Contact Anisotropy Research Articles

Rheology and structure of polydisperse three-dimensional packings of spheres

We use three-dimensional contact dynamics simulations to analyze the rheology of polydisperse packings of spherical particles subjected to simple shear. The macroscopic and microstructural properties of several packings are analyzed as a function of their size span (from nearly monodisperse to highly polydisperse). Consistently with previous two-dimensional simulations, we find that the shear strength is independent of the size span despite the increase of packing fraction with size polydispersity. At the grain scale, we analyze the particle connectivity, force transmission, and the corresponding anisotropies of the contact and force networks. We show that force distributions become increasingly broader as the size span increases. In particular, stronger forces are captured by large particles, which are also better connected creating the so-called granular backbone. Throughout this backbone friction mobilization is rare and compressive forces control the stability of such structure. In return, small particles create an important population of rattlers discarded of the strength and granular structure analysis. As a consequence, the contact anisotropy declines with size span, whereas the force and branch anisotropies increase. These microstructural compensations allow us to explain the independence of the shear strength from particle size polydispersity.

Evolving pore orientation, shape and size in sheared granular assemblies

This paper presents new insights into the deformation response of sheared granular assemblies by characterising pore space properties from discrete element simulations of monodisperse particle assemblies in two-way cyclic shearing. Individual pores are characterized by a modified Delaunay tessellation, where tetrahedral Delaunay cells can be merged to form polyhedral cells. This leads to a natural partition of the pore space between individual pores with tetrahedral and polyhedral geometry. These are representative of small compact pores and larger well-connected pores, respectively. A scalar measure of pore orientation anisotropy during shearing is introduced. For triaxial shearing, larger pores align in the loading direction, while small pores are aligned perpendicular to the larger pores. Pore anisotropy mobilises at a slower rate than contact anisotropy or macroscopic stress state, and hence, is an important element to characterise in granular assemblies. Further, the distribution of pore volume remains isotropic. Pore shape was found to be a good micro-scale indicator of macroscopic density, with a strong relationship between averaged shape factor and macroscopic void ratio. Combining results for pore shape and orientation reveals an interesting interplay, where large elongated pores were aligned with the loading direction. These results highlight the importance of considering pore space characteristics in understanding the behaviour of granular materials.

Rheological transition in simple shear of moderately dense assemblies of dry cohesive granules.

The rheology of homogeneous cohesive granular assemblies under shear at moderate volume fractions is investigated using the discrete element method for both frictionless and frictional granules. A transition in rheology from inertial to quasistatic scaling is observed at volume fractions below the jamming point of noncohesive systems, which is a function of the granular temperature, energy dissipation, and cohesive potential. The transition is found to be the result of growing clusters, which eventually percolate the domain, and change the mode of momentum transport in the system. Differences in the behavior of the shear stress normalized by the pressure are observed when frictionless and frictional cases are compared. These differences are explained through contact anisotropy after percolation occurs. Both frictionless and frictional systems are found to be vulnerable to instabilities after full system percolation has occurred, where the former becomes thermodynamically unstable and the latter may form shear bands. Finally, implications for constitutive modeling are discussed.

Rheology of granular materials composed of crushable particles.

We investigate sheared granular materials composed of crushable particles by means of contact dynamics simulations and the bonded-cell model for particle breakage. Each particle is paved by irregular cells interacting via cohesive forces. In each simulation, the ratio of the internal cohesion of particles to the confining pressure, the relative cohesion, is kept constant and the packing is subjected to biaxial shearing. The particles can break into two or more fragments when the internal cohesive forces are overcome by the action of compressive force chains between particles. The particle size distribution evolves during shear as the particles continue to break. We find that the breakage process is highly inhomogeneous both in the fragment sizes and their locations inside the packing. In particular, a number of large particles never break whereas a large number of particles are fully shattered. As a result, the packing keeps the memory of its initial particle size distribution, whereas a power-law distribution is observed for particles of intermediate size due to consecutive fragmentation events whereby the memory of the initial state is lost. Due to growing polydispersity, dense shear bands are formed inside the packings and the usual dilatant behavior is reduced or cancelled. Hence, the stress-strain curve no longer passes through a peak stress, and a progressive monotonic evolution towards a pseudo-steady state is observed instead. We find that the crushing rate is controlled by the confining pressure. We also show that the shear strength of the packing is well expressed in terms of contact anisotropies and force anisotropies. The force anisotropy increases while the contact orientation anisotropy declines for increasing internal cohesion of the particles. These two effects compensate each other so that the shear strength is nearly independent of the internal cohesion of particles.

