Force chains based mesoscale simulation on the dynamic response of Al-PTFE granular composites

Force chains based mesoscale simulation is conducted to investigate the response behavior of aluminumpolytetrafluoroethylene(Al-PTFE)granular composites under a low-velocity impact.A two-dimensional model followed the randomly normal distribution of real Al particles size is developed.The dynamic compressive process of Al-PTFE composites with varied Al mass fraction is simulated and validated against the experiments.The results indicate that,force chains behavior governed by the number and the size of agglomerated Al particles,significantly affects the impact response of the material.The failure mode of the material evolves from shear failure of matrix to debonding failure of particles with increasing density.A high crack area of the material is critical mechanism to arouse the initiation reaction.The damage maintained by force chains during large plastic strain builds up more local stresses concentration to enhance a possible reaction performance.In addition,simulation is performed with identical mass fraction but various Al size distribution to explore the effects of size centralization and dispersion on the mechanical properties of materials.It is found that smaller sized Al particle of composites are more preferred than its bulky material in ultimate strength.Increasing dispersed degree is facilitated to create stable force chains in samples with comparable particle number.The simulation studies provide further insights into the plastic deformation,failure mechanism,and possible energy release capacity for Al-PTFE composites,which is helpful for further design and application of reactive materials.

Correlation mechanism between force chains and friction mechanism during powder compaction

The relation between friction mechanism and force chains characteristics has not yet been fully studied in the powder metallurgy research area.In this work,a uniaxial compression discrete element model is established based on the compaction process of ferrous powder.Furthermore,the correlation mechanism between force chains and the friction mechanism during powder compaction is investigated.The simulation results reveal a strong correlation between the variation of the friction coefficient and the evolution of force chains.During the powder compaction,the friction coefficient would eventually tend to be stable,a feature which is also closely related to the slip ratio between particles.The side wall friction and the friction between particles would have an important effect on the direction of force chain growth in about one-third of the area near the side wall.The research results provide theoretical guidance for improving the densification process of the powder according to the force chain and friction.

Study on force chain evolution of rice straw with different length during vibrational compression

This paper explores the mechanism of force chain evolution and voidage change under vibrational and non-vibrational compression conditions of rice straw of different lengths.Simulations were used to explore the force chain evolution and voidage variation mechanism under different conditions.The re-sults show that under non-vibrational compression,the strong force chain passes from top to bottom in vertical direction and from center to periphery in tangential direction.Under vibrational compression,the force chain passes from top and bottom to center in vertical direction and the force chain evolves from outer ring to interior and exterior in tangential direction.The number of strong chains,voidage and standard deviation of the mean pressure under vibratory compression are lower than the values under non-vibratory compression.Vibration promotes stress transfer and enhancement,velocity enhancement and density enhancement.This study analyzes the mechanical properties of different lengths straw during vibrational and non-vibrational compression from a detailed viewpoint.

Study on the force chain characteristics with coal dust layer and the three-body contact stiffness

To explore the influence of the meso-mechanical behaviors of the wet coal dust layers on the contact stiffness of mechanical bonding surfaces,a three-body contact model incorporating an interface with wet coal dust was constructed based on breakage theory.The model considered the mechanical surface morphology and contact characteristics of the wet coal dust.The force chain evolution laws of the wet coal dust layer were elucidated under the effects of gap filling and the cover layer,and the bearing characteristics of the three-body contact bonding surfaces were revealed by quantitative analyses of the number,length,collimation coefficient,and coordination number of the force chains within the wet coal dust layer.Finally,the three-body normal contact stiffness under various preload forces was computed and experimentally validated.The results demonstrate that the external load transfer path of the three-body contact bonding surfaces was from mechanical surface(macroscopic stress)to wet coal dust layer(mesoscopic force chains)and then to mechanical surface(peaks and valleys).The interactions among these three elements contributed to transforming the distributions of the macroscopic stresses and mesoscopic force chains to the locations at the peaks and valleys of the mechanical surface.Among them,the proportion of short force chains in the wet coal dust layer increased from approximately 0.8%–91%,while the proportion of long force chains exhibited an opposite changing trend.The force chain collimation coefficient initially increased and subsequently stabilized,reaching a maximum value of 0.93.A large number of broken,small particles in the wet coal dust layer mainly served to fill the gaps among large particles.The maximum relative error between the experimental and simulated values on the three-body contact stiffness is 7.26%,indicating that the simulation results can be an approximate substitute for the experimental results with a certain degree of accuracy and practicality.The research results are of great significance for understanding the contact characteristics of mechanical surfaces containing particulate media.

Characterizing dynamic load propagation in cohesionless granular packing using force chain

When dynamic load is applied on a granular assembly,the time-dependent dynamic load and initial static load(such as gravity stress)act together on individual particles.In order to better understand how dynamic load triggers the micro-structure's evolution and furtherly the ensemble behavior of a granular assembly,we propose a criterion to recognize the major propagation path of dynamic load in 2D granular materials,called the“dynamic force chain”.Two steps are involved in recognizing dynamic force chains:(1)pick out particles with dynamic load larger than the threshold stress,where the attenuation of dynamic stress with distance is considered;(2)among which quasi-linear arrangement of three or more particles are identified as a force chain.The spatial distribution of dynamic force chains in indentation of granular materials provides a direct measure of dynamic load diffusion.The statistical evolution of dynamic force chains shows strong correlation with the indentation behaviors.

Automatic extraction method of force chain information and its application in the flow photoelastic experiment of granular matter

The force chain is the core of the multi-scale analysis of granular matter.Accurately extracting the force chain information among particles is of great significance to the study of particle mechanics and geological hazards caused by particle flow.However,in the photoelastic experiment,the precise identification of the branching points of force chains has not been effectively realized.Therefore,this study proposes an automatic extraction method of force chain key information.First,based on the Hough transform and the Euclidean distance,a particle geometric information identification model is established and geometric information such as particle circle center coordinates,radius,contact point location,and contact angle is extracted.Then,a particle contact force information identification model is established following the color gradient mean square method.The model realizes the rapid calibration and extraction of a large number of particle media contact force information.Next,combined with the force chain composition criterion and its quasilinear feature,an automatic extraction method of force chain information is established,which solves the problem of the accurate identification of the force chain branch points.Finally,in the photoelastic experiment of ore drawing from a single drawpoint,the automatic extraction method of force chain information is verified.The results show that the macroscopic distribution of force chains during ore drawing from a single drawpoint is left–right symmetrical.Strong force chains are mostly located on the two sides of the model but in small numbers and they mainly develop vertically.Additionally,the ends are mostly in a combination of Y and inverted Y shapes,while the middle is mostly quasilinear.Weak force chains are abundant and mostly distributed in the middle of the model,and develop in different directions.The proposed extraction method accurately extracts the force chain network from the photoelastic experiment images and dynamically characterizes the force chains of granular matter,which has significant advantages in particle geometry information extraction,force chain branch point discrimination,force chain retrieval,and force chain distribution and its azimuthal characterization.The results provide a scientific basis for studying the macroscopic and microscopic mechanical parameters of granular matter.

Earth Pressure of the Trapdoor Problem Using Three-Dimensional Discrete Element Method

Load transformation from the yielding part of the soil to the adjacent part is known as the soil arching effect,which plays an important role in the design of various geotechnical infrastructures.Terzaghi’s trapdoor test was an importantmilestone in the development of theories on soil arching.The research on earth pressure of the trapdoor problem is presented in this paper using the three-dimensional(3D)discrete element method(DEM).Five 3D trapdoor models with different heights are established by 3DDEMsoftware PFC 3D.The variation of earth pressure on the trapdoor with the downward movement of the trapdoor,the distribution of vertical earth pressure along the horizontal direction,the distribution of vertical earth pressure along the vertical direction,the distribution of lateral earth pressure coefficient along the depth direction,the magnitude and direction of contact force chain are studied,respectively.Related research results show that the earth pressure on the trapdoor decreases rapidly after the downward movement of the trapdoor,and then reaches the minimum earth pressure.After that,the earth’s pressure will rise slightly,and whether this phenomenon occurs depends on the depth ratio.For the bottom soil,due to the stress transfer caused by the soil arching effect,the ratio of earth pressure in the loose area decreases,while the ratio of earth pressure in the stable area increases.With the trapdoor moving down,the vertical earth pressure along the depth in the stable zone is basically consistent with the initial state,which shows an approximate linear distribution.After the trapdoor moves down,the distribution of earth pressure along with the depth in the loose area changes,which is far less than the theoretical value of vertical earth pressure of its self-weight.Because of the compression of the soil on both sides,the lateral earth pressure coefficient of most areas on the central axis of the loose zone is close to the passive earth pressure coefficient Kp.The existence of a‘soil arch’can be observed intuitively from the distribution diagram of the contact force chain in the loose zone.

