5.00 credits
30.0 h + 30.0 h
Q2
Teacher(s)
Chatelain Philippe; Doghri Issam;
Language
French
Main themes
a. General theory of continuous media.
 Basic principles and physical justification of the continuity assumption. Tensor field representation. Invariance. Cylindrical and spherical coordinates.
 Principal concepts and tools to analyze the kinematics of deformable media (velocity, acceleration, strain, rotation, strain and rotation rates, Eulerian and Lagrangian representations).
 Principal concepts and laws governing the dynamics of continuous media. Stresses, Mohr circles. Conservation laws.
 Elementary Thermodynamics of continuous media. Constitutive equations.
b. Applications.
 Solid Mechanics: Basic infinitesimal ThermoElasticity (elastic moduli, thermal effects). Classical analytical examples.
 Fluid Mechanics: Pressure, viscosity, and compressibility concepts. Newtonian viscous fluid model. Classical examples (e.g. flow in a pipe). Perfect fluid approximation and elementary applications.
 Basic principles and physical justification of the continuity assumption. Tensor field representation. Invariance. Cylindrical and spherical coordinates.
 Principal concepts and tools to analyze the kinematics of deformable media (velocity, acceleration, strain, rotation, strain and rotation rates, Eulerian and Lagrangian representations).
 Principal concepts and laws governing the dynamics of continuous media. Stresses, Mohr circles. Conservation laws.
 Elementary Thermodynamics of continuous media. Constitutive equations.
b. Applications.
 Solid Mechanics: Basic infinitesimal ThermoElasticity (elastic moduli, thermal effects). Classical analytical examples.
 Fluid Mechanics: Pressure, viscosity, and compressibility concepts. Newtonian viscous fluid model. Classical examples (e.g. flow in a pipe). Perfect fluid approximation and elementary applications.
Learning outcomes
At the end of this learning unit, the student is able to :  
1 
In consideration of the reference table AA of the program "Masters degree in Mechanical Engineering", this course contributes to the development, to the acquisition and to the evaluation of the following experiences of learning:

Content
Introduction: Continuity assumption, tensorial field representation, invariance. Elements of kinematics: Velocity, acceleration, pathlines, strain and rotation rates, Eulerian and Lagrangian motion representations, material derivative, small displacements, strain, rotation, compatibility equations, transport theorem (Reynolds). Dynamics: Stresses, Mohr circles, conservation laws (mass, momentum, moment of momentum, energy). Thermodynamics: ClausiusDuhem inequality. Constitutive equations. Application to Solid Mechanics: Infinitesimal ThermoElasticity, isotropic media, elastic moduli. Isothermal or adiabatic problems: solution existence and uniqueness, examples, beam theory (StVenant), elastic waves. Nonisothermal problems. Application to Fluid Mechanics: Viscous Newtonian fluid, NavierStokes equations, Poiseuille and Couette flows, flow in a pipe, Reynolds number, nonisothermal problems. Perfect isentropic or incompressible fluid flow approximation, irrotational flows, lift of an airfoil. Acoustic waves. Appendices: Introduction to tensor calculus. Cartesian and curvilinear coordinates.
Teaching methods
Lectures:
Supports: blackboard or virtual board using a tablet. Slides are used for the main results.
Small Wooclap evaluations are performed during some of the lectures to provide a selfevaluation of the previous lectures
Exercises :
sessions supervised by a TA and tutor student, including corrections
Supports: blackboard or virtual board using a tablet. Slides are used for the main results.
Small Wooclap evaluations are performed during some of the lectures to provide a selfevaluation of the previous lectures
Exercises :
sessions supervised by a TA and tutor student, including corrections
Evaluation methods
A midterm evaluation is organized. The obtained grade is included in the final grade if one passed the final exam (grade >= 10).
Written exam: theory (3040%) and exercises (6070%)
The lecturers will organize oral exams in case of technical problems during the written exam or whenever a fraud/cheating is suspected.
Written exam: theory (3040%) and exercises (6070%)
The lecturers will organize oral exams in case of technical problems during the written exam or whenever a fraud/cheating is suspected.
Other information
Prerequisite: Basic knowledge in Mathematics and Physics as obtained from previous basic formation. Evaluation procedure: Normal written exam, half on the theory and half on original exercises. Support: Lecture notes available on web page (www.mema.ucl.ac.be/teaching/meca2901). Some document photocopies are supplied if necessary. Teaching framework: exercises (in classes), and one or two interrogations (taken into account in the final evaluation in case of success). Associated stream: Basic module in Mechanics 50.10. Reduced part: Part A of the course (which does not include the application of the theory to Fluid Mechanics), includes 22,5h of theory and 22,5h of exercises, for 3,5 credits.
Online resources
Bibliography
 Support de cours accessible sur page Web (https://moodle.uclouvain.be/course/view.php?id=1317).
 Photocopies de documents si nécessaire.
Teaching materials
 Transparents fournis par enseignants
 Notes prises en cours par étudiants, contenu de tableau virtuel fourni par enseignant
Faculty or entity
MECA
Programmes / formations proposant cette unité d'enseignement (UE)
Title of the programme
Sigle
Credits
Prerequisites
Learning outcomes
Additionnal module in Physics
Specialization track in Mechanics
Minor in Applied Chemistry and Physics
Specialization track in applied Chemestry and Physics
Minor in Mechanics
Mineure Polytechnique