Advanced solid mechanics

ME-437: Course Book

Lecturer: Curtin William

Language: English


This course will cover major topics of importance and value for the application and understanding of Solid Mechanics, aiming especially at the micromechanical analyses of problems that connect small scale phenomena to macroscopic engineering performance.


The course will be topical but evolving in a natural flow.  Topics will include:

Anisotropic Elasticity: beyond isotropic elasticity

Homogenization methods: the connection between microstructure of a material and the macroscopic effective properties that can be used in continuum analyses

Inclusions and Eshelby analysis: stresses and strains around particles embedded in a matrix and undergoing transformations that affect functional performance and failure, with connections to homogenization theory.

Laminate theory: the special case of fiber composites as layered anisotropic materials, connecting fiber/matrix properties to macroscopic structural response.

Fracture mechanics: basic understanding of the driving forces for crack growth, from both energy and stress perspectives, with advanced concepts for implementation in numerical methods.

Contact mechanics: basic analysis of bodies in contact and the generation of local stresses, and implications for friction and wear.

Other topics may be covered as interest and time permit.


Mechanics, Elasticity, Homogenization, Laminate theory, Composites, Fracture, Contact, Dislocations, Applied Mechanics, Theory, Computational Mechanics

Learning Prerequisites

Required courses

ME-331: Solid Mechanics, or equivalent course using tensor-based mechanics analyses

Important concepts to start the course

Definitiions of stress and strain

Mechanical equilibrium

Isotropic elasticity (Hooke’s Law)

Boundary value problems in small-strain elasticity

Second-rank tensors: properties and applications in mechanics

Index notation


Learning Outcomes

By the end of the course, the student must be able to:

  • Estimate elastic moduli of two-phase materials
  • Analyze stress and strains around inclusions
  • Compute stresses in laminated structures
  • Integrate concepts for failure
  • Design materials/microstructures with specified properties

Transversal skills

  • Set objectives and design an action plan to reach those objectives.
  • Use a work methodology appropriate to the task.
  • Continue to work through difficulties or initial failure to find optimal solutions.
  • Demonstrate the capacity for critical thinking
  • Write a scientific or technical report.

Teaching methods

Lectures on mechanics theory

Examples to illustrate theory and application

Exercises for cementing and applying new knowledge

Course may include:

Mini-projects to perform analyses

Project on topic of student interest

Expected student activities

In-class participation

Collaborative problem solving

Execution of mini-projects

Assessment methods

Graded mini-projects

Final written exam


Office hours Yes
Assistants Yes
Forum Yes


Virtual desktop infrastructure (VDI)



To be provided

In the programs

Semester Exam form
Fall  Written
Credits Subject examined
5 Advanced solid mechanics
Lecture Exercises
3 Hour(s) per week x 14 week 2 Hour(s) per week x 14 weeks
Semester Exam form
Fall  Written
Credits Subject examined
5 Advanced solid mechanics
Lecture Exercises
3 Hour(s) per week x 14 weeks 2 Hour(s) per week x 14 weeks

Reference week

  Lu Ma Me Je Ve
9-10 BS160        
16-17   CM1100
17-18   CM1100
Exercise, TP  Project, other


  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German