Inertial shear flow of assemblies of frictionless polygons: Rheology and microstructure.

Motivated by the understanding of shape effects in granular materials, we numerically investigate the macroscopic and microstructural properties of anisotropic dense assemblies of frictionless polydisperse rigid pentagons in shear flow, and compare them with similar systems of disks. Once subjected to large cumulative shear strains their rheology and microstructure are investigated in uniform steady states, depending on inertial number I, which ranges from the quasistatic limit ([Formula: see text]) to 0.2. In the quasistatic limit both systems are devoid of Reynolds dilatancy, i.e., flow at their random close packing density. Both macroscopic friction angle [Formula: see text], an increasing function of I , and solid fraction [Formula: see text], a decreasing function of I, are larger with pentagons than with disks at small I, but the differences decline for larger I and, remarkably, nearly vanish for [Formula: see text]. Under growing I , the depletion of contact networks is considerably slower with pentagons, in which increasingly anisotropic, but still well-connected force-transmitting structures are maintained throughout the studied range. Whereas contact anisotropy and force anisotropy contribute nearly equally to the shear strength in disk assemblies, the latter effect dominates with pentagons at small I, while the former takes over for I of the order of 10-2. The size of clusters of grains in side-to-side contact, typically comprising more than 10 pentagons in the quasistatic limit, very gradually decreases for growing I.

Anisotropic friction and wear rules with account for contact state evolution

The present study is related to analysis of coupled friction and wear process in sliding along the rough surface with an anisotropic asperity pattern characterized by single or mutually orthogonal striations. Due to wear process the initial anisotropic response evolves with the variation of asperity distribution, tending to a steady-state pattern. The orthotropic friction sliding model and the related wear rule are analytically formulated assuming evolution of contact anisotropy to its steady state. The orthotropic frictional sliding model and the related wear rule are analytically formulated assuming evolution of contact anisotropy to its steady state. The experimental study is next presented for orthotropic asperity patterns induced on steel plate surface. The transient and steady states are characterized and the respective evolution parameters calibrated. The numerical finite element wear analysis aimed at validation of model-predictions and wear parameter calibration is presented at the end of paper.

Study of the effects of anisotropic consolidation on granular materials under complex stress paths using the DEM

We adopt the discrete element method with a periodic boundary to investigate the comprehensive effects of initial anisotropic consolidation derived from an initial stress ratio ( $$K_{\mathrm{c}})$$ under complex stress paths (b). Both the initial stiffness and deformation mechanisms are systematically analyzed. The dilatancy rate and the stress–dilatancy relationship depend on stress paths and $$K_{\mathrm{c}}$$ . Meanwhile, the distinction between the critical-state mechanical responses under different stress paths also depends on the initial stress ratio. The equation of the relationship between the excess friction angle and peak state parameter is conceptually given, where the coefficients are related to both the initial stress ratio and stress path. At the microscopic level, the properties of contact forces, coordination number, and anisotropies of the assemblies are discussed. The samples with different initial stress ratios exhibit different extents of distinction in terms of various coordinate numbers. The probability density functions of both contact normal and tangential forces are evidently affected by the initial stress ratio, and the effects of the initial stress ratio gradually vanish as shearing proceeds. The strong force chain networks under different conditions of $$K_{\mathrm{c}} $$ and b are explored, showing the comprehensive mechanism of force transmission. At the same strain level, the proportion and the magnitude of strong contact forces strengthen with the improvement of initial anisotropic consolidation, and the initial anisotropic consolidation can evidently improve the ability of the assemblies to cluster along the intermediate principal direction with the increase of b. Different anisotropy parameters show different sensitivities to the initial stress ratio. The fabric-based strength descriptor is linearly correlated to the stress ratio under different $$K_{\mathrm{c}} $$ conditions. The fabric and small-strain stiffness are combined to investigate the macro- and microscopic connections that are subject to inherent anisotropic consolidation as well as the intermediate stress ratio.

