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.
出处
《计算力学学报》
EI
CAS
CSCD
北大核心
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