Particle Methods for Engineering Mechanics I

Particulate systems are ubiquitous in engineering mechanics. One distinctive feature – the discrete interactive behaviour among rigid bodies- from the soil matrix failure to the rock joint sliding – is universally shared. Discrete element method (DEM) is regarded as the most powerful tool for analysing these mechanical behaviours of particulate systems. Many commercial DEM programs have been developed and incorporated into the daily routine of geotechnical engineering in soil and rock mechanics.

This course offers the theoretical foundations, mathematical derivations and computational implementations for DEM, concentrating on geomechanics. Notably, the functionality and physical origins of DEM’s contact models and numerical parameters will be intensively discussed. Students will learn to interpret and analyse geomechanical problems from a discrete-body perspective based on engineering conditions. Programming skills regarding collision detection algorithms and data structure optimizations will also be highlighted in the learning process.

Graduated students of this course will be able to independently develop DEM programs, choose and implement correct contact models, and perform DEM-based analysis for geotechnical problems using commercial software platforms. For excellent graduates interested in reaching out for other important engineering subjects such as rock, granular mechanics or powder technology, this course can be very helpful for their future studies.

1. Understand the physical and mathematical fundamentals of discrete particle-based methods.
2. Formulate implicit and explicit algorithms for solving the dynamics and motion of discrete particle-based systems.
3. Formulate the interactive models for the material behaviours of discrete particle-based systems, including elasticity, viscoelasticity, cohesion, and fracture.
4. Design and implement discrete particle-based methods for various applications such as rock mechanics, soil mechanics, and granular material transport.

The course offers comprehensive information on the physical origin, mathematical derivation and numerical implementation of discrete element method (DEM). Detailed contents will be covered as follows:

1. Introduction of discrete systems
2. Concepts and Governing equations of DEM
3. Discussions on DEM’s contact models and parameters
4. Constructing DEM using spherical particles
5. Constructing DEM using irregularly shaped particles
6. DEM applications and case studies of rock mechanics.
7. DEM applications and case studies for granular mechanics.
8. DEM applications and case studies for powder technology
9. Looking ahead: Multiscale and Mutiphysical DEM