关于采用粗粒化提高颗粒材料多尺度模拟守恒特性的研究

连续体-颗粒耦合方法常用来描述连续-非连续颗粒行为或解决颗粒材料与其他可变形构件间相互作用问题。粗粒化coarse-graining (CG)是基于统计力学的均匀化方法,由离散的颗粒运动定义连续的宏观物理场。本文利用粗粒化(CG)推导有限元-离散元(FEM-DEM)表面和体积耦合的一般性表达式。对于表面耦合,CG可以将耦合力分布到颗粒-单元接触点以外的位置,如相邻的积分点;对于体积耦合,CG可以将颗粒尺度的运动均匀化到耦合单元上。由粗粒化推导出的耦合项仅包含一个参数,即粗粒化宽度,为均匀化后的宏观场定义了一个可调整的空间尺度。当粗粒化宽度为零时,表面和体积耦合表达式简化为常规局部耦合。本文通过弹性立方体冲击颗粒床和离散-连续介质间波传播两个数值算例,展示使用粗粒化方法提高耦合系统能量守恒的优势,并结合其他耦合参数(如体积耦合深度)讨论了粗粒化参数对数值稳定性和计算效率的影响。

On the conservation properties of CG-enriched concurrent coupling methods for multi-scale modeling of granular materials

Particle and continuum methods are usually coupled to handle particle-structure contact problems and transitional material behavior between discontinuous and continuous.In this work,we reformulate the surface and volume coupling methods based on a micro-macro transition technique called coarse-graining(CG).For surface coupling,coarse graining allows distributing the coupling forces beyond the elements that the particles are locally coupled with,e. g.,from contact points to the neighboring integration points.For volume coupling,coarse-graining enriches the homogenization operation with a non-local contribution from the particles.The generalized coupling terms contain one user-defined parameter,namely,the CG width,setting a length scale for the coarse-grained fields.The advantages of CG in surface and volume coupling are demonstrated via two numerical examples:an elastic cube falling on a granular bed and wave propagation between discrete and continuum media.In this paper,we focus on how the conservation properties of the coupled system are influenced by the CG width.Together with other numerical parameters relevant to the coupling,we show that the CG-enriched formulations lead to better numerical stability and less computational cost for a given energy dissipation ratio.