Discrete element method and soft materials

Duration

20h Th, 15h Proj.

Number of credits

Lecturer

Eric Opsomer

Language(s) of instruction

French language

Organisation and examination

Teaching in the second semester

Schedule

Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

This course unit introduces the Discrete Element Method (DEM) for the numerical modelling of soft matter systems and granular media. It covers the fundamental principles of the method, from the design of the simulation algorithm to its implementation and adaptation to specific physical problems.

The main topics covered are:

• Object-oriented programming: introduction to the object-oriented programming concepts required to design and implement a discrete element simulation code. Organisation of data and particle interactions, class structures, and principles of code modularity and reusability.
  
  
• Time integration schemes: presentation and implementation of numerical schemes suitable for integrating the equations of motion of particles. Analysis of their stability and accuracy, as well as the constraints associated with the choice of the time step.
  
  
• Modelling of normal contact forces: formulation of normal interactions between particles using contact models appropriate for the mechanical properties of the systems under study. Numerical implementation and analysis of the influence of model parameters on the dynamics of the system.
  
  
• Modelling of tangential contact forces: description of tangential interactions and friction between particles. Introduction to contact laws accounting for dissipative behaviour and sliding phenomena.
  
  
• Neighbour search and long-range forces: methods for identifying and managing neighbouring particles in order to improve computational efficiency. Extension of the algorithm to account for long-range interactions.
  
  
• Projects and algorithm adaptation: application of the concepts covered throughout the course to simulation projects. Adaptation and extension of the algorithm to specific physical problems, including the choice of appropriate models and parameters, and the analysis and interpretation of numerical results.
  
  
• Practical work sessions: sessions dedicated to computer-based implementation, problem solving, and project development. These sessions provide an opportunity to connect theoretical concepts with their practical application and to develop students' autonomy in building and analysing numerical simulations.
  
  

Learning outcomes of the learning unit

After completing this course, students will be able to:

• implement the numerical methods introduced in the course to model and simulate physical phenomena relevant to the field of soft matter;
  
  
• analyse and interpret numerical simulation results, and compare them with experimental data in order to assess the relevance of the models used;
  
  
• adapt simulation code and make use of existing libraries to investigate an original physical system in the field of soft matter;
  
  
• identify and implement the necessary adaptations to a numerical model or algorithm according to the specific characteristics of the physical problem under study.
  
  

Prerequisite knowledge and skills

Students should have a basic knowledge of:

• Classical mechanics: in particular Newtonian dynamics and conservation laws.
  
  
• Applied mathematics: in particular differential and integral calculus, linear algebra, and ordinary differential equations.
  
  
• Numerical methods: in particular numerical methods for solving differential equations and time integration.
  
  
• Programming: with prior experience in at least one scientific programming language.
  
  

Planned learning activities and teaching methods

The course is organised into two complementary phases.

During the first phase, each session consists of a theoretical component followed by computer-based practical work, allowing students to apply the concepts, methods, and tools introduced through concrete and progressively more complex situations.

During the second phase, the course takes the form of an individual project. Each student develops a numerical simulation addressing an original problem in the field of soft matter. The sessions are devoted to project development, with regular guidance from the instructor and opportunities for interaction with the other students. This organisation promotes the practical application of the knowledge acquired, autonomy in problem solving, and the ability to adapt numerical methods and tools to a specific problem.

Mode of delivery (face to face, distance learning, hybrid learning)

Face-to-face course

Course materials and recommended or required readings

Platform(s) used for course materials:
- eCampus


Further information:

Slides, Mathematica notebooks, and C++ source code are avilable on eCampus. 

Exam(s) in session

Any session

- In-person

oral exam

Continuous assessment


Further information:

Assessment is based on two complementary components:

• Continuous assessment during the project phase: students are assessed throughout the development of their project. This assessment focuses in particular on their ability to implement the methods introduced in the course, analyse and solve problems encountered, adapt numerical tools to the problem under study, and demonstrate autonomy in carrying out the project.
  
  
• Oral project defence: at the end of the course, each student presents their project and the main results obtained during an oral defence. The presentation is given in front of the other students in the course, the instructor, and invited experts in the field. The assessment focuses in particular on the quality of the presentation, the student's understanding and mastery of the work carried out, the analysis of the results, and their ability to answer questions and justify their methodological choices.
  
  

Work placement(s)

Organisational remarks and main changes to the course

The teacher will answer to all questions during the teaching period. During the exams and official holidays, the teacher will not answer anymore. Practical informations will be given via email or eCampus.

Contacts

eric.opsomer@uliege.be

Association of one or more MOOCs

Items online