Surface reconstruction with spherical harmonics and its application for single particle crushing simulations

Particle morphology has great influence on mechanical behaviour and hydro/thermal/electrical conductivities of granular materials.Surface reconstruction and mesh generation are critical to consider realistic particle shapes in various computational simulations.This study adopts the combined finitediscrete element method(FDEM)to investigate single particle crushing behaviour.Particle shapes were reconstructed with spherical harmonic(SH)in both spherical and Cartesian coordinate systems.Furthermore,the reconstructed surface mesh qualities in two coordinate systems are investigated and compared.Although the efficiency of the two SH systems in reconstructing star-like shapes is nearly identical,SH in Cartesian coordinate system can reconstruct non-star-like shapes with the help of surface parameterisation.Meanwhile,a higher triangular mesh quality is generated with spherical coordinate.In single particle crushing tests,the low mesh quality produces more fluctuations on load-displacement curves.The particles with more surficial mesh elements tend to have a lower contact stiffness due to more contact stress concentrations induced by complexity of morphology features and more volumetric tetrahedral elements.The fracture patterns are also influenced by mesh quality and density,e.g.a particle with fewer mesh elements has a simpler fragmentation pattern.This study serves as an essential step towards modelling particle breakage using FDEM with surface mesh directly from SH reconstruction.

On the measurements of individual particle properties via compression and crushing

An experimental study is presented to measure the elastic,yielding,and crushing properties of individual particles under compression using substrates made of aluminum alloy,stainless steel,and sapphire.Carefully selected,highly spherical individual Ottawa sand particles of 0.75e1.1 mm in nominal diameter were compressed between two smooth substrates,and the loadedeformation curves were analyzed by Hertz elastic contact theory to derive their reduced modulus and Young’s modulus as well as yielding and crushing strengths,which vary significantly with the type of substrate materials.Further analysis of the yielding and plastic deformation at the particle-substrate contact shows that the yield strength or hardness of the substrate materials dominates the local contact behavior and hence affects the measured apparent yielding and crushing strengths.The two softer substrates(aluminum alloy and stainless steel)actually lead to underestimated apparent shear yield strengths of quartz particles by 60.4%and 54.2%,respectively,which are actually the yielding of substrates,while the true particle yielding occurs in the sapphire-particle contact.Moreover,the two softer substrates cause much overestimated crushing strengths of the quartz particles by 50.4%and 36.4%,respectively.Selection of inappropriate substrate materials and inappropriate interpretation of the particle-substrate contact can lead to significant errors in the measured yielding and crushing strengths.It is recommended that single particle compression testing uses substrates with yield strength greater than that of the tested particles and result interpretation also considers the elastic and yielding behaviors of the substrates.

Discrete element simulation of effects of multicontact loading on single particle crushing

Particle crushing commonly occurs in granular materials and affects their structures and mechanical properties.Unlike idealized particles in experimental single particle crushing tests with two loading points,natural particles are crushed under multicontact loading.To date,the criteria and patterns of par-ticle crushing under multicontact conditions are not fully understood.By using the three-dimensional discrete element method,this report explores the effect of multicontact loading on the crushing criterion of a single particle,the crushing pattern,and the relationship between the particle crushing strength and loading distribution.The particles are modelled as aggregates of glued Voronoi polyhedra.The numer-ical results indicate that the logarithm of the mean principal stress has a good linear correlation with the coordination number.For a specific coordination number,the number of child particles presents a significant normal distribution.For a specific number of child particles,the volumes of child particles can be statistically described as normal or gamma distribution.Three typical models are proposed to qual-itatively analyse the relationship between the loading distribution and crushing strength.The relevant conclusions can be helpful in engineering practice and in further studies on crushable granular materials via the discrete element method.

Analysis of One-Dimensional Compression under a Wide Range of Stress with Densely Arrayed BPM

In this paper,the densely arrayed bonded particle model is proposed for simulation of granular materials with discrete element method(DEM)considering particle crushing.This model can solve the problem of pore calculation after the grains are crushed,and reduce the producing time of specimen.In this work,several one-dimensional compressing simulations are carried out to investigate the effect of particle crushing on mechanical properties of granular materials under a wide range of stress.The results show that the crushing process of granular materials can be divided into four different stages according to er-logσy curves.At the end of the second stage,there exists a yield point,after which the physical and mechanical properties of specimens will change significantly.Under extremely high stress,particle crushing will wipe some initial information of specimens,and specimens with different initial gradings and void ratios present some similar characteristics.Particle crushing has great influence on grading,lateral pressure coefficient and compressibility of granular materials,and introduce extra irreversible volume deformation,which is necessary to be considered in modelling of granular materials in wide stress range.

A numerical test method of California bearing ratio on graded crushed rocks using particle flow modeling

In order to better understand the mechanical properties of graded crushed rocks （GCRs） and to optimize the relevant design, a numerical test method based on the particle flow modeling technique PFC2D is developed for the California bearing ratio （CBR） test on GGRs. The effects of different testing conditions and micro-mechanical parameters used in the model on the CBR numerical results have been systematically studied. The reliability of the numerical technique is verified. The numerical results suggest that the influences of the loading rate and Poisson＇s ratio on the CBR numerical test results are not significant. As such, a loading rate of 1.0-3.0 mm/min, a piston diameter of 5 cm, a specimen height of 15 cm and a specimen diameter of 15 cm are adopted for the CBR numerical test. The numerical results reveal that the GBR values increase with the friction coefficient at the contact and shear modulus of the rocks, while the influence of Poisson＇s ratio on the GBR values is insignificant. The close agreement between the CBR numerical results and experimental results suggests that the numerical simulation of the CBR values is promising to help assess the mechanical properties of GGRs and to optimize the grading design. Be- sides, the numerical study can provide useful insights on the mesoscopic mechanism.