A. Bignon, M. Renouf, R. Sicard and E. Azéma Nonlinear effect of grain elongation on the flow rate in silo discharge, Phys. Rev. E, 108, 054901 (2023)

By means of two-dimensional numerical simulations based on contact dynamics, we present a systematic analysis of the joint effects of grain shape (i.e., grain elongation) and system size on silo discharge for increasing orifice sizes D. Grains are rounded-cap rectangles whose aspect ratio are varied from 1 (disks) to 7. In order to clearly isolate the effect of grain shape, the mass of the grains is keeping constant as well as the condition of the discharge by reintroducing the exiting grains at the top of the silo. In order to quantify the possible size effects, the thickness W of the silos is varied from 7 to 70 grains diameter, while keeping the silos aspect ratio always equal to 2. We find that, as long as size effects are negligible, the flow rate Q increases as a Beverloo-like function with D, also for the most elongated grains. In contrast, the effects of grain elongation on the flow rate depend on orifice size. For small normalized orifice sizes, the flow rate is nearly independent with grain elongation. For intermediate normalized orifice sizes the flow rate first increases with grain elongation up to a maximum value that depends on the normalized size of the orifice and saturates as the grains become more elongated. For larger normalized orifice size, the flow rate is an increasing function of grains’ aspect ratio. Velocity profiles and packing fraction profiles close to the orifice turn out to be self-similar for all grain shapes and for the whole range of orifice and system sizes studied. Following the methodology introduced by Janda et al. [Phys. Rev. Lett. 108, 248001 (2012)], we explain the nonlinear variation of Q with grain elongation, and for all orifice sizes, from compensation mechanisms between the velocity and packing fraction measured at the center of the orifice. Finally, an equation to predict the evolution of Q as a function of the aspect ratio of the grains is deduced.

J. Barés, M. Cárdenas-Barrantes, G. Pinzón, E. Andò, M. Renouf, G. Viggiani, and E. Azéma Compacting an assembly of soft balls far beyond the jammed state: Insights from three-dimensional imaging, Phys. Rev. E, 108, 044901 (2023) https://journals.aps.org/pre/abstract/10.1103/PhysRevE.108.044901

Very soft grain assemblies have unique shape-changing capabilities that allow them to be compressed far beyond the rigid jammed state by filling void spaces more effectively. However, accurately following the formation of these systems by monitoring the creation of new contacts, monitoring the changes in grain shape, and measuring grain-scale stresses is challenging. We developed an experimental method that overcomes these challenges and connects their microscale behavior to their macroscopic response. By tracking the local strain energy during compression, we reveal a transition from granular-like to continuous-like material. Mean contact geometry is shown to vary linearly with the packing fraction, which is supported by a mean field approximation. We also validate a theoretical framework which describes the compaction from a local view. Our experimental framework provides insights into the granular micromechanisms and opens perspectives for rheological analysis of highly deformable grain assemblies in various fields ranging from biology to engineering.

N. Coppin, M. Henry, M. Cabrera, E. Azéma, F. Dubois, V. Legat, J. Lambrechts, Collapse dynamics of two-dimensional dry and immersed granular columns of elongated grains, Phys. Rev. Fluids, 8,094303 (2023)

The collapse dynamics and runout of columns of elongated grains in two dimensions are numerically investigated in dry and immersed conditions, by means of an unresolved finite elements/discrete elements model. The elongated grains are modeled as rigid aggregates of disks. The column aspect ratio is systematically varied from 0.125 to 16 in order to span short and tall columns. To analyze the effect of the initial grain orientation, columns with an initial grain orientation that is either random or aligned with a given direction are both considered. Collapse dynamics, both in dry and immersed cases, are found analogous to that previously observed for circular grain columns, particularly with respect to the power law dependency for the runout as a function of the column aspect ratio. The effect of the fluid mainly results in a decrease of the runout distance. Inter- estingly, the collapse dynamics and runout are not significantly affected by the initial orientation of the grains, except maybe in the extreme case where the grains are all horizontally oriented, which geometrically prevents the collapse. Finally, a scaling based on the front propagation energy is proposed allowing one to unify the runout of short to tall and dry to immersed columns in a single description, regardless of the initial grain orientation.

O. Polania, M. Cabrera, M. Renouf, E. Azéma and Nicolas Estrada, Grain size distribution does not affect the residual shear strength of granular materials: An experimental proof, Phys. Rev. E-Letter, 107, L052901 (2023)

Granular materials are used in several fields and in a wide variety of processes. An important feature of these materials is the diversity of grain sizes, commonly referred to as polydispersity. When granular materials are sheared, they exhibit a predominant small elastic range. Then, the material yields, with or without a peak shear strength depending on the initial density. Finally, the material reaches a stationary state, in which it deforms at a constant shear stress, which can be linked to the residual friction angle φr. However, the role of polydispersity on the shear strength of granular materials is still a matter of debate. In particular, a series of investigations have proved, using numerical simulations, that φr is independent of polydispersity. This counterintuitive observation remains elusive to experimentalists, and especially for some technical communities that use φr as a design parameter (e.g., the soil mechanics community). In this Letter, we studied experimentally the effects of polydispersity on φr . In order to do so, we built samples of ceramic beads and then sheared these samples in a triaxial apparatus. We varied polydispersity, building monodisperse, bidisperse, and polydisperse granular samples; this allowed us to study the effects of grain size, size span, and grain size distribution on φr. We find that φr is indeed independent of polydispersity, confirming the previous findings achieved through numerical simulations. Our work fairly closes the gap of knowledge between experiments and simulations.

