Construction of irregular particles with superquadric equation in DEM

Non-spherical particles are widely present in industrial production,and significantly affect the macro and micro characteristics of granular materials.Although the superquadric equation can be used to construct non-spherical particles,its disadvantage is that the particle shape is geometrically symmetric and strictly convex.In this study,two composed approaches are used to describe geometrically asymmetric and concave particle shapes,including a multi-superquadric model and a poly-superquadric model.The multi-superquadric model is a combination of several superquadric elements,and can construct concave and geometrically asymmetric particle shapes.The poly-superquadric model is a combination of eight one-eighth superquadric elements,and can construct convex and geometrically asymmetric particle shapes.Both composed models are based on superquadric equations,and Newton’s iterative method is used to calculate the contact force between the elements.Furthermore,superquadric elements,multi-superquadric elements,and poly-superquadric elements are applied for the formation of complex granular beds,and the influences of particle shape on the packing fraction can be successfully captured by the proposed models.

Discrete element modeling of acoustic emission in rock fracture

The acoustic emission （AE） features in rock fracture are simulated numerically with discrete element model （DEM）. The specimen is constructed by using spherical particles bonded via the parallel bond model. As a result of the heterogeneity in rock specimen, the failure criterion of bonded particle is coupled by the shear and tensile strengths, which follow a normal probability distribution. The Kaiser effect is simulated in the fracture process, for a cubic rock specimen under uniaxial compression with a constant rate. The AE number is estimated with breakages of bonded particles using a pair of parameters, in the temporal and spatial scale, respectively. It is found that the AE numbers and the elastic energy release curves coincide. The range for the Kaiser effect from the AE number and the elastic energy release are the same. Furthermore, the frequency-magnitude relation of the AE number shows that the value of B determined with DEM is consistent with the experimental data.

Modified virtual internal bond model based on deformable Voronoi particles

In last time,the series of virtual internal bond model was proposed for solving rock mechanics problems.In these models,the rock continuum is considered as a structure of discrete particles connected by normal and shear springs(bonds).It is well announced that the normal springs structure corresponds to a linear elastic solid with a fixed Poisson ratio,namely,0.25 for threedimensional cases.So the shear springs used to represent the diversity of the Poisson ratio.However,the shearing force calculation is not rotationally invariant and it produce difficulties in application of these models for rock mechanics problems with sufficient displacements.In this letter,we proposed the approach to support the diversity of the Poisson ratio that based on usage of deformable Voronoi cells as set of particles.The edges of dual Delaunay tetrahedralization are considered as structure of normal springs(bonds).The movements of particle’s centers lead to deformation of tetrahedrals and as result to deformation of Voronoi cells.For each bond,there are the corresponded dual face of some Voronoi cell.We can consider the normal bond as some beam and in this case,the appropriate face of Voronoi cell will be a cross section of this beam.If during deformation the Voronoi face was expand,then,according Poisson effect,the length of bond should be decrees.The above mechanism was numerically investigated and we shown that it is acceptable for simulation of elastic behavior in 0.1–0.3 interval of Poisson ratio.Unexpected surprise is that proposed approach give possibility to simulate auxetic materials with negative Poisson’s ratio in interval from–0.5 to–0.1.

Modeling of deformation processes in rock massif in the vicinity of underground goafs considering the formation of discontinuity zones

The construction of mechanical-mathematical model and numerical method for the deformation processes of rock massifs with goafs and underground structures is very complex and also important task in modern rock mechanics.In this study,the mechanical-mathematical model is developed for rock massif in vicinity of underground goafs considering the internal block-layered structure of the rock massif.A new constitutive model is introduced in this study to describe the negative Poisson’s ratio for the lock-layered structure.Two types of defining equations systems for studying the state of a rock massif taking into account the block-layered structure are described.Finally,several examples are given using the present mechanical-mathematical model.

Numerical Analysis of Ice Rubble with a Freeze-Bond Model in Dilated Polyhedral Discrete Element Method

Freezing in ice rubble is a common phenomenon in cold regions,which can consolidate loose blocks and change their mechanical properties.To model the cohesive effect in frozen ice rubble,and to describe the fragmentation behavior with a large external forces exerted,a freeze-bond model based on the dilated polyhedral discrete element method(DEM)is proposed.Herein,imaginary bonding is initialized at the contact points to transmit forces and moments,and the initiation of the damage is detected using the hybrid fracture model.The model is validated through the qualitative agreement between the simulation results and the analytical solution of two bonding particles.To study the effect of freeze-bond on the floating ice rubble,punch-through tests were simulated on the ice rubble under freezing and nonfreezing conditions.The deformation and resistance of the ice rubble are investigated during indenter penetration.The influence of the internal friction coefficient on the strength of the ice rubble is determined.The results indicate that the proposed model can properly describe the consolidated ice rubble,and the freeze-bond effect is of great significance to the ice rubble properties.

