# Fiches de cours

## Numerical methods in biomechanics

#### Enseignant(s) :

Terrier Alexandre

English

#### Withdrawal

It is not allowed to withdraw from this subject after the registration deadline.

#### Summary

Students understand and apply numerical methods (FEM) to answer a research question in biomechanics. They know how to develop, verify and validate multi-physics and multi-scale numerical models. They can analyse and comment results in an oral presentation and a written report.

#### Content

• Use of numerical methods in biomechanics through some examples (tissue engineering, mechanical biology, artificial organs, external lectures from academics and industry)
• Partial Differential Equations reviewed in this context.
• General physics (solid, fluid, heat, transport) reviewed and extended through examples.
• Finite Element Method explained through practical examples.
• Multi-physics and coupling problems
• Importance of verification and validation
• Practical examples discussed in classroom
• Weekly exercises in different fields of biomechanics
• Group projects

#### Keywords

Biomechanics, numerical methods, multi-physics, coupling

#### Learning Prerequisites

##### Important concepts to start the course

• Partial Differential Equations
• Linear algebra
• General Physics (solid, fluid, heat)
• Numerical analysis

#### Learning Outcomes

By the end of the course, the student must be able to:
• Compute the kinematics and the forces in articulations, B3
• Compute shear stresses in blood in particular flow conditions, B4
• Compare the range of validity of different constitutive laws, B7
• Implement a constitutive law in a simulation software, B8
• Describe the feedback loop that, starting from a mechanical signal translated into a chemical signal, allows for the adaptation of the mechanical properties of tissues, B9
• Compute the stresses and strains at the interface of an implant and in the surrounding tissues, B10
• Compute the kinematics and forces in an implant, B11

#### Transversal skills

• Set objectives and design an action plan to reach those objectives.
• Identify the different roles that are involved in well-functioning teams and assume different roles, including leadership roles.
• Continue to work through difficulties or initial failure to find optimal solutions.
• Take feedback (critique) and respond in an appropriate manner.
• Access and evaluate appropriate sources of information.
• Write a scientific or technical report.
• Make an oral presentation.

#### Teaching methods

The course is divided into ex cathedra sessions, with interactive examples. Exercises are organised to applied concepts presented in the course. A mini-project is carried out in groups. Examples, exercises and mini-projects are done with Comsol.

#### Expected student activities

• Attend cours and do interactive exemples
• Do the exercices
• Do a project in a group

#### Assessment methods

• Midtem text (1/4)
• Oral presentation of project (1/4)
• Written rapport of project (1/4)
• Writtn exam (1/4)

#### Supervision

 Office hours Yes Assistants Yes Forum Yes

#### Resources

##### Bibliography

Computational Modeling in Biomechanics, 2010

http://library.epfl.ch/ebooks/?pg=search&isbn=978-90-481-3574-5

### Dans les plans d'études

• Semestre
Printemps
• Forme de l'examen
Ecrit
• Crédits
3
• Matière examinée
Numerical methods in biomechanics
• Nombre de places
30
• Cours
2 Heure(s) hebdo x 14 semaines
• Exercices
1 Heure(s) hebdo x 14 semaines
• Semestre
Printemps
• Forme de l'examen
Ecrit
• Crédits
3
• Matière examinée
Numerical methods in biomechanics
• Nombre de places
30
• Cours
2 Heure(s) hebdo x 14 semaines
• Exercices
1 Heure(s) hebdo x 14 semaines
• Semestre
Printemps
• Forme de l'examen
Ecrit
• Crédits
3
• Matière examinée
Numerical methods in biomechanics
• Nombre de places
30
• Cours
2 Heure(s) hebdo x 14 semaines
• Exercices
1 Heure(s) hebdo x 14 semaines
• Semestre
Printemps
• Forme de l'examen
Ecrit
• Crédits
3
• Matière examinée
Numerical methods in biomechanics
• Nombre de places
30
• Cours
2 Heure(s) hebdo x 14 semaines
• Exercices
1 Heure(s) hebdo x 14 semaines
• Semestre
Printemps
• Forme de l'examen
Ecrit
• Crédits
3
• Matière examinée
Numerical methods in biomechanics
• Nombre de places
30
• Cours
2 Heure(s) hebdo x 14 semaines
• Exercices
1 Heure(s) hebdo x 14 semaines
• Semestre
Printemps
• Forme de l'examen
Ecrit
• Crédits
3
• Matière examinée
Numerical methods in biomechanics
• Nombre de places
30
• Cours
2 Heure(s) hebdo x 14 semaines
• Exercices
1 Heure(s) hebdo x 14 semaines

### Semaine de référence

LuMaMeJeVe
8-9
9-10
10-11   INF213
11-12   INF213
INF3

12-13   INF213
INF3

13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22

Cours
Exercice, TP
Projet, autre

### légende

• Semestre d'automne
• Session d'hiver
• Semestre de printemps
• Session d'été
• Cours en français
• Cours en anglais
• Cours en allemand