A numerical study of macro-mesoscopic mechanical properties of gangue backfill under biaxial compression

Based on the Particle Flow Code(PFC^(2D)) program,we set up gangue backfill models with different gangue contents and bond strength,and studied the stress-strain behaviours,the pattern of shear band and force chains,motion and fragmentation of particles under biaxial compression.The results show that when the bond strength or contents of gangue are high,the peak strength is high and the phenomena of post-peak softening and fluctuation are obvious.When gangue contents are low,the shape of the shear band is symmetrical and most strong force chains transfer in soil particles.With an increase in gangue content,the shape of the shear band becomes irregular and the majority of strong force chains turn to transfer in gangue particles gradually,most of which distribute along the axial direction.When the gangue content is higher than 50%,the interconnectivity of strong force chains decreases gradually:at the same time,the strong force chains become tilted and the stability of the system tends to decrease.With an increase in external loading,the coordination numbers of the system increase at first and then decrease and the main pattern of force chains changes into columnar from annular.However,after the forming of the advantageous shear band,the force chains external to the shear band maintain their columnar shape while the inner ones bend obviously.As a result,annular force chains form.

The Material Deformation and Internal Structure Development of Granular Materials under Different Cyclic Loadings

Common structures in engineering such as slopes,roadbeds,ballasts,etc.,are closely related to granular materials.They are usually subjected to long-term cyclic loads.This study mainly focused on the mechanical behaviors of randomly arranged granular materials before they reach a stable state under different cyclic loads.The variation of the maximum axial strain and the influence of CSR(cyclic stress ratio)were analyzed.The energy consumed in each cycle under constant confining stress loading condition is significantly greater than that of the fixed wall loading condition.The internal deformation evolution of granular materials is studied in detail.The deformation mode of granular material under cyclic loading at different positions inside the material is different according to the strain variation.In addition,the strain,force chain structure and contact force magnitude are combined to explore their effects on local deformation of granular materials under cyclic loading.From the perspective of the deformation form,the material sample can be divided into several regions,and the ability to adjust particle positions determines the deformation mode of different regions.The changes of local strain with the cyclic loading also reflect the contribution of particle displacements to the evolution ofmicrostructure.This research will provide insights into the understanding of granular materials behaviors under cyclic loading.

Laboratory Model Tests and DEM Simulations of Unloading-Induced Tunnel Failure Mechanism

Tunnel excavation is a complicated loading-unloading-reloading process characterized by decreased radial stresses and increased axial stresses.An approach that considers only loading,is generally used in tunnel model testing.However,this approach is incapable of characterizing the unloading effects induced by excavation on surrounding rocks and hence presents radial and tangential stress paths during the failure process that are different from the actual stress state of tunnels.This paper carried out a comparative analysis using laboratory model testing and particle flow code(PFC2D)-based numerical simulation,and shed light upon the crack propagation process and,microscopic stress and force chain variations during the loading-unloading process.The failure mode observed in the unloading model test is shear failure.The force chains are strongly correlated with the concrete fracture propagation.In addition,the change patterns of the radial and tangential stresses of surrounding rocks in the broken region,as well as the influence of the initial stress on failure loads are revealed.The surrounding soil of tunnel failure evolution as well as extent and shape of the damage zone during the excavation-induced unloading were also studied.

Probability analysis of contact forces in quasi-solid-liquid phase transition of granular shear flow

The quasi-solid-liquid phase transition exists widely in different fields,and attracts more attention due to its instinctive mechanism.The structure of force chains is an important factor to describe the phase transition properties.In this study,the discrete element model(DEM) is adopted to simulate a simple granular shear flow with period boundary condition on micro scale.The quasi-solid-liquid phase transition is obtained under various volume fractions and shear rates.Based on the DEM results,the probability distribution functions of the inter-particle contact force are obtained in different shear flow phases.The normal,tangential and total contact forces have the same distributions.The distribution can be fitted as the exponential function for the liquid-like phase,and as the Weibull function for the solid-like phase.To describe the progressive evolution of the force distribution in phase transition,we use the Weibull function and Corwin-Ngan function,respectively.Both of them can determine the probability distributions in different phases and the Weibull function shows more reasonable results.Finally,the force distributions are discussed to explain the characteristics of the force chain in the phase transition of granular shear flow.The distribution of the contact force is an indicator to determine the flow phase of granular materials.With the discussions on the statistical properties of the force chain,the phase transition of granular matter can be well understood.

