Divided Media and Numerical Methods

This course provides a general introduction to 1) the physics and mechanics of granular media and 2) their modeling using discrete methods (DEM). The multiscale nature of a granular material is discussed, ranging from the microscopic scale (contact interactions) to the macroscopic scale (structural scale). A phenomenological description of macroscopic behavior as well as microscopic properties is discussed for the static, quasi-static, and flow states of granular media. Micromechanical models and scale-change approaches based on dimensionless analyses, averaged quantities, stress transmission, and the presence of anisotropies are introduced. The influence of particle properties and contact interactions on the microstructure is also discussed. Numerical approaches such as discrete methods (Discrete Element Methods, DEM), regular methods (Molecular Dynamics), and non-regular methods (Contact Dynamics) are presented. In particular, the Contact Dynamics method will be applied to simple examples using the LMGC90 computational code.

By the end of the course, students should 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 irregular approaches.

4) Use the LMGC90 platform as a tool for simulating discrete-event systems using non-regular methods

Rigid-body dynamics. Mathematical and statistical tools. Algorithms and the Python programming language

- Continuous Control
- project

The course consists of two main sections, each of which is divided into several chapters.

Part 1: Rheology of Discrete Media
Chapter 1: Introduction and General Principles
Chapter 2: Interactions at the Contact and Particle Scales
Chapter 3: Granular Solids
Chapter 4: Quasi-Static Behavior
Chapter 5: Granular Microstructure and Micromechanics
Chapter 6: Granular Flow
Assessment through continuous evaluation (50%).

Part 2: Numerical Methods
Chapter 1: Introduction and General Principles
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- and Post-Processing Methods.
Assessment based on 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.