O. Polania, M. Cabrera, M. Renouf, and E. Azéma,Collapse of dry and immersed polydisperse granular columns: A unified runout description, Phys. Rev. Fluids, 7, 084304 (2022).
https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.7.084304

The granular column collapse is a simplified version of granular flows such as landslides, avalanches, and other industrial processes mobilized in air or within a fluid. In this configu- ration, the particles collapse in an accelerating phase, reaching a state of constant spreading velocity until they decelerate and stop. Granular flows commonly involve particles of different sizes, a property termed polydispersity. Understanding the role of polydispersity remains a challenging task that is often analyzed with nearly monodisperse systems and demanding a series of simplifications when coupled with a fluid in a numerical model. Here, we study the effect of particle-size polydispersity in dry and immersed granular columns, using a finite element method-discrete element method model for fluid-particle interactions. We show that the velocity of the column collapse and runout distance decrease with an increase in the level of polydispersity in immersed conditions, and remain nearly independent of the level of polydispersity in dry conditions. Moreover, we find that the runout scales with the spreading front kinetic energy, weighted by the ratio between the particles’ density and the density difference between particles and fluid. This scaling helps in identifying the governing processes in polydisperse granular columns, unifying the runout description of both dry and immersed collapses, and indicating that the column initial packing fraction is the governing parameter.

M. Cárdenas-Barrantes, J. Barés, M. Renouf, and E. Azéma,Experimental validation of a micromechanically based compaction law for mixtures of soft and hard grains, Phys. Rev. E, 106, L022901 (2022)

In this Letter, we report on an experimental study which analyzes the compressive behavior of two-dimensional bidisperse granular assemblies made of soft (hyperelastic) and hard grains in varying proportions (κ is the portion of soft grains). By means of a recently developed uniaxial compression setup [Vu and Barés, Phys. Rev. E 100, 042907 (2019)] and using an advanced digital image correlation method, we follow, beyond the jamming point, the evolution of the main mechanical observables, from the global scale down to the strain field inside each deformable grain. First, we validate experimentally and extend to the uniaxial case a recently proposed micromechanical compaction model linking the evolution of the applied pressure P to the packing fraction ϕ [Cantor  et al., Phys. Rev. Lett. 124, 208003 (2020)]. Second, we reveal two different linear regimes depending on whether the system is above or below a crossover strain unraveling a transition from a discrete to a continuous-like system. Third, the evolution of these linear laws is found to vary linearly with κ. These results provide a comprehensive experimental and theoretical framework that can now be extended to a more general class of polydisperse soft granular systems.

D. Cantor, C. Ovalle and  E. Azéma, Microstructural origins of crushing strength for inherently anisotropic brittle materials , International Journal of Solids and Structures 238 (2022) 111399.

We study the crushing strength of brittle materials whose internal structure (e.g., mineral particles or grains) 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 lets us reproduce experimental observations regarding the shape of the failure strength curve, the Weibull modulus, failure patterns of rocks, and quantify 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.

Manuel Cárdenas-Barrantes, David Cantor, Jonathan Barés, Mathieu Renouf, and Emilien Azéma. Soft Matter, 2022, https://doi.org/10.1039/D1SM01241J

This paper analyzes the compaction behavior of assemblies composed of soft (elastic) spherical particles beyond the jammed state, using three-dimensional non-smooth contact dynamic simulations. The assemblies of particles are characterized using the evolution of the packing fraction, the coordination number, and the von Misses stress distribution within the particles as the confining stress increases. The packing fraction increases and tends toward a maximum value close to 1, and the mean coordination number increases as a square root of the packing fraction. As the confining stress increases, a transition is observed from a granular-like material with exponential tails of the shear stress distributions to a continuous-like material characterized by Gaussian-like distributions of the shear stresses. We develop an equation that describes the evolution of the packing fraction as a function of the applied pressure. This equation, based on the micromechanical expression of the granular stress tensor, the limit of the Hertz contact law for small deformation, and the power-law relation between the packing fraction and the coordination of the particles, provides good predictions from the jamming point up to very high densities without the need for tuning any parameters.

M. Cardenas-Barrantes, D. Cantor, J. Barés, M. Renouf and  E. Azéma, Micromechanical description of the compaction of soft pentagon assemblies , Phys. Rev. E, 103, 062902 (2021)

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 experience larger particle rearrangements than circular particles, 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.