颗粒材料多尺度分析的连接尺度方法

本文提出了耦合细尺度上基于离散颗粒集合体模型的离散单元法（DEM）和粗尺度上基于Cosserat连续体模型的有限元法（FEM）的连接尺度方法（BSM）以研究颗粒材料的力学行为。采用Cosserat连续体模型和FEM模拟的粗尺度域覆盖全域，而采用离散颗粒集合体模型的DEM模拟的细尺度域仅限于需特别关注材料微结构演变和非连续变形行为的局部区域。对这两个区域间的界面提出了适当的界面条件及其实施方案。通过采用适当的连接尺度投影算子，空间离散的粗、细尺度耦合系统多尺度运动方程具有解耦和允许分别求解、因而也允许分别采用不同时间步长对粗、细尺度计算的特点，可极大地提高BSM的计算效率。文中二维地基数值算例结果说明了所陈述方法的可应用性，以及相对基于Cosserat连续体模型的FEM和基于离散颗粒集合体模型的DEM的优越性。 

A Bridging Scale Method for Multi-scale Analysis of Granular Materials

The bridging scale method (BSM) that couples the discrete particle assembly modeling with discrete element method (DEM) and the Cosserat continuum modeling with finite element method (FEM) in both fine and coarse scales respectively is proposed to study the mechanical behaviors in granular materials. The coarse scale domain, which is modeled with the Cosserat continuum and numerically simulated with the FEM, covers the whole medium concerned. While the fine scale one, which is modeled with the discrete particle assembly and numerically simulated with the DEM, is limited to a localized region, where the material microstructure and discontinuous deformation behaviors and their evolutions are needed to pay particular attentions. The interfacial condition between the two domains is presented and the scheme for its numerical implementation is proposed. By using a proper bridging scale projection operator, two decoupling sets of equations of motion of the combined coarse-fine scale system are allowed to solve with two separate solvers and to use distinct time step sizes, that will greatly enhance the computational efficiency of the BSM. The numerical results for a 2D example problem of the soil foundation illustrate the applicability and performance of the proposed method, and its advantages as compared with the FEM based on the Cosserat continuum modeling and the DEM based on the discrete particle assembly modeling.