离散颗粒集合体-Cosserat连续体模型的连接尺度方法

摘要

On the basis of the bridging scale method （BSM） initially proposed for molecular dynamics- Cauchy continuum modeling , a new version of the BSM that couples the discrete particle assembly model using the discrete element method （DEM） and the Cosserat continuum model using the finite ele- ment method （FEM） in fine and coarse scales respectively is presented. The present BSM applies the DEM only to limited local regions of the whole computational domain for the purpose of accurate simula- tion of material failure with discontinuous deformation characteristics in microscopic scale,and meantime applies the FEM that costs much less both computational time and storage space to the whole domain. In addition,different time step sizes are allowed to the time integration schemes used to the coarse and fine scales respectively,as a consequence, both computational accuracy and efficiency of the present BSM is greatly enhanced. With the coarse and fine scale decomposition of translational and rotational displace- ments,in light of the principle of virtual work applied to the FEM nodes of Cosserat continuum and the particle centers of discrete particle assembly respectively, two decoupling sets of equations of motion of the combined coarse-fine scale system are derived. The interfacial condition between coarse and fine do- mains in the case of quasi-static loading,and the non-reflecting boundary condition （NRBC）, which is ca- pable of effectively eliminating spurious reflective waves at the interface between coarse and fine domains under dynamic loads are presented and discussed. The numerical results for 2D example problems illus- trate the applicability and advantages of the present BSM,as well as the availability of the proposed in- terfacial condition for dynamical response simulations of granular materials.%基于针对分子动力学-Cauchy连续体模型提出的连接尺度方法（BSM）[1,2],发展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BSM。仅在有限局部区域内采用DEM以从细观层次模拟非连续破坏现象,而在全域则采用花费计算时间和存储空间较少的FEM。通过连接尺度位移（包括平移和转动）分解,和基于作用于Cosserat连续体有限元节点和颗粒集合体颗粒形心的离散系统虚功原理,得到了具有解耦特征的粗细尺度耦合系统运动方程。讨论和提出了在准静态载荷条件下粗细尺度域的界面条件,以及动态载荷条件下可以有效消除粗细尺度域界面上虚假反射波的非反射界面条件（NRBC）。本文二维数值算例结果说明了所提出的颗粒材料BSM的可应用性和优越性,及所实施界面条件对模拟颗粒材料动力学响应的有效性。