Rycroft Chris H, Bazant Martin Z, Grest Gary S, Landry James W
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 May;73(5 Pt 1):051306. doi: 10.1103/PhysRevE.73.051306. Epub 2006 May 24.
We present a multiscale simulation algorithm for amorphous materials, which we illustrate and validate in a canonical case of dense granular flow. Our algorithm is based on the recently proposed spot model, where particles in a dense random packing undergo chainlike collective displacements in response to diffusing "spots" of influence, carrying a slight excess of interstitial free volume. We reconstruct the microscopic dynamics of particles from the "coarse grained" dynamics of spots by introducing a localized particle relaxation step after each spot-induced block displacement, simply to enforce packing constraints with a (fairly arbitrary) soft-core repulsion. To test the model, we study to what extent it can describe the dynamics of up to 135,000 frictional, viscoelastic spheres in granular drainage simulated by the discrete-element method (DEM). With only five fitting parameters (the radius, volume, diffusivity, drift velocity, and injection rate of spots), we find that the spot simulations are able to largely reproduce not only the mean flow and diffusion, but also some subtle statistics of the flowing packings, such as spatial velocity correlations and many-body structural correlations. The spot simulations run over 100 times faster than the DEM and demonstrate the possibility of multiscale modeling for amorphous materials, whenever a suitable model can be devised for the coarse-grained spot dynamics.
我们提出了一种用于非晶材料的多尺度模拟算法，并在密集颗粒流的典型案例中对其进行了说明和验证。我们的算法基于最近提出的斑点模型，在该模型中，密集随机堆积中的颗粒会响应扩散的影响“斑点”而经历链状集体位移，这些斑点携带少量多余的间隙自由体积。我们通过在每个斑点引起的块体位移后引入局部颗粒松弛步骤，从斑点的“粗粒度”动力学重建颗粒的微观动力学，只是为了用（相当任意的）软核排斥来强制实施堆积约束。为了测试该模型，我们研究了它在多大程度上能够描述由离散元方法（DEM）模拟的颗粒排水中多达135,000个摩擦、粘弹性球体的动力学。仅用五个拟合参数（斑点的半径、体积、扩散率、漂移速度和注入率），我们发现斑点模拟不仅能够在很大程度上再现平均流动和扩散，还能再现流动堆积的一些微妙统计特性，如空间速度相关性和多体结构相关性。斑点模拟的运行速度比DEM快100倍以上，并证明了只要能为粗粒度斑点动力学设计出合适的模型，就有可能对非晶材料进行多尺度建模。
