PhD DEFENSE BY MATHIAS TOLOMEO

This PhD project was supervised by Vincent Richefeu, Gaël Combe and Cino Viggiani (3SR).

The defense will take place at 2pm at the LEGI

Abstract

In the experimental study of the micro-mechanics of granular materials, measuring inter-particle contact forces is still a challenging task, if compared to the well-established tools and techniques for the kinematic characterisation at particle scale. This doctoral thesis addresses this problem. The proposed approach consists of two parts: an experimental characterisation of the granular network geometry and of particle-scale kinematics, which can be carried out with common imaging techniques such as Digital Image Correlation; a numerical approach aiming to exploit these measurements for the estimation of forces. One imposed constraint was to only make use of the rigid motions of particles, together with the knowledge of the contact network, to infer contact forces. Three dierent numerical techniques have been proposed to this purpose, referred to as Contact Elasticity Method (CEM), Contact Dynamics-based Method (CDM) and Quasi-Static Method (QSM). Each of these techniques is based on the formulation of common approaches in the family of Discrete Element Methods, respectively the classical Cundall-like DEM, the Non Smooth Contact Dynamics and a quasi-static approach accounting for both contact elasticity and plasticity. It is shown that memory of the history of the packing is the main concern with all the chosen techniques. The three methods are rst presented and validated by applying them to the estimation of forces in 2D granular systems generated by means of explicit-time DEM simulations. We refer to these simulations as \ideal" experiments since they are meant to provide the same information that can be extracted from experiments, but without any measurement error. An obvious benet of this strategy is to get reference force sets that are taken as ground truth. Based on this, the main aspects that aect the determination of forces can be investigated. In particular, the crucial role of history is emphasised here, and some solutions to take it into account in the force inference have been investigated. An assessment of the in uence of measurement error has also been carried out, to predict the applicability of each method to real experiments. A short analysis of the variability of the solutions is also provided. Finally, some attempts have been made to infer forces from experiments carried out in the "1G2E" device. Particle kinematics and connectivity have been assessed by means of the Digital Image Correlation technique. The benets and drawbacks of the three methods have been demonstrated. They conduct us to envision a combined usage of the three methods. In the future, studying the stability of equilibrium might help reducing the variability of the solutions.