Transient Dynamic Analysis Of Multi-point Contact Collision In Granular Medium

Granular materials is a form of material organization widely existed in nature,traffic engineering,construction engineering and other fields.There is a big gap between the results of experiment,simulation and theoretical analysis,according to the existing research on distribution of force in granular media.A more precise and accurate theoretical model needs to be built.Some scholars have studied the dynamic response of the granular medium under known loads.There is a lack of the research on mechanical behavior of granular media under impact or collision.The impact load is related to the shape,material and contact stiffness of the contact region.Furthermore,the nonlinear unilateral contact constraints should be considered in the calculation of the impact load.Therefore,it is difficult to analyze the response of granular media under multi point collision.In this paper,the theoretical and numerical methods are used to analyze the mechanical response of granular media under multi point contact collision.The specific study is as follows:(1)Two approximate methods for studying the probability of distribution of forces in granular media are discussed.Based on these two methods,a new theoretical model of the transfer probability of force is proposed.The distribution of the vertical force in the particles of hexagonal close-packed granular materials under concentrated static load is studied.The result shows that the forces on two frontal lines decay by power function as the number of layers increases.The distribution of vertical force in each layer of the two peaks is observed.It is found that the equal distribution ratio leads to a single peak.The unequal partition ratio leads to a two-peak with the same height.The method of the paper leads to a two-peak,but the peak value is lower than the second one,and the finite element solution is validated.(2)The dynamic response of the granular medium under concentrated dynamic loads are analyzed by finite element method,considering the deformation effect of the particles and contact zone as well as the friction between the particles.The contact forces between particles and the transmission paths of the force are obtained.According to the calculation results,the steady contact force chain and contact force network in granular medium are constructed and the arch effect is analyzed.When a pair of symmetric concentrated dynamic loads are applied,the contact force between the underlying particles and the boundary is the superposition of the results when a single concentrated dynamic load is applied.This method can make up for the deficiency that the friction and the deformation of the particles themselves can't be considered in the traditional theory,and can be used to verify the correctness of the theoretical method.(3)The transient dynamic response of the particle medium under impact is analyzed with finite element method.The contact forces between the bottom particles and the boundary in the granular materials are calculated and the transmission paths of the contact force are got.According to the calculation results,the contact force chains and contact force networks of the granular materials at different times of collision are constructed,and the growth rules of contact force chains and contact force networks are obtained.(4)The transient response of granular materials and continuous materials under multi-point collision load is compared.The similarities and differences between the transmission paths and the ranges of the forces under the collision are obtained.The results show that the stress wave propagates downward along the crest in granular materials,while the stress waves in continuous materials disperse around the collision point with the wave front of elliptic line.By comparing the effects of different friction coefficients on the transient response of granular materials,it is found that the friction coefficient increases,which leads to the approach of granular materials to continuous materials,The attenuation of stress wave aggravates,but it has little effect on the Newton's recovery coefficient.