Visualization of force networks in 2D dense granular materials

Dense granular matter is a conglomeration of discrete solid and closely packed particles.As subjected to external loadings,the stress is largely transmitted by heavily stressed chains of particles forming a sparse network of larger contact forces.To understand the structure and evolution of force chains,a photoelastic technique was improved for determining stresses and strains in the assemblies of photoelastic granular disks in this paper.A two-dimensional vertical slab was designed.It contains 7200 polydispersed photoelastic disks and is subjected to a localized probe penetrating at the top of the slab to mimic the cone penetration test.The interparticle contact force distribution was found a peak around the mean value,a roughly exponential tail for greater force and a dip toward zero for smaller force.The force chain network around the probe tip was depicted,and the contact angle distribution of particles in force chains was found to be well aligned in the directions of major principal stress.

Force fluctuations in sheared granular disks

The internal structure established within granular materials,often observed as force chains,is dominant in controlling bulk mechanical properties.We designed a two-dimensional Hele-Shaw cell to contain photoelastic disks,and two servos were used on the top and right boundaries individually.We experimentally monitored the fluctuations in force on the top plate while slowing the shearing of the well-confined disks and keeping the right boundary at a contactconfined force of 0.2 kN.The particle rearrangements were found to correspond to bulk force drops and were observed in a localized zone with a length of approximately 5 particle diameters.These results help reveal the structure and mechanics of granular materials,and further investigations are ongoing.

STUDIES ON STRUCTURAL AND MECHANICAL PROPERTIES UNDER ISOSTATIC COMPRESSION WITH LARGE-SCALE DISCRETE ELEMENT SIMULATIONS

Granular systems undergo a jamming transition at point J simply by increasing the packing fraction. A large-scale parallel discrete element code （THDEM： TsingHua Discrete Element Method） was used to obtain a satisfying statistical description of the structural and me- chanical properties near point J. The isostatic compressions of 100,000 polydispersed frictionless particles were simulated on high performance computers to clearly observe the sophisticated con- figurations of force chains. The first peak of the pair correlation function, coordination number, spatial distribution of the packing fraction, and stress were calculated to analyze their variations with increasing packing fraction. The critical packing fraction at point J is determined to be 0.62. The incremental stress and coordination number from point J scale well with the power law, and coincide with previous theoretical predications. The distribution of the packing frac- tion is a normal distribution around the average value. The standard deviation decreases with increasing packing fraction, indicating the system is more uniform with a denser packing.

Experimental investigation of granular friction behaviors during reciprocating sliding

Granular friction behaviors are crucial for understanding the ubiquitous packing and flow phenomena in nature and industrial production.In this study,a customized experimental apparatus that can simultaneously measure the time history of normal and tangential forces on the inside-shearing unit is employed to investigate the granular friction behaviors during a linear reciprocating sliding process.It is observed that the evolution behaviors of two normal forces distributed separately on the shearing unit can qualitatively reflect the effects of the force chain network.During the half-loop of the reciprocating sliding,the total normal force,which indicates the load-bearing capacity of the granular system,experiences the following typical stages:decreases abruptly and stabilizes momentarily,further decreases significantly to the minimum,gradually increases to the maximum,and then remains stable.These stages are associated closely with the relaxation,collapse,reconstruction,and stabilization of the force chain,respectively.Interestingly,the coefficient of friction(COF)can reach a stable value rapidly within the initial sliding stage and subsequently remain constant.The average COF within stable ranges decreases significantly with the external load G in the power function form,G^(-0.5).Meanwhile,the COF increases slightly with the sliding velocity.Finally,a complete illustration of the dependences of the granular COF on the external load and sliding velocity is provided.Our study contributes to granular friction research by providing an innovative experimental approach for directly measuring the COF and implicitly correlating the evolution of the force chain network.

Crowd evacuation of pairs of pedestrians

The crowd evacuation of pairs of pedestrians(i.e.pairs consisting of a parent and a child)is numerically investigated.Here,it is assumed that all pedestrians have their own partners,and move randomly inside the bounded domain of the right-hand room as an initial state.All pedestrians start their evacuations after they contact their partners.The evacuations are completed by the transfer of all the pairs from the right-hand room to the left-hand room through an exit.A frozen swarm tends to appear in the right-hand room as the total number of pedestrians increases.The frozen swarm moves without changing its form,unless it is dissolved by a strong collision with a pair of pedestrians that comes back from the left-hand room by accident.Finally,the evacuation speed also depends on the area of the Escape Zone,whereas an obstacle placed in front of an exit also changes the speed of the evacuation in accordance with the type of motion of the children.