梯度增强Cosserat连续体的广义Hill定理

摘要

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.%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。