Dilated Discrete Element Model Based On Minknowski Sums And Its Applications

The human life is closely related with granular materials,such as the storage and transition of the grain,railway ballast settlement,sandstorm and debris flows.All of them belong to the category of granular matter.Granular matter is a random combination of particulate material.Its macro performance can be regarded neither as solid media,nor as liquid media,but behave as solid or liquid media,and even there is a quasi-solid-liquid phase transition.To study the macroscopic behavior of granular material,some researchers use the finite element mothed based on Cosserat continuum model to simulate the granular material.Discrete element method(DEM)is a powerful tool to study granular material,which is fully reflect the micro-information of granular material,such as particle shape,size,distribution and the large deformation of granular material.The DEM is based on the individual particles.In this method,the granular material is described by particle shape,size,and physical properties.In the study of DEM,the sphere particle,due to its simplified geometry and programing,is becoming the most popular and classical particle model.Although sphere particle based model is avalaible to simulate some studies of granular material,most of the natural materials are not perfectly spherical.For accurately calculating the contact force,it is critical to develop an irregular model,which could represent natural granulars well.In this study,there are two kind of irregular particle model dilated disk modle and dilated polyhedral model is studied.The applications of those irregular particles are also present in this paper.Considering the shape of the pancake ice in Bohai Bay,the dilated pancake modle is used to dtudy the ice force.the dilated pancake modle is builtup with Minkowski Sum operator of a sphere and a 2D disk under.Since the pancake ice includes the surface and curve segments,the contacts between particles are in subcategory to surface-surface and surface-curve.The impact of ice floes on vertical structure is studied based on dilated disk elements.The environmental load from ice as well as wave and current are investigated with DEM.The hydrodanymics load exponentially increases with wave heightfor the given range of parameters.Increasing ice concentration or adding a current to waves substantially increases the impact load.The instantaneous loads on the structure were significant for the studied cases.On the other hand,the mean values are much lower than the theoretical value fromlinear wave theory.In this paper the bonding model between pancake ices is also considered.The pancake ice is bond together to represent ice sheet,under the influence of current,the ice sheet acts on conical structure.The field date is used to build simulation model,and the ice load get from simulation results is agree with the fullscale measurement.Considering the irregular shapes of rock particles,a 3D dilated polyhedral element is generated with a basic sphere and real polyhedron based on the theory of Minkowski Sums.The element generation,contact resolution and detection are introduced in this paper.All inter-element contacts are grouped as three categories:edge-edge,vertex-surface,and surface-surface.This dilated polyhedra element is applied to simulate the dynamic behaviours of rock rubbles of railway ballast.The settlement and the bulk stilfness of ballast are analyzed under cyclic loading.The results show that permanent deformation increased with the loading frequency and number of loading cycle.The influence of inter-element friction is tested in the DEM simulations.The shear flow behaviors of granular materials exist widely in the natural disasters(such as landslide and debris flow)and the industrial process(such as transportation and pumping of mineralmaterials).The process of landslide is also studied with this dilated polyhedra model.Spherical and tetrahedral particles are used in the simulation.The shape,length,maximum thickness and leading edge position of the pile are obtained from these simulations.The results with angular grains,rounded grains and point mass model were compared in this paper.The maximum thicknesses for the cases with spherical grains decrease faster than the cases with angular grains.Both of the avalanches with granular material cases move faster than point mass model.The change of kinetic theory,potential energy and all of the dissipation parts of the energy are presented in time series.From study of the energy dissipation,the main contribution is from sliding friction and viscous force.On the other hand,the energy dissipation from elastic deformation is negligible.From the study basied on DEM with sphere particle model to simulate the shear tests of granular materials it shows,that rolling friction cannot be negligible.The author study DEM with sphere particle model.The experiment for friction coefficients under the influences of normal loads,roughness of contact surfaces,particle shapes has been carried out;and the transition mechanism of the rolling-sliding friction is studied.It is shown that the rolling-sliding friction affects the form of sphere motion.The investigation of a shear flow process provides an insight to understand the mechanism behind the phase transition of granular materials.In this study,a medium-size annular shear cell was developed to study the shear flow states of granular materials and their transition.The shear stress and the volume dilation rate were measured under various normal stresses and shear rates.The experimental results show that the shear stress and the volume dilation rate increase with increasing shear rate.Both of them increase with the square of shear rate piecewise linearly.With the analysis of effective friction coefficient under various shear rates and inertia numbers,the phase transition process between the slow flow and the rapid flow was discussed.The phase transition occurs at the critical shear rate.Finally,summary the work of this thesis on the irregular partilcle model in DEM,and some future works have been pointed out,such as considering the fluid-particle coupling in DEM.