Archives de catégorie : Articles

Effects of particle shape mixture on strength and structure of sheared granular materials

Theechalit Binaree, Itthichai Preechawuttipong,  and Emilien Azéma. PHYSICAL REVIEW E 100, 012904 (2019)

Closeup views of some of the samples at the end of the isotropic compression.

Using bi-dimensional discrete element simulations, the shear strength and microstructure of granular mixtures composed of particles of different shapes are systematically analyzed as a function of the proportion of grains of a given number of sides and the combination of different shapes (species) in one sample. We varied the angularity of the particles by varying the number of sides of the polygons from 3 (triangles) up to 20 (icosagons) and disks. The samples analyzed were built keeping in mind the following cases: (1) increase of angularity and species starting from disks; (2) decrease of angularity and increase of species starting from triangles; (3) random angularity and increase of species starting from disks and from polygons. The results show that the shear strength vary monotonically with increasing numbers of species (it may increase or decrease), even in the random mixtures (case 3). At the micro-scale, the variation in shear strength as a function of the number of species is due to different mechanisms depending on the cases analyzed. It may result from the increase of both the geometrical and force anisotropies, from only a decrease of frictional anisotropy, or from compensation mechanisms involving geometrical and force anisotropies.

Rheology and structure of polydisperse three-dimensional packings of spheres

David Cantor, Emilien Azéma, Philippe Sornay and Farhang Radjaï, Physical Review E,98, 052910 (2018)

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.

Scaling behavior of cohesive self-gravitating aggregates

Emilien Azéma,  Paul Sánchez, and Daniel J. Scheeres. Physical review E (Rapid Communication) 98 030901(R) (2018)

Snapshots of a simulated granular asteroid under diamet- rical compression for (a) εh = 0 and (b) εh = 0.1. Force chains are represented by lines joining the centers of two touching particles. Compressive forces in red, and tensile forces in blue.

By means of extensive three-dimensional contact dynamics simulations, we analyze the strength properties and microstructure of a granular asteroid, modeled as a self-gravitating cohesive granular aggregate composed of spherical particles, and subjected to diametrical compression tests. We show that, for a broad range of system parameters (shear rate, cohesive forces, asteroid diameter), the behavior can be described by a modified inertial number that incorporates interparticle cohesion and gravitational forces. At low inertial numbers, the behavior is ductile with a well-defined stress peak that scales with internal pressure with a prefactor ≃ 0.9. As the inertial number increases, both the prefactor and fluctuations around the mean increase, evidencing a dynamical crisis resulting from the destabilizing effect of particle inertia. From a micromechanical description of the contact and force networks, we propose a model that accounts for solid fraction, local stress, particle connectivity, and granular texture. In the limit of small inertial numbers, we find a very good agreement of the theoretical estimate of compressive strength, evidencing the major role of these structural parameters for the modeled aggregates.

Rheology of granular materials composed of crushable particles

D.-H. Nguyen, E. Azéma,  P. Sornay and F. Radjaï, «Rheology of granular materials composed of crushable particles  » Eur. Phys. J. E (2018) 41: 50

Snapshots of a portion of the contact network. The contacts are represented by segments joining particle centers. The gray level of particles is proportional to the coordination number.

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

Emilien Azéma, Farhang Radjaï and Jean-Noël Roux, Eur. Phys. J. E (2018) 41: 2

Clusters of particles at I = 4.10−5 (a), I = 10−3 (b), I = 10−2 (c) and I = 0.25 (d) Disjoint clusters are represented in different colors (green, orange, purple and cardinal red). The Inset shows the evolution of macroscopic friction with I.

Motivated by the understanding of shape effects ingranular 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, de- pending on inertial number I, which ranges from the quasistatic limit (I ∼ 10−5) 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 φ, an increasing function of I, and solid fraction ν, a decreasing function of I, are larger with pentagons than with disks at small I, but the differences decline for larger I and, remark- ably, nearly vanish for I ∼ 0.2. 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.

