粗糙颗粒的随机离散元模拟——随机法向接触定律

真实颗粒的力学性质会受到其随机粗糙表面的影响，然而在传统离散元模拟中通常假设颗粒具有光滑表面，因此有必要在定量考虑颗粒表面粗糙度的基础上改进离散元的接触模型。本文基于经典 Greenwood-Williamson(GW)模型通过理论分析和数值模拟提出了一种可以考虑颗粒表面粗糙度的法向接触定律；开发了基于 Newton-Raphson迭代的数值计算方法，通过输入颗粒重叠量和一系列表面粗糙系数计算总接触力；讨论了改进计算方法效率和准确性的相关问题。相对于 GW模型中接触关系的复杂积分表示，拟合得到新随机接触定律的表达式具有类似 Hertz定律的简单结构，只包含一个表征颗粒表面粗糙度标准偏差的新增参数，σ，可以方便的引入当前离散元模拟程序中进行计算。

Stochastic discrete element modelling of rough particles-a random normal interaction law

Particles are assumed smooth in classical discrete element modelling,but real particles have random rough surfaces which may influence their mechanical properties.It is necessary therefore to quantitatively improve the conventional discrete element model particles by taking their surface roughness into consideration.In this work,a new random normal contact law is established for particles that have random rough surfaces.The contact law,based on the classic Greenwood and Williamson (GW)model,is derived by both theoretical derivation and numerical simulation.A Newton-Raphson based numerical solution procedure is proposed to obtain the total contact force for a given overlap and a set of rough surface parameters.Some related computational issues key to improve computa-tional efficiency and accuracy are addressed.Instead of a complicated integral expression involved in the GW model, the curve fitted empirical formula of the random contact law retains the closed form and simplicity of the Hertz model,with only one added parameter,σ,the standard deviation of the surface roughness,and therefore can be readily incorporated into the current discrete element modelling framework.