• Informatique/Modélisation et simulation
  
• Physique/Mécanique/Mécanique des solides
  

Granular asteroids are naturally occurring gravitational aggregates (rubble piles) bound together by gravitational forces. For this reason, it is reasonable to use the theoretical concepts and numerical tools developed for granular media to study them. In this paper, we extend the field of applicability of the Contact Dynamic (CD) method, a class of non smooth discrete element approach, for the simulation of three dimensional granular asteroids. The CD method is particularly relevant to address the study of dense granular assemblies of a large number of particles of complex shape and broad particles size distribution, since it does not introduces numerical artefacts due to contact stiffness. We describe how the open source software LMGC90, interfaced with an external library for the calculation of self-gravity, is used to model the accretion process of spherical and irregular polyhedral particles.

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 artefacts due to contact stiffness. So that it can be used for Small Body research, we implement a parallelised 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 behaviour through the entire evolution and find agreement with previous research.

Discrete Element Method aim to model the collective behavior of a media composed of distinct interacting particles, and constitute a significant support to experimentation in the sense that they give us access to informations that are difficult to obtain experimentally. Discrete element methods can be classified into two main families: 1) Non Smooth approaches based on non-regular mechanics that take into account shocks without grain interpenetration; and 2) Smooth approaches allowing grains interpenetration. Here, we aim to introduce the Non-smooth Contact Dynamics method, its implementation in LMGC90, as a class of Non Smooth approach, to the Planetary Sciences community. We apply the CD method to model the accretion of spherical and polyhedral particles, and we discuss on the numerical efficiency of the CD method for modeling granular asteroids.

Xper est un outil numérique parallèle développé dans le cadre du laboratoire commun MIST pour l’étude des interactions entre corps rigides ou déformables. Les interactions concernent d’une part la séparation dans le cadre de la rupture thermo-mécanique et dynamique de matériaux hétérogènes et d’autre part le contact frottant entre particules en présence de fluide. La plateforme numérique repose sur le couplage du logiciel LMGC90 (Dynamique des Contacts) pour la prise en compte d’interactions com- plexes entre les corps et de la bibliothèque PELICANS pour la résolution des comportements volumiques (Éléments finis ou Volumes Finis) des corps.

LMGC90 is an open platform dedicated to the modeling of large collections of interacting objects (2D/3D). It aims at modeling objects of any shape with various mechanical behavior and to take into account interaction laws as complex as necessary. Furthermore multiple physics couplings (thermal effects, fluids, etc ) are progressively taken into account.