Discrete Element Simulations of Ice Load and Mooring Force on Moored Structure in Level Ice

Moored structures are suitable for operations in ice-covered regions owing to their security and efficiency.This paper aims to present a new method for simulating the ice load and mooring force on the moored structure during ice-structure interaction with a spherical Discrete Element Method(DEM).In this method,the level ice and mooring lines consist of bonded sphere elements arranged in different patterns.The level ice model has been widely validated in simulation of the ice load of fixed structures.In the mooring line simulation,a string of spherical elements was jointed with the parallel bond model to simulate the chains or cable structure.The accuracy of the mooring line model was proved by comparing the numerical results with the nonlinear FEM results and model towing experiment results.The motion of the structure was calculated in the quaternion method,considering the ice load,mooring force,and hydrodynamic force.The hydrodynamic force comprised wave-making damping,current drag,and buoyancy force.Based on the proposed model,the interaction of a semi-submersible structure with level ice was simulated,and the effect of ice thickness on the ice load was analyzed.The numerical results show that the DEM method is suitable to simulate the ice load and mooring force on moored floating structures.

A modified discrete element method for concave granular materials based on energy-conserving contact model

The development of a general discrete element method for irregularly shaped particles is the core issue of the simulation of the dynamic behavior of granular materials.The general energy-conserving contact theory is used to establish a universal discrete element method suitable for particle contact of arbitrary shape.In this study,three dimentional(3D)modeling and scanning techniques are used to obtain a triangular mesh representation of the true particles containing typical concave particles.The contact volumebased energy-conserving model is used to realize the contact detection between irregularly shaped particles,and the contact force model is refined and modified to describe the contact under real conditions.The inelastic collision processes between the particles and boundaries are simulated to verify the robustness of the modified contact force model and its applicability to the multi-point contact mode.In addition,the packing process and the flow process of a large number of irregular particles are simulated with the modified discrete element method(DEM)to illustrate the applicability of the method of complex problems.

DEM Simulations of Resistance of Particle to Intruders during Quasistatic Penetrations

Based on the discrete element method and hydrostatics theory,an improved Archimedes principle is proposed to study the rules pertaining to resistance changes during the penetration process of an intruder into the particulate materials.The results illustrate the fact that the lateral contribution to the resistance is very small,while the tangential force of the lateral resistance originates from friction effects.Conversely,the resistance of particulate materials on the intruder mainly occurs at the bottom part of the intruding object.Correspondingly,the factors that determine the resistance of the bottom part of the intruding object and the rules pertaining to resistance changes are analyzed.It is found that when the volume density and friction coefficient of the particles and the radius of the bottom surface of the cylindrical intruder are varied,the resistance–depth curve consists of a nonlinear segment and a linear region.The intersection of the two stages occurs at the same location h/˜R=0.15±0.055.The slope of the linear stage is determined by the friction coefficient of the particles.Accordingly,the relationship between the slope and the friction coefficient is quantified.Finally,it is shown that the slope is independent of the geometry of the intruder.

Modeling calving process of glacier with dilated polyhedral discrete element method

Mass loss caused by glacier calving is one of the direct contributors to global sea level rise.Reliable calving laws are required for accurate modelling of ice sheet mass balance.Both continuous and discontinuous methods have been used for glacial calving simulations.In this study,the discrete element method(DEM)based on dilated polyhedral elements is introduced to simulate the calving process of a tidewater glacier.Dilated polyhedrons can be obtained from the Minkowski sum of a sphere and a core polyhedron.These elements can be utilized to generate a continuum ice material,where the interaction force between adjacent elements is modeled by constructing bonds at the joints of the common faces.A hybrid fracture model considering fracture energy is introduced.The viscous creep behavior of glaciers on long-term scales is not considered.By applying buoyancy and gravity to the modelled glacier,DEM results show that the calving process is caused by cracks which are initialized at the top of the glacier and spread to the bottom.The results demonstrate the feasibility of using the dilated polyhedral DEM method in glacier simulations,additionally allowing the fragment size of the breaking fragments to be counted.The relationship between crack propagation and internal stress in the glacier is analyzed during calving process.Through the analysis of the Mises stress and the normal stress between the elements,it is found that geometric changes caused by the glacier calving lead to the redistribution of the stress.The tensile stress between the elements is the main influencing factor of glacier ice failure.In addition,the element shape,glacier base friction and buoyancy are studied,the results show that the glacier model based on the dilated polyhedral DEM is sensitive to the above conditions.

GPU-Based Simulation of Dynamic Characteristics of Ballasted Railway Track with Coupled Discrete-Finite Element Method

Considering the interaction between a sleeper,ballast layer,and substructure,a three-dimensional coupled discrete-finite element method for a ballasted railway track is proposed in this study.Ballast granules with irregular shapes are constructed using a clump model using the discrete element method.Meanwhile,concrete sleepers,embankments,and foundations are modelled using 20-node hexahedron solid elements using the finite element method.To improve computational efficiency,a GPU-based(Graphics Processing Unit)parallel framework is applied in the discrete element simulation.Additionally,an algorithm containing contact search and transfer parameters at the contact interface of discrete particles and finite elements is developed in the GPU parallel environment accordingly.A benchmark case is selected to verify the accuracy of the coupling algorithm.The dynamic response of the ballasted rail track is analysed under different train speeds and loads.Meanwhile,the dynamic stress on the substructure surface obtained by the established DEM-FEM model is compared with the in situ experimental results.Finally,stress and displacement contours in the cross-section of the model are constructed to further visualise the response of the ballasted railway.This proposed coupling model can provide important insights into high-performance coupling algorithms and the dynamic characteristics of full scale ballasted rail tracks.