On the kinematics and dynamics of crystal‐rich systems

AbstractPartially molten rocks, often called a mush, are examples of a hydrogranular mixture where the dynamics are controlled by both fluid and crystal‐crystal interactions. An obstacle to progress in understanding high‐temperature hydrogranular systems has been the lack of adequate levels of description of microphysical processes. Here we rationalize the hydrogranular kinematic and dynamic states by applying the concept of particle (crystal) force chains. We exemplify this with discrete‐element computational fluid dynamic simulations of the intrusion of a basaltic melt into an olivine‐basalt mush, where crystal‐scale force chains, crystal transport, and melt mixing are resolved. To describe the microscale kinematics of the system, we introduce the coordination number and the fabric tensors of particle contacts and forces. We quantify the changing contact and force fabric anisotropy, coaxiality, and the connectedness of the mush, under dynamic conditions. To describe the dynamics, particle and fluid characteristic response times are derived. These are used to define local and bulk Stokes numbers, and viscous and inertia numbers, which quantify the multiphase coupling under crystal‐rich conditions. We employ the Sommerfeld number, which describes the importance of crystal‐melt lubrication, with a viscous number to illustrate the dynamic regimes of crystal‐rich magmas. We show that the notion of mechanical “lock up” is not uniquely identified with a particular crystal volume fraction and that distinct mechanical behaviors can emerge simultaneously within a crystal‐rich system. We also posit that this framework describes magmatic fabrics and processes which “unlock” a crystal mush prior to eruption or mixing.

Electric field control of magnetic anisotropy in bilayer contacts with Rashba-type spin–orbit interaction

Theoretical analysis of the uniaxial magnetic anisotropy (MA) in bilayer contacts composed of a non-magnetic layer with Rashba-type spin–orbit interaction and a ferromagnetic one with L − S coupling has been performed. The Rashba-type spin–orbit interaction contributes to the MA of the bilayer via band-mixing of the Rashba-split conduction band of the non-magnetic layer and the exchange-split bands of the ferromagnetic layer. Numerical results of a simple model show that the Rashba-induced MA could have the same order of magnitude as the MA produced in the ferromagnetic layer, indicating that the electric-field dependence of the Rashba spin–orbit interaction may be used to control the uniaxial MA in bilayer contacts.

Anisotropy of contact networks in granular media and its influence on mobilised internal friction

The anisotropy associated with the contact network in granular media is investigated. A unique expression for mobilised internal friction has been discovered using numerical simulations of monodisperse and polydisperse spherical assemblies under two-way cyclic axisymmetric and simple shear load paths. This uniqueness is described by a linear relationship between the macroscopic stress ratio and the geometric configuration of only the strong and non-sliding contacts, where strong contacts are those with a normal force magnitude greater than the mean normal force. A stress–force–fabric expression for arbitrary partitions of the contact network was derived analytically, providing a mathematical connection between the macroscopic state of stress and interparticle characteristics. Numerical simulations revealed that only strong and non-sliding contacts provided a non-zero contribution to the stress–force–fabric expression. Previous studies suggest the dominance of force anisotropy in the complete contact network, but this study indicates that geometric anisotropy of contacts is the dominant contributor in the stress–force–fabric relationship when particular subsets of the contact network are considered.

Micro-scale anisotropy of contacts and pores in granular media

This paper considers the anisotropy associated with the interparticle contact network and interconnected pore space, which is quantified through a scalar quantity based on the fabric tensor. The study focused on the anisotropy associated with subsets of contacts and pores. It is shown that the stress ratio can be directly related to the geometric anisotropy of strong and non-sliding contacts, and that the anisotropy of pores is correlated with the anisotropy of contacts.

Effect of contact anisotropy on the crushing strength of aggregates

This work deals with the effect of the contact orientation distribution on the crushing of granular materials. At first, a simple drop weight experiment was designed in order to study the effect of the location of three contact edges on the fracture pattern and the strength of a model cylindrical particle. The sample was placed on two bottom contact edges symmetrically distributed with reference to the vertical symmetry plane of the particle and subjected to an impact at the top. Angle α between the plane connecting a bottom contact edge to the centerline of the cylinder and a vertical plane was varied. The energy required to fracture the particle was shown to be an increasing function of angle α. Peculiar crack patterns were also observed. Then, we present a discrete model of grain fracture [1] and employ it for a numerical analysis of the problem. The cylindrical particle is discretized by means of a space filling Voronoi tessellation, and submitted to a compression test for different values of angle α. In agreement with experiments, simulations predict a strong effect of the contact orientation on the strength of the particle as well as similar fracture patterns. The proposed numerical model is therefore an interesting tool for understanding fracture mechanisms with the purpose of optimizing the crushing process.

Micromechanics-Based Investigation of Fouled Ballast Using Large-Scale Triaxial Tests and Discrete Element Modeling

AbstractRailway ballast comprises unbounded discrete grains that are often used to form a load-bearing platform for tracks. Ballast degradation as trains pass over the tracks and infiltration of external fines including slurried (pumped) fine subgrade soils are two of the main reasons for ballast fouling. Fouling causes tracks to settle and also reduces the load-bearing capacity, which is associated with a reduction in internal friction and increased lateral spreading of the ballast layer. This paper presents a study of mobilized friction angle, volumetric behavior, and associated evolutions of contact and fabric anisotropy of fouled ballast subjected to monotonic triaxial loading using a series of large-scale triaxial tests and discrete element modeling. Monotonically loaded and drained triaxial tests were carried out on ballast with levels of clay fouling that varied from 10 to 50% void contamination index (VCI) subjected to three confining pressures of 10, 30, and 60 kPa. The results showed that an inc...

