Multiscale modelling in mechanics

Summary

This course introduces the principles and techniques for modeling materials across different spatial scales, from the level of atoms or grains to the continuum or structural scale. Emphasis is placed on hierarchical upscaling (homogenization), while concurrent techniques are also covered.

Content

Keywords

Multiscale modeling, solid mechanics, homogenization, molecular dynamics, discrete
element method

Learning Prerequisites

Required courses

Continuum Mechanics (e.g. CIVIL-225), Finite Elements (e.g.
CIVIL-321), Numerical analysis (e.g. MATH-251a)

Important concepts to start the course

Mechanics of deformable media,
Linear algebra, Tensor analysis, Numerical analysis

Learning Outcomes

By the end of the course, the student must be able to:

• Assess / Evaluate mechanical modeling techniques at different scales.
• Apply theoretical and computational approaches for bridging scales in solid mechanics.
• Develop and implement scale-bridging algorithms in Python.

Transversal skills

• Set objectives and design an action plan to reach those objectives.
• Demonstrate the capacity for critical thinking
• Use both general and domain specific IT resources and tools
• Make an oral presentation.

Teaching methods

2 hours lectures, 2 hours in exercise or computer room.

Expected student activities

Active participation, home study, programming assignments and exercises.

Assessment methods

Individual computational project in Python (80%), presentation of a research paper (20%).

Supervision

Resources

Virtual desktop infrastructure (VDI)

No

Bibliography

- Lecture notes and articles given during the lecture
- Modeling Materials by E. Tadmor
- Multiscale Modeling by D. Kochmann

Ressources en bibliothèque

• Modeling Materials / Tadmor
• Multiscale Modeling / Kochmann

Moodle Link

• https://go.epfl.ch/CIVIL-408