Introduction to the Special Issue on Computational Mechanics of Granular Materials and its Engineering Applications

1 Introduction The purpose of this special issue“Computational Mechanics of Granular Materials and its Engineering Applications”is to introduce the latest research progress in computational mechanics and engineering applications of granular materials,with particular emphasis on the theoretical constructions of arbitrarily shaped particles,flow pattern transitions,bond-fracture model,neural network algorithm,CFD-DEM coupled method,and coarse-graining model,and to improve our understanding of the physical and mechanical properties of granular systems from the perspective of practical engineering applications.

Editorial:Computational granular mechanics

Granular materials exist widely in nature,industry and engineering applications and perform complex mechanical behaviors.Theoretical analysis,numerical simulations and physical experiments were adopted to investigate the mechanical properties of granular systems and to solve the engineering problems.The discrete element method(DME)was proposed in 1970s and has been a practical approach to study the macro and mesoscopic behaviors of various granular materials.Although numerical methods have been successfully applied to the study of basic physical and mechanical properties of granular materials,there are still many challenges in computational granular mechanics,such as the construction of real particle morphology,flow characteristics of granular materials,multi-media and multiscale modelling and high-performance computational algorithms.

Rheological behaviors of spherical granular materials based onDEM simulations

A comprehensive study of the rheological properties of granular materials is essential for predicting and mitigating natural disasters.Man et al.[1]developed a theoretical model of rheology for spherical granular materials,which incorporates inter-particle friction,inertia numbers,and particle temperature.The rheological model is of great significance for establishing a more general constitutive theory of granular materials and an in-depth understanding of the micro-topology of complex granular systems.

Flow characteristics of nonspherical granular materials simulated with multi-superquadric elements

The superquadric equation is typically used to mathematically describe nonspherical particles and construct particle shapes with different surface sharpness and aspect ratios.However,nonspherical elements constructed using the superquadric equation are strictly convex,limiting their engineering application.In this study,a multi-superquadric model based on a superquadric equation is developed.The model combines several superquadric elements that can be used to construct concave and convex particle shapes.Four tests are performed to examine the applicability of the multi-superquadric approach.The first involves a comparison of theoretical results for a single spherocylinder impacting a flat wall.The second involves the formation of a nonspherical granular bed.The third investigates the effects of the particle shape on the hopper discharge and angle of repose.The final test evaluates the mixing behaviors of granular materials within a horizontally rotating drum.These tests demonstrate the applicability of the multi-superquadric approach to nonspherical granular systems.Furthermore,the effects of particle shape on the packing density,discharge rate,angle of repose,and Lacey mixing index are discussed.Results indicate that concave particles have a lower packing density,flow rate,and mixing rate and higher angles of repose than convex particles.Interlocking of elements becomes more pronounced for concave particles and results in local cluster structures,thereby enhancing the stability of granular systems and limiting sliding or rotation between nonspherical particles.

Superquadric DEM-SPH coupling method for interaction between non-spherical granular materials and fluids

The research on the coupling method of non-spherical granular materials and fluids aims to predict the particle-fluid interaction in this study.A coupling method based on superquadric elements is developed to describe the interaction between non-spherical solid particles and fluids.The discrete element method(DEM)and the smoothed particle hydrodynamics(SPH)are adopted to simulate granular materials and fluids.The repulsive force model is adopted to calculate the coupling force and then a contact detection method is established for the interaction between the superquadric element and the fluid particle.The contact detection method captures the shape of superquadric element and calculates the distance from the fluid particle to the surface of superquadric element.Simulation cases focusing on the coupling force model,energy transfer,and large-scale calculations have been implemented to verify the validity of the proposed coupling method.The coupling force model accurately represents the water entry process of a spherical solid particle,and reasonably reflects the difference of solid particles with different shapes.In the water entry process of multiple solid particles,the total energy of the water entry process of multiple solid particles tends to be stable.The collapse process of the partially submerged granular column is simulated and analyzed under different parameters.Therefore,this coupling method is suitable to simulate fluid-particle systems containing solid particles with multiple shapes.

Buffer capacity of granular matter to impact of spherical projectile based on discrete element method

Granular matter possesses impact-absorbing property due to its energy dissipation character.To investigate the impact-absorbing capacity of granular matter,the discrete element method(DEM)is adopted to simulate the impact of a spherical projectile on to a granular bed.The dynamic responses of the projectile are obtained for both thin and thick granular bed.The penetration depth of the projectile and the first impact peak are investigated with different bed thicknesses and impact velocities.Determining a suitable bed thickness is crucial to the buffering effect of granular matter.The first impact peak is independent of bed thickness when the thickness is larger than the critical thickness.