The Instability Control In Correspondence Peridynamics And Single-particle Crush Simulation

Granular materials are widely spread in the nature and used in the production and living activities of human beings.The study of their crushing behavior is of theoretical and practical significance in the area of civil engineering,medicine and chemistry engineering,grain processing,preparation of nanoparticles,etc.The fragmentation of granule changes the contact status of particles and their size distribution,which influences the mechanical behavior of granular materials.The investigation of crushing a single particle helps better understand the fragmentation of particle assemblies.Peridynamics(PD)is a mathematical model and a numerical method that aims to solve mechanical problems with discontinuity.And it takes advantages in simulating the spontaneous crack initiation and the propagation of multiple cracks.Among the three peridynamic models: bond-based peridynamics(BBPD),ordinary state-based peridynamics(OSBPD)and non-ordinary state-based peridynamics(NOSBPD),nonordinary state-based peridynamic correspondence model has its zero-energy mode instability.Many attentions have been paid to suppress such instability.This thesis investigates mechanical behavior of a single particle crushed under the unidirectional compressive load utilizing peridynamics.The main contents and results are as follows.Firstly,an improved supplemental force state method is presented to suppress zero-energy modes.The dispersion curves in one-dimensional linear elastic bar of this method are plotted and compared with previous stabilized method,which demonstrates the effectiveness of the improved method in the zero-energy mode suppression.The displacement results of two-dimensional plate under tension with previous stabilized method,the improved method and no suppression method case are compared with the results of finite element analysis.A more precise solution is found with the improved method.Using the improved method,dynamic crack propagation is simulated with a plate under different stress loads.And crack branching is observed.An orthotropic plate with prepared central crack under tensile load is investigated,which shows the crack behavior can be uniquely simulated with the improved method while previous stabilized method encounters the difficulty in selecting the spring constant.Secondly,different crushing behaviors of a single round particle or spherical particle using three peridynamic models are studied.Among the three models,a more convenient,efficient and realistic model is preferred.Then the results show that crushing results of bond-based peridynamic model accords more with the existing experiment observation.Hence bond-based peridynamic model is more suitable in simulating single particle crushing.Finally,bond-based peridynamics is used to simulate particle's unidirectional compressive crushing behavior with different load velocity,different load positions and different horizon sizes whose influences are investigated.The larger the velocity load is,the more durability is found of the particle.Also for spherical particle,increasing velocity load results in an increasing number of cracks and fragments.Load position affects greatly the final results of particle crushing.Different load positions cause different crack propagation paths and different fragments' shapes.This means a change of particles' arrangement leads to a variety of particle crushing results.When the horizon size is larger than two times than the distance of two neighboring particles,the force displacement curves changes slightly via the increased horizon size,which shows m-convergence holds.A suggested horizon size of three times the distance between two neighboring particles will reach a satisfied simulating result.