Divided Media and Numerical Methods

This course gives a general introduction to 1) the physics and mechanics of divided media and 2) their modeling using discrete methods (DEM). The multi-scale character of a divided material is discussed from the microscopic scale (contact interactions) to the macroscopic scale (structure scale). A phenomenological description of macroscopic behavior and microscopic properties are discussed for static, quasi-static and flowing states of granular media. Micromechanical models and change-of-scale approaches based on adimensional analyses, averaged quantities, stress transmissions and the existence of 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 using the LMGC90 computational code.

At the end of the course, students are 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 of regular and non-regular approaches.

4) Use the LMGC90 platform to simulate discrete systems using non-regular methods

Rigid body dynamics. Statistical mathematical tools. Algorithms and Python language

- Control continue
- project

The course is divided into two main parts, each of which is made up of several chapters.

Part 1: Rheology of divided media
Chapter 1: Introduction and generality
Chapter 2: Interactions at contact and particle scales
Chapter 3: The granular solid
Chapter 4: Quasi-static behavior
Chapter 5: Granular microstructure and micromechanics
Chapter 6: Granular flows
Assessment by 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.
Assessment 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.