Divided Environments

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 granular materials is discussed from the microscopic scale (contact interactions) to the macroscopic scale (structure scale). A phenomenological description of macroscopic behavior and microscopic properties is discussed for the static, quasi-static, and flow states of granular media. Micro-mechanical models and scale-changing approaches based on dimensionless analyses, averaged quantities, force transmissions, and the existence of anisotropies are introduced. The influence of particle properties and contact interactions on microstructure is also discussed. Discrete approaches (Discrete Element Methods (DEM)), regular approaches (Molecular Dynamics) and non-regular approaches (Contact Dynamics) are presented. In particular, the Contact Dynamics method will be implemented on simple examples using the LMGC90 calculation 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 regular and non-regular approaches.

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

Dynamics of rigid bodies. Statistical mathematical tools. Algorithms and Python language.

Recommended prerequisites:

Programming basics, Unix.

- Continuous assessment
- Project

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

Part 1: Rheology of divided media
Chapter 1: Introduction and general overview
Chapter 2: Interactions at the contact and particle scale
Chapter 3: Granular solids
Chapter 4: Quasi-static behavior
Chapter 5: Granular microstructure and micromechanics
Chapter 6: Granular flow
Assessment through continuous assessment (50%).

Part 2: Numerical methods
Chapter 1: Introduction and general overview
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.

[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.