Interplay between the inclusions of different sizes and their proximity to the wall boundaries on the nature of their stress distribution within the inclusions inside particulate packing

Micromechanical responses of granular materials are complex to understand when their behaviour is viewed in a single grain-scale. Experimental sensing of stresses within a grain-scale inside three dimensional particulate packing is still difficult to perform. In this work, photo stress analysis tomography (PSAT) is used to sense the fundamental nature of the stress experienced by different sizes of optically-sensitive inclusions inside granular packing (quasi-three dimensional) under an external axial-compression loading. The distribution of the maximum shear stress and the direction of the major principal stress experienced by the inclusions are analysed to understand the interplay between the size of the inclusions and their proximity to the wall boundary. The outcomes of this study provide a new understanding on the dual nature of stress transmission experienced by the inclusions, as a result of the combined size and wall effects. Relatively large inclusions experience dominantly shear stress close to the wall boundaries while this nature tends towards hydrostatic away from the wall boundaries. Smaller size inclusions could experience shear at both close to and away from wall boundaries of the granular assembly. Computer simulations using three-dimensional discrete element method (DEM) are also performed to compare the qualitative nature of stress experienced by inclusions inside particulate media. Qualitatively, the simulation results also agree with the experimental outcomes, that an increase in the relative size of the inclusion decreases its ability to experience shear. Using DEM simulations, the fabric structure of the inclusions is examined in depth under mechanical loading. An increase in the size of the inclusions tends to decrease the fabric anisotropy of the contacts and in particular the strong contacts, surrounding them. Hence the microscale origin of the weak mobilisation of shear in the large inclusions could be attributed to their relatively weak fabric anisotropy of the strong contacts surrounding them. These findings help to advance our understanding of the micromechanics of particulate systems, due to their size and proximity to wall boundaries: different sizes of the particles could sustain different nature of stresses within single-particle scale depending on their proximity to the wall boundaries.

Effects of shape and size polydispersity on strength properties of granular materials.

By means of extensive contact dynamics simulations, we analyze the combined effects of polydispersity both in particle size and in particle shape, defined as the degree of shape irregularity, on the shear strength and microstructure of sheared granular materials composed of pentagonal particles. We find that the shear strength is independent of the size span, but unexpectedly, it declines with increasing shape polydispersity. At the same time, the solid fraction is an increasing function of both the size span and the shape polydispersity. Hence, the densest and loosest packings have the same shear strength. At the scale of the particles and their contacts, we analyze the connectivity of particles, force transmission, and friction mobilization as well as their anisotropies. We show that stronger forces are carried by larger particles and propped by an increasing number of small particles. The independence of shear strength with regard to size span is shown to be a consequence of contact network self-organization, with the falloff of contact anisotropy compensated by increasing force anisotropy.

Non-uniform breaking of molecular bonds, peripheral morphology and releasable adhesion by elastic anisotropy in bio-adhesive contacts.

Biological adhesive contacts are usually of hierarchical structures, such as the clustering of hundreds of sub-micrometre spatulae on keratinous hairs of gecko feet, or the clustering of molecular bonds into focal contacts in cell adhesion. When separating these interfaces, releasable adhesion can be accomplished by asymmetric alignment of the lowest scale discrete bonds (such as the inclined spatula that leads to different peeling force when loading in different directions) or by elastic anisotropy. However, only two-dimensional contact has been analysed for the latter method (Chen & Gao 2007 J. Mech. Phys. Solids 55, 1001-1015 (doi:10.1016/j.jmps.2006.10.008)). Important questions such as the three-dimensional contact morphology, the maximum to minimum pull-off force ratio and the tunability of releasable adhesion cannot be answered. In this work, we developed a three-dimensional cohesive interface model with fictitious viscosity that is capable of simulating the de-adhesion instability and the peripheral morphology before and after the onset of instability. The two-dimensional prediction is found to significantly overestimate the maximum to minimum pull-off force ratio. Based on an interface fracture mechanics analysis, we conclude that (i) the maximum and minimum pull-off forces correspond to the largest and smallest contact stiffness, i.e. 'stiff-adhere and compliant-release', (ii) the fracture toughness is sensitive to the crack morphology and the initial contact shape can be designed to attain a significantly higher maximum-to-minimum pull-off force ratio than a circular contact, and (iii) since the adhesion is accomplished by clustering of discrete bonds or called bridged crack in terms of fracture mechanics terminology, the above conclusions can only be achieved when the bridging zone is significantly smaller than the contact size. This adhesion-fracture analogy study leads to mechanistic predictions that can be readily used to design biomimetics and releasable adhesives.

