Monday 7th june 2021- Visio
Aline Lefebvre-Lepot, CMAP, École Polytechnique .

Title: Contacts in granular materials: numerical schemes based on convex optimization problems


In this presentation we focus on the numerical simulation of granular materials: collections of macroscopic non-Brownian and rigid grains (sand, cereals, sugar, rubble…).

The contacts between grains lead to singular interactions for which adapted numerical schemes must be developed. We consider the framework of “Contact Dynamics” type models developed by J.J. Moreau, using non-smooth convex analysis. The friction models between grains lead to complex non-convex optimization problems.

The objective of the presentation is to show how algorithms based, at each time, on convex optimization problems allow to obtain numerical simulations of large numbers of particles in long time. In these schemes, the contact forces are obtained implicitly, as Lagrange multipliers associated with the constraints. The fundamental principle of dynamics is then obtained (in a discretized version) from the Euler (optimality) equations of the minimization problem. In the case of frictionless grains, we come back to minimization problems under affine constraints. In order to introduce friction (Coulomb model) between grains, we have to consider minimization problems under conical constraints, for which the constraint is non derivable.

We will illustrate this work with numerical simulations, showing that the obtained schemes can be used to study macroscopic behavior of granular materials.

Part of the work was done in collaboration with Sylvain Faure, Philippe Gondret, Yvon Maday, Anne Mangeney, Hugo Martin, Bertrand Maury and Antoine Seguin.

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