Microstructural origins of crushing strength for inherently anisotropic brittle materials

We study the crushing strength of brittle materials whose internal structure (e.g., mineral particles or graining) presents a layered arrangement reminiscent of sedimentary and metamorphic rocks. Taking a discrete-element approach, we probe the failure strength of circular-shaped samples intended to reproduce specific mineral configurations. To do so, assemblies of cells, products of a modified Voronoi tessellation, are joined in mechanically-stable layerings using a bonding law. The cells' shape distribution allows us to set a level of inherent anisotropy to the material. Using a diametral point loading, and systematically changing the loading orientation with respect to the cells' configuration, we characterize the failure strength of increasingly anisotropic structures. This approach ends up reproducing experimental observations and lets us quantify the statistical variability of strength, the consumption of the fragmentation energy, and the induced anisotropies linked to the cell's geometry and force transmission in the samples. Based on a fine description of geometrical and mechanical properties at the onset of failure, we develop a micromechanical breakdown of the crushing strength variability using an analytical decomposition of the stress tensor and the geometrical and force anisotropies. We can conclude that the origins of failure strength in anisotropic layered media rely on compensations of geometrical and mechanical anisotropies, as well as an increasing average radial force between minerals indistinctive of tensile or compressive components.Comment: 17 pages, 16 figures, submitted to the Journal of the Physics and Mechanics of Solid

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

Royal Golden Jubilee Ph.D Program (Grant No. PHD/0062/2558) under Thailand Research Fund (TRF) and French Embassy in ThailandInternational audienceUsing 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

Comparison of the effects of rolling resistance and angularity in sheared granular media

International audienceIn this paper, we compare the effect of rolling resistance at the contacts in granular systems composed of disks with the effect of angularity in granular systems composed of regular polygonal particles. For this purpose, we use contact dynamics simulations. By means of a simple shear numerical device, we investigate the mechanical behavior of these materials in the steady state in terms of shear strength, solid fraction, force and fabric anisotropies, and probability distribution of contact forces. We find that, based on the energy dissipation associated with relative rotation between two particles in contact, the effect of rolling resistance can explicitly be identified with that of the number of sides in a regular polygonal particle. This finding supports the use of rolling resistance as a shape parameter accounting for particle angularity and shows unambiguously that one of the main influencing factors behind the mechanical behavior of granular systems composed of noncircular particles is the partial hindrance of rotations as a result of angular particle shape

Structuration des écoulements granulaires

Nous analysons les propriétés microstructurales de systèmes granulaires cisaillés par simulations numériques discrètes. Les lois rhéologiques décrivant les écoulements de grains (i.e. relations entre contraintes normales, tangentielles, vitesse de cisaillement et compacité) peuvent être formulées à l’aide d’un nombre sans dimension I défini comme le rapport du temps inertiel par le temps de cisaillement. Les systèmes analysés sont dans un état quasi-statique, d’écoulement dense et collisionnel (ou gazeux), respectivement, en fonction de I. Nos données numériques, appuyées par des données expérimentales extraites de la littérature, montrent que la transition entre les régimes est caractérisée par une variation rapide de l’angle de frottement. Considérant un critère énergétique, nous montrons que la transition entre le régime d’écoulement dense et le régime collisionnel peut être identifié explicitement par un nombre inertiel critique I_0. De manière remarquable, nous montrons que la transition entre les régimes quasi-statique et d’écoulement dense se produit exactement à I_0^2, qui correspond au point où l’énergie cinétique injectée équilibre l’énergie potentielle du système. En analysant les corrélations spatiales entre particules flottantes (particules ne portant pas de contacts) nous montrons que des zones « fluidisées » se créent dans le régime d’écoulement dense. La taille de ces zones augmente avec I et diverge à l’approche de la transition vers le régime collisionel révélant ainsi la percolation des zones fluidisées. Par une décomposition additive du tenseur de contrainte basée sur une approximation harmonique des orientations moyennes des contacts et des forces, nous mettons en évidence que la variation de l’angle de frottement se déduit de celle de l’anisotropie structurelle elle-même liée à l’évolution de la connectivité moyenne des particules dans chaque régime. La diminution de l’anisotropie des forces normales en fonction du nombre d'inertie (due à l’inhomogénéité grandissante des forces normales) est compensée par l’augmentation de l’anisotropie tangentielle (mobilisation du frottement)

