This paper presents a theoretical model on the normal(head-on)collision between soft-spheres on the basis of elastic loading of the Hertz contact for compression process and a nonlinear plastic unloading for restituti...This paper presents a theoretical model on the normal(head-on)collision between soft-spheres on the basis of elastic loading of the Hertz contact for compression process and a nonlinear plastic unloading for restitution one,in which the parameters all are determined in terms of the material and geometric ones of the spheres,and the behaviors of perfect elastic,inelastic,and perfect plastic collisions appeared in the classical mechanics are fully described once a value of coefficient of restitution is specified in the region of 0≤ε≤1.After an empirical formula of the coefficient of restitution dependent on the impact velocity is suggested to fit the existing experimental measurements by means of the least square method,the predictions of the dependency and the collision duration are in well quantitative agreement with their experimental measurements.It is found that the measurable quantities are dependent on both the impact velocity and the parameters of spheres.Following this model,finally,an approach to determine the spring coefficient in the linear viscoelastic model of the collision is also displayed.These results obtained here will be significantly beneficial for the applications where a collision model is requested in the simulations of relevant grain flows and impact dynamics etc..展开更多
The n-body instability is investigated with the soft-sphere discrete element method.The divergence of nearby trajectories is quantifed by the dynamical memory time.Using the inverse proportionality between the dynamic...The n-body instability is investigated with the soft-sphere discrete element method.The divergence of nearby trajectories is quantifed by the dynamical memory time.Using the inverse proportionality between the dynamical memory time and the largest Lyapunov exponent,the soft-sphere discrete ele-ment method results are compared to previous hard-sphere molecular dynamics data for the first time.Good agreement is observed at low concentrations and the degree of instability is shown to increase asymptotically with increasing spring sifness.At particle concentrations above 30%,the soft-sphere Lya-punov exponents increase faster than the corresponding hard-sphere data.This paper concludes with a demonstration of how this case study may be used in conjunction with regression testing and code verification activities.展开更多
本文采用 DEM（Discrete Element Method）软球模型来研究颗粒间的碰撞过程,用金属球代替流场中的颗粒,研究这些金属球在平面上的运动。运用DEM软球模型求出碰撞过程中小球所受的瞬时接触力以及碰撞时间,并分析这些参数随颗粒物性以及...本文采用 DEM（Discrete Element Method）软球模型来研究颗粒间的碰撞过程,用金属球代替流场中的颗粒,研究这些金属球在平面上的运动。运用DEM软球模型求出碰撞过程中小球所受的瞬时接触力以及碰撞时间,并分析这些参数随颗粒物性以及运动参数的变化规律。计算得出:颗粒间的接触力以及碰撞时间与颗粒的相对速度、碰撞角度以及杨氏模量等参数有关。展开更多
基金supported by the Key Fund of the National Natural Science Foundation of China(11032006)
文摘This paper presents a theoretical model on the normal(head-on)collision between soft-spheres on the basis of elastic loading of the Hertz contact for compression process and a nonlinear plastic unloading for restitution one,in which the parameters all are determined in terms of the material and geometric ones of the spheres,and the behaviors of perfect elastic,inelastic,and perfect plastic collisions appeared in the classical mechanics are fully described once a value of coefficient of restitution is specified in the region of 0≤ε≤1.After an empirical formula of the coefficient of restitution dependent on the impact velocity is suggested to fit the existing experimental measurements by means of the least square method,the predictions of the dependency and the collision duration are in well quantitative agreement with their experimental measurements.It is found that the measurable quantities are dependent on both the impact velocity and the parameters of spheres.Following this model,finally,an approach to determine the spring coefficient in the linear viscoelastic model of the collision is also displayed.These results obtained here will be significantly beneficial for the applications where a collision model is requested in the simulations of relevant grain flows and impact dynamics etc..
文摘The n-body instability is investigated with the soft-sphere discrete element method.The divergence of nearby trajectories is quantifed by the dynamical memory time.Using the inverse proportionality between the dynamical memory time and the largest Lyapunov exponent,the soft-sphere discrete ele-ment method results are compared to previous hard-sphere molecular dynamics data for the first time.Good agreement is observed at low concentrations and the degree of instability is shown to increase asymptotically with increasing spring sifness.At particle concentrations above 30%,the soft-sphere Lya-punov exponents increase faster than the corresponding hard-sphere data.This paper concludes with a demonstration of how this case study may be used in conjunction with regression testing and code verification activities.
文摘本文采用 DEM（Discrete Element Method）软球模型来研究颗粒间的碰撞过程,用金属球代替流场中的颗粒,研究这些金属球在平面上的运动。运用DEM软球模型求出碰撞过程中小球所受的瞬时接触力以及碰撞时间,并分析这些参数随颗粒物性以及运动参数的变化规律。计算得出:颗粒间的接触力以及碰撞时间与颗粒的相对速度、碰撞角度以及杨氏模量等参数有关。
