2023-2024 / MECA0012-6

Solid mechanics


26h Th, 26h Pr, 15h Proj.

Number of credits

 Bachelor of Science (BSc) in Architectural Engineering5 crédits 
 Bachelor of Science (BSc) in Engineering5 crédits 
 Master of Science (MSc) in Aerospace Engineering5 crédits 
 Master of Science (MSc) in Civil Engineering5 crédits 
 Master of Science (MSc) in Electromechanical Engineering5 crédits 
 Master of Science (MSc) in Mechanical Engineering (EMSHIP+, Erasmus Mundus)5 crédits 


Laurent Duchene

Language(s) of instruction

French language

Organisation and examination

Teaching in the second semester


Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

General overview: This course provides the basic knowledge in Solid Mechanics: concept of stress tensor, strain tensor, material's constitutive law, Hooke's law, deformation energy and link with thermodynamics, virtual work principle and energy theorems, isotropic linear elasticity theory.

These concepts are then applied to various practical cases: thick tubes under pressure, pressurized sphere, force on an infinite medium, contact between two elastic solids, torsion of prismatic solids, tensile and bending of prismatic solids, corner shaped solids, stress concentration...

The topics of the course are:
* Introduction to tensorial calculus and index notation. Application to the statics: stress tensor, balance equations...

* Fatigue: introduction to the concept of fatigue, origin of fatigue failure, Wöhler curves, number of cycle to failure, endurance limit

* Kinematics: strain in 1D, rigid body motion, tensoriel definition, F=RU, Green strain tensor, volumic strain, Cauchy strain tensor, Saint-Venant compatibility equations

* Virtual work principle + energy theorems (Engesser, Castigliano...)

* 3D Hooke's law, material mechanical properties, additivity rule, strain energy, uniqueness of the solution

* Fundamental equations of linear elasticity (Navier's equations and Beltrami-Michell's equations)

* 3D elastic problems: pressurised tubes, pressurised sphere, Kelvin's problem, Boussinesq's problem, Hertz contact problem

* Torsion of general prismatic solid: Prandtl's function, warping of the sections...

* 2D elastic problems: Airy's function, applications in cartesian coordinates (tensile and bending of prismatic solids)
* 2D elastic problems: applications in polar coordinates (bending of a curved beam, corner shaped solids, plate with a hole, stress concentration)

Learning outcomes of the learning unit

During this course, the students will be taught the basic concepts of Solid Mechanics. They will be able to tackle the problem of a solid deformed under a particular loading. The important concept of material constitutive law in the linear elastic regime will be taught. The theoretical concepts will then be used to solve various basic applications in the engineering field.

This course contributes to the learning outcomes I.1, I.2, II.1, III.1, III.2, IV.1, IV.2, V.2, VI.1, VI.2, VII.1, VII.2 of the BSc in engineering.

This course contributes to the learning outcomes I.1, I.2, II.1, III.1, III.2, IV.1, IV.2, V.2, VI.1, VI.2, VII.1, VII.2 of the MSc in biomedical engineering.


Prerequisite knowledge and skills

Basic concepts learned during the courses of "Physics", "Mathematics" (analysis and algebra) form the engineering cursus are necessary for the understanding of the theoretical developments of the Solid Mechanics course. Besides, this course is directly related to the Mechanics of Materials course of the 1st semester. The concepts presented in the first course (Mechanics of Materials) will be extended and generalised in this second course.

Planned learning activities and teaching methods

Practical work sessions will permit the students to understand how the theoretical concepts can be applied. During these practical works, selected exercises are solved and explained to the students. Then, the students are invited to solve some exercises. These sessions last 2 hours. The students will also have homeworks to achieve individually. The aim of these homeworks is to check the capability of each student to apply the concepts taught during the theoretical course and the practical work sessions.

Mode of delivery (face to face, distance learning, hybrid learning)

Face-to-face course

Additional information:

The course is divided in 4 hour units: 2 hours for the theory and 2 hours for the practical work sessions. Theoretical course sessions are taught in the auditorium in French. Students are invited to ask questions during the course.
During the practical work sessions, students should be active. Exercises are solved in order to show some applications of the theoretical concepts. These sessions are also in French.

Recommended or required readings

The syllabi are written in French (theory and exercises) and they are sold at the 'Centrale des Cours' (CDC).They are: - the syllabus of 'Mécanique du Solide' from S. Cescotto. - the book 'Mécanique des Matériaux" from C. Massonnet and S. Cescotto (only chapter 13) is used for the session on the energy theorems (the other chapters are taught during the course Mechanics of Materials). The syllabi were scaned and the files are downloadable (for the students of the course) on e-Campus platform. The slides of the theoretical sessions are also available on e-Campus and are a part of the course.

Exam(s) in session

Any session

- In-person

written exam ( open-ended questions )

Continuous assessment

Additional information:

Students will have to do homeworks every week. They consist in some small exercises to solve. These exercises are related to the topics of the theoretical as well as the practical sessions. The homework are available from e-Campus platform. The students should provide their answers to the questions on-line.
Written exam (in French): open questions about the theory (1 hour) and resolution of exercises (3 hours).
During the written exam, the students have access to: - for the theoretical part: no lecture note, no calculator - for the exercise part: only the lecture notes related to the theory are allowed (no solved exercises); a calculator is required.
To calculate the final mark, the following weighting will be approximately applied: - homeworks: 20% - written exam, theoretical part: 20% - written exam, exercise part: 60%
The personal work of the students (solving exercises) is the crucial point to adequately understand the course.

Work placement(s)

Organisational remarks and main changes to the course

Unless otherwise stated, theoretical and practical sessions will be held in Sart Tilman. The rooms will be announced in due time.
The theoretical sessions and the practical sessions (2 X 2 hours a week) are planned on Friday morning.


Teacher : Laurent Duchêne, Professor, phone : 04/366 9328, l.duchene@uliege.be

Assistant: Calogero Gallo, tel: 04/366 9835, cgallo@uliege.be

Secretary : Laurence Defrere, phone: 04/366 9357, laurence.defrere@uliege.be

Association of one or more MOOCs