Continuum mechanics provides tools for modelling the behaviour of dense media on a scale considered as macroscopic, since the notion of the microstructure of materials is absent and simply represented by more or less sophisticated equivalent properties (c/f Mechanics of Materials Unit). Conversely, at their microstructure scale, materials are heterogeneous and behaviour observed at the macroscopic scale is the result of elementary physical mechanisms, active at the microstructure scale.
During the course the student will gradually come to understand the notions of scale and separation of scale and its influence on observed behaviour.
The student will be capable of defining an Elementary Representative Volume and of making the link with the notion introduced in continuum mechanics.
The student will know the principle methods of scale changing, allowing a deduction of the effective behaviour of a heterogeneous material based on knowledge of its microstructure, but will also be able to estimate local constraints inside a microstructure.
Finally an application of the various notions of high performance composite materials, commonly used in many industries (in particular the aeronautical industry), will be proposed at the end of the course.
Teaching methods include courses and supervised studies and two practical numerical courses. An experimental practical course is also planned.
| On completion of the unit, the student will be capable of: | Classification level | Priority |
|---|---|---|
| Describing the microstructure of a material in micromechanical terms | 1. Knowledge | Important |
| Determining the pertinent scales for studying a material | 3. Apply | Essential |
| Calculating the effective behaviour of a heterogeneous material | 3. Apply | Important |
| Understanding the different methods of scale change | 2. Understand | Important |
| Designing a composite structure according to the requirements in effective behaviour | 7. Create | Important |
| Estimating the effective behaviour of a composite material | 6. Assess | Important |
| Percentage ratio of individual assessment | Percentage ratio of group assessment | ||||
|---|---|---|---|---|---|
| Written exam: | 75 | % | Project submission: | 0 | % |
| Individual oral exam: | 0 | % | Group presentation: | 0 | % |
| Individual presentation: | 0 | % | Group practical exercise: | 0 | % |
| Individual practical exercise: | 25 | % | Group report: | 0 | % |
| Individual report: | 0 | % | |||
| Other(s): 0 % | |||||
| Type of teaching activity | Content, sequencing and organisation |
|---|---|
| (inter)active Amphitheatre |
|
| Supervised studies | When possible each course will be followed by a session of exercises to apply the notions dealt with in class. Approx. n° of hours : 12h |
| Practical courses | 3h (or 6h) in common with the structural materials unit. Characterisation of the mechanical behaviour of composite structures. |
| Practical courses | 2 numerical practical work sessions are proposed : 1/ simple numerical calculation of effective behaviour (Mori-Tanaka type) and 2/ auto-coherent type |