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

Contribution of Probabilistic Grammar Inference with K-Testable Language for Knowledge Modeling: Application on aging people

International audienceWe investigate the contribution of unsupervised learning and regular grammatical inference to respectively identify profiles of elderly people and their development over time in order to evaluate care needs (human, financial and physical resources). The proposed approach is based on k-Testable Languages in the Strict Sense Inference algorithm in order to infer a probabilistic automaton from which a Markovian model which has a discrete (finite or countable) state-space has been deduced. In simulating the corresponding Markov chain model, it is possible to obtain information on population ageing. We have verified if our observed system conforms to a unique long term state vector, called the stationary distribution and the steady-state

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

Numerical simulations of granular media composed with irregular polyhedral particles: effect of particles’ angularity

We use contact dynamic simulations to perform a systematic investigation of the effects of particles shape angularity on mechanicals response in sheared granular materials. The particles are irregular polyhedra with varying numbers of face from spheres to “double pyramid” shape with a constant aspect ratio. We study the quasi-static behavior, structural and force anisotropies of several packings subjected to triaxial compression. An interesting finding is that the shear strength first increases with angularity up to a maximum value and then saturates as the particles become more angular. Analyzing the anisotropies induced by the angular distributions of contacts and forces orientations, we show that the saturation of the shear strength at higher angularities is a consequence of fall-off of the texture anisotropies compensated by an increase of the tangential force anisotropy. This is attributed to the fact that at higher angularity, particles are better connected (or surrounded) leading to an increase of friction mobilization in order to achieve the deformation. Moreover, the most angular particles also have very few sides so that, this effect is enhanced by the increase of the proportion of face-side and side-side contacts with angularity

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

Short-time dynamics of a packing of polyhedral grains under horizontal vibrations

We analyze the dynamics of a 3D granular packing composed of particles of irregular polyhedral shape confined inside a rectangular box with a retaining wall sub jected to horizontal harmonic forcing. The simulations are performed by means of the contact dynamics method for a broad set of loading parameters. We explore the vibrational dynamics of the packing, the evolution of solid fraction and the scaling of dy- namics with the loading parameters. We show that the motion of the retaining wall is strongly anharmonic as a result of jamming and grain rearrangements. It is found that the mean particle displacement scales with inverse square of frequency, the inverse of the force amplitude and the square of gravity. The short- time compaction rate grows in proportion to frequency up to a characteristic frequency, corresponding to collective particle rearrangements between equilibrium states, and then it declines in inverse proportion to frequency

Internal friction and absence of dilatancy of packings of frictionless polygons

International audienceBy means of numerical simulations, we show that assemblies of frictionless rigid pentagons in slow shear flow possess an internal friction coefficient (equalto0.183±0.008 with our choice of moderately polydisperse grains) but no macroscopic dilatancy. In other words, despite side-side contacts tending to hinder relative particle rotations, the solidfraction under quasistatic shear coincides with that of isotropic random close packings of pentagonal particles. Properties of polygonal grains are thus similar to those of disks in that respect. We argue that continuous reshuffling of the force-bearing network leads to frequent collapsing events at the microscale, thereby causing the macroscopic dilatancy to vanish. Despite such rearrangements, the shear flow favors an anisotropic structure that is at the origin of the ability of the system to sustain shear stress

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

Multiplicative decompositions and frequency of vanishing of nonnegative submartingales

In this paper, we establish a multiplicative decomposition formula for nonnegative local martingales and use it to characterize the set of continuous local submartingales Y of the form Y=N+A, where the measure dA is carried by the set of zeros of Y. In particular, we shall see that in the set of all local submartingales with the same martingale part in the multiplicative decomposition, these submartingales are the smallest ones. We also study some integrability questions in the multiplicative decomposition and interpret the notion of saturated sets in the light of our results.Comment: Typos corrected. Close to the published versio