Modèles et algorithmes pour la simulation du contact frottant dans les matériaux complexes : application aux milieux fibreux et granulaires

Abstract : This dissertation focuses on the numerical simulation of mechanical systems consisting of a large number of discrete pieces interacting with each other through contacts and dry friction. Examples of such systems --- for instance, sand or human hair --- are common in natural environments; being able to predict their dynamics is therefore of great importance for diverse applications ranging from geotechnical considerations to engaging visual effects for feature films.A major difficulty that complicates the numerical simulation of such complex systems stems from the nonsmoothness of their dynamics. For instance, from a macroscopic viewpoint, the velocity of the individual constituents may exhibit instantaneous jumps when impacts occur.The first part of this manuscript will be dedicated to the establishment of efficient algorithms for the numerical simulation of discrete mechanical systems subject to contacts and Coulomb friction. We advocate using a Gauss--Seidel algorithm with a hybrid local solver, and show that this strategy performs robustly in the challenging context of virtual hair simulation.The second part of this dissertation will focus on much bigger systems, consisting of millions or billions of grains.As computing every force between pairs of contacting grains quickly becomes intractable, we embrace a continuum viewpoint instead. We show how the numerical methods devised for the simulation of discrete mechanical systems can be adapted to thesimulation of flows governed by the Drucker--Prager rheology --- a constitutive relationship between the material's stress and strain rate that macroscopically models the action of frictional contact forces. This approach allows us to capture qualitative features of granular flows that have been observed experimentally. Finally, we propose a new numerical model for the coupled simulation of a granular continuum with a surrounding fluid, and show that once again, we are able to leverage efficient algorithms from discrete contact mechanics to solve the resulting equations.
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Gilles Daviet. Modèles et algorithmes pour la simulation du contact frottant dans les matériaux complexes : application aux milieux fibreux et granulaires. Algorithme et structure de données [cs.DS]. Université Grenoble Alpes, 2016. Français. ⟨NNT : 2016GREAM084⟩. ⟨tel-01684673⟩

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