Macroscopic model with anisotropy based on micro–macro information

Physical experiments can characterize the elastic response of granular materials in terms of macroscopic state variables, namely volume (packing) fraction and stress, while the microstructure is not accessible and thus neglected. Here, by means of numerical simulations, we analyze dense, frictionless granular assemblies with the final goal to relate the elastic moduli to the fabric state, i.e., to microstructural averaged contact network features as contact number density and anisotropy. The particle samples are first isotropically compressed and then quasi-statically sheared under constant volume (undrained conditions). From various static, relaxed configurations at different shear strains, infinitesimal strain steps are applied to “measure” the effective elastic response; we quantify the strain needed so that no contact and structure rearrangements, i.e. plasticity, happen. Because of the anisotropy induced by shear, volumetric and deviatoric stresses and strains are cross-coupled via a single anisotropy modulus, which is proportional to the product of deviatoric fabric and bulk modulus (i.e., the isotropic fabric). Interestingly, the shear modulus of the material depends also on the actual deviatoric stress state, along with the contact configuration anisotropy. Finally, a constitutive model based on incremental evolution equations for stress and fabric is introduced. By using the previously measured dependence of the stiffness tensor (elastic moduli) on the microstructure, the theory is able to predict with good agreement the evolution of pressure, shear stress and deviatoric fabric (anisotropy) for an independent undrained cyclic shear test, including the response to reversal of strain.

Internal Structure of Inertial Granular Flows

We analyze inertial granular flows and show that, for all values of the inertial number I, the effective friction coefficient μ arises from three different parameters pertaining to the contact network and force transmission: (1)contact anisotropy, (2)force chain anisotropy, and (3)friction mobilization. Our extensive 3D numerical simulations reveal that μ increases with I mainly due to an increasing contact anisotropy and partially by friction mobilization whereas the anisotropy of force chains declines as a result of the destabilizing effect of particle inertia. The contact network undergoes topological transitions, and beyond I≃0.1 the force chains break into clusters immersed in a background "soup" of floating particles. We show that this transition coincides with the divergence of the size of fluidized zones characterized from the local environments of floating particles and a slower increase of μ with I.

Nonlinear effects of particle shape angularity in sheared granular media

We analyze the effects of particle shape angularity on the macroscopic shear behavior and texture of granular packings simulated by means of the contact dynamics method. The particles are regular polygons with an increasing number of sides ranging from 3 (triangles) to 60. The packings are analyzed in the steady shear state in terms of their shear strength, packing fraction, connectivity, and fabric and force anisotropies, as functions of the angularity. An interesting finding is that the shear strength increases with angularity up to a maximum value and saturates as the particles become more angular (below six sides). In contrast, the packing fraction declines towards a constant value, so that the packings of more angular particles are looser but have higher shear strength. We show that the increase of the shear strength at low angularity is due to an increase of both contact and force anisotropies and the saturation of the shear strength for higher angularities is a consequence of a rapid falloff of the contact and normal force anisotropies compensated for by an increase of the tangential force anisotropy. This transition reflects clearly the rather special geometrical properties of these highly angular shapes, implying that the stability of the packing relies strongly on the side-side contacts and the mobilization of friction forces.

Crystallinity Control of Ferromagnetic Contacts in Stressed Nanowire Templates and the Magnetic Domain Anisotropy

We report the controlled growth of single-crystalline ferromagnetic contacts through solid state reaction at nanoscale. Single-crystal Mn(5)Si(3) and Fe(5)Ge(3) contacts were grown within stressed Si and Ge nanowire templates, where oxide-shells were used to exert compressive stress on the silicide or germanide. Compared to polycrystalline silicide and germanide structures observed within bare nanowires, the built-in high strain in the oxide-shelled nanostructures alters the nucleation behavior of the ferromagnetic materials, leading to single crystal growth in the transverse/radial direction. Interestingly, the compressive stress is also found to affect the magnetic anisotropy of the ferromagnetic contacts. In-plane and out-of-plane magnetization were observed in Fe(5)Ge(3) for different crystal orientations, showing distinctly preferred domain orientations. These interesting results display the capability to control both the crystallinity and the magnetic anisotropy of ferromagnetic contacts in engineered nanostructures.