Archives de catégorie : Articles

A contact dynamics code implementation for the simulation of asteroid evolution and regolith in the asteroid environment

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.

Compaction of mixtures of rigid and highly deformable particles: A micromechanical model

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.

Combined effects of contact friction and particle shape on strength properties and microstructure of sheared granular media

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.

Particle-scale views of the normal force network of six packings, for different values of local friction μs and particle angularity. Forces are represented as lines, whose thickness is proportional to the force magnitude.

Microstructural analysis of sheared polydisperse polyhedral grains

David Cantor, Emilien Azéma, and Itthichai Preechawuttipong Phys. Rev. E 101, 062901 – Published 1 June 2020

Snapshots of samples composed of 19000 octahedra with grain size span corresponding to  S = 0.8.

This article presents an analysis of the shear strength of numerical samples composed of polyhedra presenting a grain size dispersion. Previous numerical studies using, for instance, disks, polygons, and spheres, have consistently shown that microstructural properties linked to the fabric and force transmission allow granular media to exhibit a constant shear resistance although packing fraction can dramatically change as a broader grain-size distribution is considered. To have a complete picture of such behavior, we developed a set of numerical experiments in the frame of the discrete element method to test the shear strength of polydisperse samples composed of polyhedral grains. Although the contact networks and force transmission are quite more complex for such generalized grain shape, we can verify that the shear strength independence still holds up for 3D regular polyhedra. We make a particular focus upon the role of different contact types in the assemblies and their relative contributions to the granular connectivity and sample strength. The invariance of shear strength at the macroscopic scale results deeply linked to fine compensations at the microstructural level involving geometrical and force anisotropies of the assembly.

Compaction Model for Highly Deformable Particle Assemblies

D. Cantor, M. Cardenas-Barrantes, I. Preechawuttipong, M. Renouf and E. Azéma, Phys. Rev. Letters 124, 208003 (2020). – Editors’ Suggestion –
go.aps.org/2LJOEhZ

The color intensities are proportional to the volumetric deformation within the particles.

The compaction behavior of deformable grain assemblies beyond jamming remains bewildering, and existing models that seek to find the relationship between the confining pressure P and solid fraction φ end up settling for empirical strategies or fitting parameters. Using a coupled discrete-finite element method, we analyze assemblies of highly deformable frictional grains under compression. We show that the solid fraction evolves nonlinearly from the jamming point and asymptotically tends to unity. Based on the micromechanical definition of the granular stress tensor, we develop a theoretical model, free from ad hocparameters, correctly mapping the evolution of φ with P. Our approach unveils the fundamental features of the compaction process arising from the joint evolution of grain connectivity and the behavior of single representative grains. This theoretical framework also allows us to deduce a bulk modulus equation showing an excellent agreement with our numerical data.

Impact of grading on steady-state strength

S. Linero, E. Azéma, N. Estrada, S. Fityus, J. Simmons, A. Lizcano « Impact of grading on steady-state strength » Geotechnique Letters, Vol 9, Issue 3 (2019)

In the mining industry, waste-dumps are earthen structures typically built by loose waste tipping. They may reach heights of hundreds of meters and undergo large deformations. For this reason, their stability design is based on the steady-state shear strength of the waste material. Waste materials are widely graded and may contain particles of up to metric order. Particle shape depends on the pattern of dissecting discontinuities at the source rock mass, and the relation between the size of the fragments and discontinuity spacing. The shear strength of this material is determined in the laboratory using scaled samples with altered Particle Size Distribution (PSD). However, altering the PSD is known to impact shear strength, and this impactis poorly studied. The representativeness of laboratory parameters obtained from scaled samples is thus arguable. Discrete element simulations are used here to investigate steady-state shear strength changes with alteration of the PSD when particle size and shape are correlated. It is observed, that shear strength changes result from the variation of the particle shapes induced by the alteration of the PSD. Consequently, identifying size-shape correlations and their potential impact on shear-strength is paramount when scaling materials for laboratory testing.

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.