Three-dimensional bonded-cell model for grain fragmentation

D. Cantor, E. Azéma, P. Sornay and  F. Radjai, Comp. Part. Mech.
DOI 10.1007/s40571-016-0129-0

Snapshots of a particle composed of 75 cells undergoing incip- ient breakage under the action of a vertical force

We present a three-dimensional numerical method for the simulation of particle crushing in 3D. This model is capable of producing irregular angular fragments upon par- ticle fragmentation while conserving the total volume. The particle is modeled as a cluster of rigid polyhedral cells gen- erated by a Voronoi tessellation. The cells are bonded along their faces by a cohesive Tresca law with independent tensile and shear strengths and simulated by the contact dynam- ics method. Using this model, we analyze the mechanical response of a single particle subjected to diametral compres- sion for varying number of cells, their degree of disorder, and intercell tensile and shear strength. In particular, we iden- tify the functional dependence of particle strength on the intercell strengths. We find that two different regimes can be distinguished depending on whether intercell shear strength is below or above its tensile strength. In both regimes, we observe a power-law dependence of particle strength on both intercell strengths but with different exponents. The strong effect of intercell shear strength on the particle strength reflects an interlocking effect between cells. In fact, even at low tensile strength, the particle global strength can still considerably increase with intercell shear strength. We finally show that the Weibull statistics describes well the particle strength variability.

Shear strength and microstructure of polydisperse packings: The effect of size span and shape of particle size distribution

Emilien Azéma, Sandra Linéro, Nicolas Estrada and Arcesio Lizcano, Phys. Rev E, 96 022902 2017

Snapshots at the end of the isotropic compression for different combinations of size span and shape of particle size distribution

By means of extensive contact dynamics simulations, we analyzed the effect of particle size distribution (PSD) on the strength and microstructure of sheared granular materials composed of frictional disks. The PSDs are built by means of a normalized β function, which allows the systematic investigation of the effects of both, the size span (from almost monodisperse to highly polydisperse) and the shape of the PSD (from linear to pronouncedly curved). We show that the shear strength is independent of the size span, which substantiates previous results obtained for uniform distributions by packing fraction. Notably, the shear strength is also independent of the shape of the PSD, as shown previously for systems composed of frictionless disks. In contrast, the packing fraction increases with the size span, but decreases with more pronounced PSD curvature. At the microscale, we analyzed the connectivity and anisotropies of the contacts and forces networks. We show that the invariance of the shear strength with the PSD is due to a compensation mechanism which involves both geometrical sources of anisotropy. In particular, contact orientation anisotropy decreases with the size span and increases with PSD curvature, while the branch length anisotropy behaves inversely.

Binary mixtures of disks and elongated particles: Texture and mechanical properties

Emilien Azéma,  Itthichai Preechawuttipong,  and Farhang Radjai, PHYSICAL REVIEW E 94, 042901 (2016)

Snapshots of force-bearing particles in a segregated packing

We analyze the shear strength and microstructure of binary granular mixtures consisting of disks and elongated particles by varying systematically both the mixture ratio and degree of homogeneity (from homogeneous to fully segregated). The contact dynamics method is used for numerical simulations with rigid particles interacting by frictional contacts. A counterintuitive finding of this work is that the shear strength, packing fraction, and, at the microscopic scale, the fabric, force, and friction anisotropies of the contact network are all nearly independent of the degree of homogeneity. In other words, homogeneous mixtures have the same strength properties as segregated packings of the two particle shapes. In contrast, the shear strength increases with the proportion of elongated particles correlatively with the increase of the corresponding force and fabric anisotropies. By a detailed analysis of the contact network topology, we show that various contact types contribute differently to force transmission and friction mobilization.

Scaling behaviour of cohesive granular flows

Nicolas Berger, Emilien Azéma, Jean-François Douce and Farhang Radjai EPL 112 (2015) 6004

Plane shear simulation. Black particles compose the rough walls. The periodic left-right boundaries are marked by gray particles.

The shear strength of dense granular flows is generally described by an effective friction coefficient, ratio of shear to normal stress, as a function of the inertial number I. However, this ratio depends on the normal stress when the particles interact via both friction and adhesion forces, and in this sense it does not properly represent a Coulomb-like friction. For the same reason, it is not a unique function of I. We used extensive contact dynamics simulations to isolate the cohesive strength from the purely frictional strength in dense inertial flows for a broad range of shear rates and adhesion forces between particles. Remarkably, while the frictional part of the strength increases with I, the cohesive strength is found to be a decreasing function of I. We show that a single dimensionless parameter, combining interparticle adhesion with I, controls not only the cohesive strength but also the packing fraction and granular text

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

Duc-Hanh Nguyen, Emilien Azéma, Philippe Sornay,  and Farhang Radjai, PHYSICAL REVIEW E 91, 032203 (2015)

Snapshots of force-bearing particles in polydisperse packing

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.