Study On Viscoelastic Contact Model And Viscous Damping For Discrete Element Method

The Discrete Element Method is an effective numerical method for the study on complex static/dynamic problems of discrete media or particle systems.It has been widely used in the fields of mechanical engineering,chemical engineering and pharmaceutical industry,agriculture and agricultural product processing,bringing great benefits to engineering design and scientific research.In the Discrete Element Method,particle systems are considered to consist of discrete particles or elements,the motion equation of each particle is builded according to the Newton's second law and solved numerically to track the dynamic information of each particle in real time,such as position and orientation,velocity and acceleration and so on,and finally to evolve the macro/micro motion of particle systems in time and space.Since all the dynamic data by numerical calculations mainly depends on the contact forces acting on any particle,the contact force calculaton will directly affect the static/dynamic simulation results.Obviously,it is very important for the Discrete Element Method to deeply study the contact problem and to establish a reasonable and accurate contact model.In this thesis,the viscoelastic contact model and viscous damping in the Discrete Element Method are studied,and the following researches are completed:Firstly,the normal contact force of viscoelastic body and its numerical calculation method are explored.Based on viscoelastic mechanics and contact mechanics,three typical ideal viscoelastic materials,namely Kelvin-Voigt,Maxwell and Standard Linear Solid,are discussed.The normal contact force of viscoelastic bodies and its two numerical calculation methods are introduced,i.e.composite integration rule and difference method.Secondly,a method for solving the central impact of viscoelastic spheres is proposed on the basis of the assumption of quasi-static approximation.In this method,the normal contact force is decomposed into an elastic force and a dissipative force.The expression of elastic force has the same form as that given by Hertz contact theory.The dissipative force is related to the viscoelastic material parameters,and the integral expression of the dissipative force may reduce to an approximate expression.The effects of the relaxation time and viscosity on the quasi-static approximation method are analyzed.Finally,the numerical simulation of the drop impact experiment with Golf and Superball is carried out,and the experimental results verify that the quasi-static approximation method can well solve the collision problems of viscoelastic bodies.Thirdly,the dissipative force in the normal contact of viscoelastic balls is discussed by dimensional reasoning analysis,which confirms that the viscous damping should has a displacement exponent of 1/2 and a displacement rate exponent of 1 for viscoelastic balls.Then,considering the effect of relaxation time on the dissipative process,a new viscous damping and Hertz-type viscoelastic contact model are proposed on the basis of the quasi-static approximation method for viscoelastic spheres.The relationship between the damping constants and the coefficient of restitution is established for the new model.Finally,the influence of the damping constants on the prediction by the new model is analyzed,where if the damping constant related to the relaxation time increases,the peak points of both the displacement and contact force predicted by the new model will go up,the peak point of the contact force will be delayed and the initial slope of the contact force will decrease,and the coefficient of restitution predicted by the new model will increase.Fourthly,a general expression for viscous damping is given by dimensional analysis to cover various forms of viscous damping.The dimensionless predictions of different Hertz-type viscoelastic contact models are compared and analyzed.Finally,the numerical simulation of the drop impact experiment with Indoor Lacrosse Ball(ILB)and Outdoor Lacrosse Ball(OLB)is carried out,where different viscoelastic contact models are compared and verified with the experimental data.It is shown that,Hertz-type viscoelastic contact models,except for Hunt model,all have "tensile" forces before the displacement(or overlap)returns to zero,which is inconsistent with the actual collision of dry particles.Viscoelastic contact models with different viscous dampers predict differently,especially in the case of large damping(such as ILB).In addition,only the new model by this thesis has the viscous damping that takes the relaxation time into account.So compared with other viscoelastic contact models,the simulated results of ILB and OLB from the new model are in the best agreement with the experimental data.This thesis studies the viscoelastic contact model and the viscous damping for the discrete element method.According to viscoelastic mechanics and contact mechanics,it discusses the calculation method of the normal contact force of viscoelastic bodies,and puts forward the viscous damping and the viscoelastic contact model with consideration on relaxation time.It also provides the relationship between the damping constant and the coefficient of restitution for Hertz-type viscoelastic contact models.The researches in this thesis are of great value and significance to the development of the discrete element method.