Title: Convex contact dynamics methods with friction: granular flow and generated elastic waves
Abstract: This work deals with the modeling of dense granular media and their interactions with acoustic phenomena at the laboratory scale. The models that are developed in order to describe the movement of grains can be classified into the category of non-smooth discrete methods, often referred to as “contact dynamics”. When we consider the friction forces between particles in these models, we obtain constrained optimization problems which are not convex in general. Two convex approaches to the modeling of friction forces in contact dynamics are proposed here. Nowadays, the links between granular flows and the elastic wave propagation are an important topic. In particular, the acoustic signal emitted by these flows as well as the wave propagation withinthe medium itself are current research topics. Two studies are proposed here that concerns the relations between granular assembly and generated elastic waves propagation. In particular, a wavepropagation model is proposed, with its variables defined as the infinitesimal perturbations of the grain positions around equilibrium configurations.
Discrete Elements Modelling: In collaboration with Bertrand MAURY and Aline LEFEBVRE-LEPOT. We are developing a new Discrete Element Method to take into account the friction between rigid spheres in a non-linear model based on the work of Bertrand MAURY in 2005. The aim is to build a numerical scheme to prevent overlaps between beads regardless of the time-step values, hence allowing the possibility of using larger time-steps during time integration. Few examples of numerical simulations: The color scale represents the velocity norm:
Waves Propagation Modelling in a Granular Assembly: In collaboration with Bertrand MAURY and Aline LEFEBVRE-LEPOT. We are developing a wave propagation model at an entirely different scale from the model described before. The mechanical system is moving around a given configuration by infinitesimal perturbations of its degrees of freedom. Some interesting quantities can be easily extracted like the main frequency of each contact or the associated amplitude.
Simulations by Discrete Elements Method, comparison with experimental data: We used the code MODY-GS, a Molecular Dynamics model developed by Patrick RICHARD to compare simulations of granular column collapse with experiments performed by Maxime FARIN.
H. Martin, B. Maury, A. Lefebvre-Lepot, Y. Maday & A. Mangeney -Full convex approach of the global multi-contacts dry friction problem (to be submitted)
H. Martin, B. Maury, A. Lefebvre-Lepot, Y. Maday & A. Mangeney - Wave propagation modeling in granular assemblies, coupling with a NSCD method (in prep.)
S. Viroulet, H. Martin, M. Peruzzetto, A. Mangeney, P.-Y. Lagrée, S. Popinet & F. Bouchut - Numerical simulations of granular column collapse: computation of the constraints applied on the ground (in prep)