Level of study
BAC +5
ECTS
4 credits
Component
Faculty of Science
Hourly volume
42h
Description
This course gives a general introduction to 1) the physics and mechanics of divided media and 2) their modeling through discrete methods (DEM). The multiscale character of a divided material is discussed from the microscopic scale (contact interactions), to the macroscopic scale (structure scale). A phenomenological description of the macroscopic behavior as well as the microscopic properties are discussed for static, quasi-static and flowing states of granular media. Micro-mechanical models and scaling approaches based on dimensionless analysis, averaged quantities, stress transmissions and anisotropies are introduced. The influence of particle properties and contact interactions on the microstructure is also discussed. Discrete Element Methods (DEM), regular (Molecular Dynamics) and non-regular (Contact Dynamics) numerical approaches are presented. In particular, the Contact Dynamics method will be implemented on simple examples through the LMGC90 computational code.
Objectives
At the end of the course, the student is expected to be able to
1) Recognize and understand the importance of granular materials in various technological contexts
2) Observe, interpret and describe the mechanical behavior of systems composed of granular materials at different scales
3) Understand the general principles of the DEM method and regular and non-regular approaches
4) Using the LMGC90 platform as a tool for simulation of discrete systems by non-regular methods
Necessary pre-requisites
Dynamics of rigid bodies. Statistical mathematical tools. Algorithms and Python language
Recommended Prerequisites:
Basics of programming, Unix.
Knowledge control
- Continuous assessment
- Project
Syllabus
The course is composed of two main parts, themselves composed of several chapters.
Part 1: Rheology of divided media
Chapter 1: Introduction and generality
Chapter 2: Interactions at the contact and particle scale
Chapter 3: The granular solid
Chapter 4: Quasi-static behavior
Chapter 5: Granular microstructure and micromechanics
Chapter 6: Granular flow
Evaluation through a continuous assessment (50%).
Part 2 : Numerical methods
Chapter 1 : Introduction and generality
Chapter 2 : Numerical schemes
Chapter 3 : Distinctions between regular and non-regular approaches
Chapter 4 : Contact detection techniques
Chapter 5 : Focus on the "Non-Smooth Contact Dynamics Method"
Chapter 6 : Numerical parameters and pre/post processing methods.
Evaluation through a numerical project to be completed (50%).
This course is based on the following two references:
[1] B. Andreotti, Y. Forterre, and O, Pouliquen. Granular Media: Between Fluid and Solid, Cambridge University Press, 2013.
[2] F. Radjaï and F. Dubois, Discrete Numerical Modeling of Granular Materials, Wiley-ISTE, 2011.
Bibliography
[1] B. Andreotti, Y. Forterre, and O, Pouliquen. Granular Media: Between Fluid and Solid, Cambridge University Press, 2013.
[2] F. Radjaï and F. Dubois, Discrete Numerical Modeling of Granular Materials, Wiley-ISTE, 2011.