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.

P. Sanchez, M. Renouf, E. Azéma, R. Mozul and F. Dubois, A contact dynamics code implementation for the simulation of asteroid evolution and regolith in the asteroid environment, ICARUS, 363, 114441 (2021). https://www.sciencedirect.com/science/article/pii/S0019103521001238?via%3Dihub

Over the last decades, simulations by discrete elements methods (DEM) have proven to be a reliable analysis tool in various domains of science and engineering. By providing access to the local physical mechanisms, DEM allows the exploration of microscopic based phenomena related to particles properties and interactions in various conditions and to revisit constitutive equations consequently. The growing computer power and memory now allow us to handle large collections of grains of various shapes and sizes by DEM simulations and in particular, it offers new perspectives in the exploration of the behavior of asteroids seen as self-gravitating and cohesive granular aggregates. In this paper we describe the Contact Dynamics (CD) method, a class of DEM based on non-smooth mechanics, and its implementation in the open-source software LMGC90. In contrast to more classical approach, Hard- and Soft-Sphere DEM, the CD method is based on an implicit time integration of the equations of motion and on a non-regularized formulation of mutual exclusion between particles. This numerical strategy is particularly relevant to the study of dense granular assemblies (even of large size) because it does not introduce numerical artifacts due to contact stiffness. So that it can be used for Small Body research, we implement a parallelized kd-tree and monitor the performance of the code as it simulates a number of granular systems. We provide examples of the simulation of the accretion of self-gravitating aggregates as well as their rotational disruption. We use the routines at our disposal in the code to monitor their behavior through the entire evolution and find agreement with previous research.

M. Cardenas-Barrantes, D. Cantor, J. Barés, M. Renouf and  E. Azéma, Compaction of mixtures of rigid and highly deformable particles: A micromechanical model , Phys. Rev. E, 102, 032904 (2020). https://journals.aps.org/pre/abstract/10.1103/PhysRevE.102.032904

We analyze the isotropic compaction of mixtures composed of rigid and deformable incompressible particles by the nonsmooth contact dynamics approach. The deformable bodies are simulated using a hyperelastic neo-Hookean constitutive law by means of classical finite elements. We characterize the evolution of the packing fraction, the elastic modulus, and the connectivity as a function of the applied stresses when varying the interparticle coefficient of friction. We show first that the packing fraction increases and tends asymptotically to a maximum value φmax , which depends on both the mixture ratio and the interparticle friction. The bulk modulus is also shown to increase with the packing fraction and to diverge as it approaches φmax . From the micromechanical expression of the granular stress tensor, we develop a model to describe the compaction behavior as a function of the applied pressure, the Young modulus of the deformable particles, and the mixture ratio. A bulk equation is also derived from the compaction equation. This model lays on the characterization of a single deformable particle under compression together with a power-law relation between connectivity and packing fraction. This compaction model, set by well-defined physical quantities, results in outstanding predictions from the jamming point up to very high densities and allows us to give a direct prediction of φmax as a function of both the mixture ratio and the friction coefficient.

Theechalit Binaree, Emilien Azéma, Nicolas Estrada, Mathieu Renouf, and Itthichai Preechawuttipong Phys. Rev. E 102, 022901 – Published 3 August 2020

We present a systematic numerical investigation concerning the combined effects of sliding friction and particle shape (i.e., angularity) parameters on the shear strength and microstructure of granular packings. Sliding friction at contacts varied from 0 (frictionless particles) to 0.7, and the particles were irregular polygons with an increasing number of sides, ranging from triangles to disks. We find that the effect of local friction on shear strength follows the same trend for all shapes. Strength first increases with local friction and then saturates at a shape-dependent value. In contrast, the effect of angularity varies, depending on the level of sliding friction. For low friction values (i.e., under 0.3), the strength first increases with angularity and then declines for the most angular shapes. For high friction values, strength systematically increases with angularity. At the microscale, we focus on the connectivity and texture of the contact and force networks. In general terms, increasing local friction causes these networks to be less connected and more anisotropic. In contrast, increasing particle angularity may change the network topology in different directions, directly affecting the macroscopic shear strength. These analyses and data constitute a first step toward understanding the joint effect of local variables such as friction and grain shape on the macroscopic rheology of granular systems.