摩擦对力链中动态能量耗散的影响机制研究

Effect of friction on dynamic energy dissipation in granular chain

本文建立了一个两侧受到约束的有限长一维颗粒系统模型,探究了摩擦对颗粒材料耗能机制的影响.本文采用离散元方法研究该动力学过程中能量的耗散机理,模型中颗粒之间、颗粒和约束之间的法向接触采用非线性Hertz接触模型,切向接触采用Mindlin剪切模型,通过分析主孤立波的幅值和波速以及颗粒间接触力的衰减规律探究颗粒材料能量耗散机制.结果表明:受到冲击的一维颗粒链中会产生一道主孤立波,孤立波的幅度在远小于颗粒间最大接触力的摩擦力作用下仍然会产生显著的衰减;摩擦力的存在使得系统中的动态能量会在有限深度内耗散;此耗散深度依赖于摩擦力的大小.根据能量传播路径上的耗散规律,将耗散过程可分为非线性接触主导过程、中间过程、摩擦和接触混合主导过程三个阶段,分别分析了每阶段相应的力学机制.

In this work,we used a one-dimensional particle system with finite length to study the effect of friction on energy propagation in granular materials.Normal contact forces acting between particles follow the nonlinear Hertz contact law,while the tangential shear forces acting between particles and plates follow the Mindlin shear force law.To simulate the wave propagation through the particle chain,a center difference method is applied,and the kinetic equation is directly solved by the discrete element method.With this model,we observed a primary solitary wave produced when a striker collides with the second particle,and the wave dissipates nonlinearly with the travelling length even when tangential frictional forces between particles and rigid boundary are very small.Energy dissipation in granular materials can be deduced by comparing the amplitude and velocity of the main solitary wave and the maximum contact force between particles.The results show that the primary solitary wave will dissipate rapidly and eventually disappear within a finite distance in the one-dimensional chain,even though the frictional forces are much smaller than the average normal contact forces between particles.This finite distance depends on the frictional forces.As the wave propagates,three stages,including nonlinear collision stage,transition stage,and friction-collision mixed stage,can be distinguished using the relation between wave speed and maximum contact force.