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
- Introduction to multiscale modeling
- Periodic and random microstructures, representative volume element
- Review of continuum mechanics and the finite element method
- Atomistic, discrete element and mesoscale methods
- Continuum-to-continuum computational homogenization, Hill-Mandel condition
- Asymptotic homogenization, Estimates and bounds for effective moduli
- Discrete-to-continuum homogenization
- Analytical methods, Cauchy-Born rule
- Concurrent multiscale modeling
- Data-driven multiscale modeling
- Applications to different classes of materials (composites, granular materials,
concrete, masonry, metals, architected materials, ...)
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
| Office hours | Yes |
| Assistants | Yes |
| Forum | Yes |
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
Moodle Link
In the programs
- Semester: Fall
- Exam form: During the semester (winter session)
- Subject examined: Multiscale modelling in mechanics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: During the semester (winter session)
- Subject examined: Multiscale modelling in mechanics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: During the semester (winter session)
- Subject examined: Multiscale modelling in mechanics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: During the semester (winter session)
- Subject examined: Multiscale modelling in mechanics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: During the semester (winter session)
- Subject examined: Multiscale modelling in mechanics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional