The teaching unit is optional
The teaching unit is taught in French.

It can be easily followed by English speaking students

  Coord. Olivier Hubert (olivier.hubert@ens-paris-saclay.fr, ENS Paris-Saclay)

Pedagogic team :

Hubert, Olivier, Professeur des universités, CNU60, ENS Paris-Saclay
olivier.hubert@ens-paris-saclay.fr

Lorong Philippe, Professeur des universités, CNU60, ENSAM
philippe.lorong@ensam.eu

Ranc, Nicolas, Professeur des universités, CNU60, ENSAM
nicolas.ranc@ensam.eu

Guilhem, Yoann, Maître de conférences, CNU 60, ENS Paris-Saclay.
Yoann.guilhem@ens-paris-saclay.fr

Schedule and practical organisation :

Course 1A: Typology of multiphysics couplings (local, global, strong, weak), unified formulation of balance equations and constitutive laws (mass conservation, momentum, energy); Chemical diffusion, heat, phase change

Course 1B: Elliptical, parabolic and hyperbolic problems (algorithms, convergence and stability).

Course 2A: Solving multiphysic problems using finite differences, explicit, implicit scheme, theta-scheme

Course 2B: Thermo-mechanics of plasticity: static, fatigue, measurement, simulation.

Course 3A: Change of scale for the simulation of free deformations: Shape memory alloys, magneto-mechanics, electro-mechanics.

3B project session: Presentation / choice of projects

Project session 4: Validation of numerical project objectives, validation of formulations

Sessions 5-10: Numerical projects.

Pedagogical objectives

Content:

The final objective is to propose a typology of multi-physical problems encountered in mechanics of materials, to present the methods and algorithms which make it possible to build an associated numerical model, and to implement these concepts through a numerical project (strong coupling with spatial-temporal evolution of the modelled physical fields).

Skills:

1 / Acquire the knowledge allowing to choose, identify and possibly develop, the most suitable model to describe one or more multiphysic couplings;

2 / Acquire the knowledge allowing to choose, identify and possibly develop, the numerical method most suited to the resolution of the targeted problem;

Complementary skills :

- matlab language, python

- writing of a scientific article

- oral presentation of work.

Prerequisite:

Continuum mechanics, elasticity, thermics, programming elements.

Bibliography:

Mécanique des matériaux solides, J. Lemaitre et J.L. Chaboche,A. Benallal, R. Desmorat, Dunod, 3e Ed. 2009.

Mechanics of solid materials, J. Lemaitre et J.L. Chaboche, Cambridge Univ. Press, 1994.

Mécanique non-linéaire des matériaux, J. Besson, G. Cailletaud, J.L. Chaboche, S. Forest, Hermès, 2001.

Modélisation numérique en sciences et génie des matériaux, Traité des matériaux (Tome 10), M. Rappaz, M. Bellet, M. Deville, Presses Polytechniques et Universitaires Romandes, Lausanne.