Teaching
[M1] Introduction to Solid Mechanics
This module introduces students to solid mechanics – continuous description of a solid, definition of strain and stress tensors, equilibrium, constitutive relation, principle of minimum potential energy and complimentary potential energy, principle of virtual work, beam model and relation with the 3D model.
[M2] Introduction to Linear Finite Element Modelling
The objective is to summarize modern and effective finite element procedures for the linear analyses of static problems with applications in biomechanics. The material that will be discussed includes the basic finite element formulations, the effective implementation of these formulations in computer programs, and recommendations on the actual use of the methods in engineering practice. We will be using the commercial software package ABAQUS. At every session, the objective is to have 2h of theoretical considerations and 2h of practical work with ABAQUS/MATLAB. The prerequisite of the lecture is linear elasticity (I will start from static equilibrium : div(σ)+f=0).
Useful Ressource: Finite Element Procedures for Solids and Structures » linear Analysis
[M2] Non-linear Finite Element Modelling
This lecture builds on the first course linear FEM and takes one step further. It will discuss the main sources of nonlinearities (geometrical, material and boundary conditions) in the framework of the finite element method. Strain- and stress measures for large displacements/deformations. Mathematical models for elastic and hyperelastic materials. Geometrical stiffness and linearized buckling. Formulation of the nonlinear finite element method. Implicit/explicit time integration. Incremental-iterative solution methods for nonlinear static and dynamic problems. Modelling of nonlinear boundary conditions. Impact- and contact problems.
Useful Ressource: Finite Element Procedures for Solids and Structures » Nonlinear Analysis
[M2] Basics in Constitutive modelling of biological tissues
Knowledge of the mechanical behavior of biological tissues is required to understand the clinical issues. This module aims to teach students how to model and characterize the mechanical behavior of biological tissues using classical models. The lectures will discuss the composition and structure of biological tissues to explain and justify the mechanical properties. Experimental methods and issues specific to biological tissues will be taught taking into account the ethical principles to conduct research on animals, human bodies and human-beings. Finally, methods for identification of parameters for mechanical and multi-physical models will be introduced.
[M2] Non-Linear Constitutive Modelling of biological tissues
The objective is to present the nonlinear theory of continuum mechanics required for the modeling of the elastic properties of soft biological tissues, with particular reference to the fiber structure of such tissues. The theory will be applied to the calibration of anisotropic hyperelastic material model parameters of aortic Valve leaflets with experimental data obtained from ex vivo biaxial tests (practical session). The theory will also be applied to the calibration of the isotropic hyperelastic material model parameters of buttock soft tissue with experimental data obtained from in vivo compression tests (homework). Recent developments aiming at the characterization of the microstructure of Intervertebral Disc tissue and skin tissue will also be explored.
[M2] Statistics, Research Methodology & Literature Review
The main objective is to introduce research methodology so that students can communicate science efficiently both orally and written (publications, masters’ these defense, master's thesis manuscript, conference, etc). The module consists of two main sections. The first section introduces the purpose, processes and methodologies of research projects. It aims at increasing their knowledge of academic standard practices (using bibliography tools, writing a research introduction and presenting scientific work orally). The second section focuses on basic statistical tools for quantitative research and more specifically on statistical hypothesis testing, with practicals using R programming language.
ENSAM "Bioengineering" Expertise
Programme head : Xavier BONNET
(Right) Design and 3D printing of a Polycentric Prosthetic Knee Joint
Collective responsibilities
[M2] IS3CX180 Open Your Mind Seminars - Organisation (2014-2021)
The BME Open Your Mind seminars are held every Friday of the first semester. The main objective is to open the eyes and mind of our students on the great diversity of research and activities in MedTech. They can focus on scientific works as well as other aspects including tech transfert, innovation and development of new technologies for Health. These are addressed to all the students of the master, about 100-150 students, coming from all the different tracks (biomechanics, biomaterials, bioimaging, neuroscience, molecular and cell therapies), with very diverse backgrounds (biology, chemistry, physics, mathematics, neurosciences, medicine, pharmacy, odontology as well as mechanical, materials or chemical engineering).
Teaching summary
Last update May 2023
Resources: Selected teachings by Stéphane AVRIL
Biomechanics of soft tissues (Mines Saint-Etienne, Franc, 2008-2019)
Cellular and tissular mechanobiology (Technische Universität Wien, Austria, 2020-2021)
Mechanics of biological tissues (Technische Universität Graz, Austria, 2021-2022)
Mechanics of proteins and cells (Technische Universität Graz, Austria, 2021-2022)
Mechanics of cells, Tissues and Biological systems (Technische Universität Wien, Austria, 2021-2022)
Summer School on Biomechanics (2021, Graz, Austria) : Tutorial. Matlab codes.
CNRS School “Mecabio” (Les Houches, France) : Presentation. Exercises. Solution (Matlab routines).
”Pure mathematicians sometimes are satisfied with showing that the non-existence of a solution implies a logical contradiction, while engineers might consider a numerical result as the only reasonable goal. Such one sided views seem to reflect human limitations rather than objective values. In itself mathematics is an indivisible organism uniting theoretical contemplation and active application.”
Richard Courant (1888-1972)