Force chains and contact network topology in packings of elongated particles

By means of contact dynamic simulations, we investigate the contact network topology and force chains in two-dimensional packings of elongated particles modeled by rounded-cap rectangles. The morphology of large packings of elongated particles in quasistatic equilibrium is complex due to the combined effects of local nematic ordering of the particles and orientations of contacts between particles. We show that particle elongation affects force distributions and force/fabric anisotropy via various local structures allowed by steric exclusions and the requirement of force balance. As a result, the force distributions become increasingly broader as particles become more elongated. Interestingly, the weak force network transforms from a passive stabilizing agent with respect to strong force chains to an active force-transmitting network for the whole system. The strongest force chains are carried by side/side contacts oriented along the principal stress direction.Comment: Soumis a Physical Review

Discrete simulation of dense flows of polyhedral grains down a rough inclined plane

International audienceThe influence of grain angularity on the properties of dense flows down a rough inclined plane are investigated. Three-dimensional numerical simulations using the Non-Smooth Contact Dynamics method are carried out with both spherical (rounded) and polyhedral (angular) grain assemblies. Both sphere and polyhedra assemblies abide by the flow start and stop laws, although much higher tilt angle values are required to trigger polyhedral grain flow. In the dense permanent flow regime, both systems show similarities in the bulk of the material (away from the top free surface and the substrate), such as uniform values of the solid fraction, inertial number and coordination number, or linear dependency of the solid fraction and effective friction coefficient with the inertial number. However, discrepancies are also observed between spherical and polyhedral particle flows. A dead (or nearly arrested) zone appear in polyhedral grain flows close to the rough bottom surface, reflected by locally concave velocity profiles, locally larger coordination number and solid fraction values, smaller inertial number values. This dead zone disappears for smooth bottom surface. In addition, unlike sphere assemblies, polyhedral grain assemblies exhibit significant normal stress differences, which increase close to the substrate

Rheology of three-dimensional packings of aggregates: Microstructure and effects of nonconvexity

International audienceWe use 3D contact dynamics simulations to analyze the rheological properties of granular materials composed of rigid aggregates. The aggregates are made from four overlapping spheres and described by a nonconvexity parameter depending on the relative positions of the spheres. The macroscopic and microstructural properties of several sheared packings are analyzed as a function of the degree of nonconvexity of the aggregates. We find that the internal angle of friction increases with nonconvexity. In contrast, the packing fraction increases first to a maximum value but declines as nonconvexity further increases. At high level of nonconvexity, the packings are looser but show a higher shear strength. At the microscopic scale, the fabric and force anisotropy, as well as friction mobilization are enhanced by multiple contacts between aggregates and interlocking, revealing thus the mechanical and geometrical origins of shear strength

Bulk modulus of soft particle assemblies under compression

Using a numerical approach based on the coupling of the discrete and finite element methods, we explore the variation of the bulk modulus K of soft particle assemblies undergoing isotropic compression. As the assemblies densify under pressure-controlled boundary conditions, we show that the non-linearities of K rapidly deviate from predictions standing on a small-strain framework or the Equivalent Medium Theory (EMT). Using the granular stress tensor and extracting the bulk properties of single representative grains under compression, we propose a model to predict the evolution of K as a function of the sample's solid fraction and a reference state as the applied pressure P tends to zero. The model closely reproduces the trends observed in our numerical experiments confirming the behavior scalability of soft particle assemblies from the individual particle scale. Finally, we present the effect of the interparticle friction on K's evolution and how our model easily adapts to such a mechanical constraint.Comment: 4 pages, 4 figure

Micromechanical description of the compaction of soft pentagon assemblies

We analyze the isotropic compaction of assemblies composed of soft pentagons interacting through classical Coulomb friction via numerical simulations. The effect of the initial particle shape is discussed by comparing packings of pentagons with packings of soft circular particles. We characterize the evolution of the packing fraction, the elastic modulus, and the microstructure (particle rearrangement, connectivity, contact force and particle stress distributions) as a function of the applied stresses. Both systems behave similarly; the packing fraction increases and tends asymptotically to a maximum value $\phi_{max}$, where the bulk modulus diverges. At the microscopic scale we show that particle rearrangements occur even beyond the jammed state, the mean coordination increases as a square root of the packing fraction and, the force and stress distributions become more homogeneous as the packing fraction increases. Soft pentagons present larger particle rearrangements than circular ones, and such behavior decreases proportionally to the friction. Interestingly, the friction between particles also contributes to a better homogenization of the contact force network in both systems. From the expression of the granular stress tensor, we develop a model that describes the compaction behavior as a function of the applied pressure, the Young modulus and the initial shape of the particles. This model, settled on the joint evolution of the particle connectivity and the contact stress, provides outstanding predictions from the jamming point up to very high densities