The teaching unit is mandatory.
The teaching unit is taught in French.
The teaching unit is taught in English.

 

Outline

3 ECTS / 10 sessions of 3 hours

Course : 15h00

Exercises : 15h00

Numerical practice : 4h00

Team

Coord. Rodrigue Desmorat (rodrigue.desmorat@ens-paris-saclay.fr, ENS Paris-Saclay)

René Billardon, rene.billardon@safrangroup.com
Rodrigue Desmorat, rodrigue.desmorat@ens-paris-saclay.fr
Karine Lavernhe, karine.lavernhe@ens-paris-saclay.fr
Martin Poncelet, martin.poncelet@ens-paris-saclay.fr

Objectives

The main models that are used to describe the thermo-mechanical behaviour of solid materials – all along the life of a structure – are presented in the general framework of the continuum thermodynamics with internal variables.

Targets

The aim is to learn how to choose, identify and, if necessary, develop, the best model to describe the thermo-mechanical behaviour of materials during the numerical simulation of manufacturing processes or of in-service structure life.

Topics

• (An)isotropic thermo-elasticity
• Continuum thermodynamics with internal variables
• Modelling of thermo-elastoplastic and thermo-elastoviscoplastic behaviour
• Continuous damage
• Thermodynamics of fracture
• Numerical exercise : Kinematic vs isotropic hardening. Application to the cyclic behaviour of a mini-structure

References

• Mécanique des matériaux solides, J. Lemaître et J.L. Chaboche, Dunod, 2004.
• Mechanics of solid materials, J. Lemaître et J.L. Chaboche, Cambridge Univ. Press, 1994.
• Mécanique non-linéaire des matériaux, J. Besson, G. Cailletaud, J.L. Chaboche, S. Forest, Hermès, 2001.
• Advanced Fracture Mechanics, M. Kanninen, C. Popelar, Oxford University Press, 1985.

Content

First session

• Course 1 : (An)isotropic thermo-elastic behaviour and continuum thermodynamics principles.
• Exercise 1 : 1-D viscoelasticity with internal variable.

Second session

• Course 2 : Linear and non-linear visco-elasticity : phenomenology, mechanisms, modelling, identification.
• Exercise 2 : Anisotropic elasticity.

Third session

• Course 3 : Continuum thermodynamics with internal variables.
• Exercise 3 : 3-D viscoelasticity (with internal variables vs. functional formulation).

4th session

• Course 4 : Thermo-elastoplastic behaviour : phenomenology, mechanisms, modelling, identification (1st part).
• Exercise 4 : Plasticity criteria.

5th session

• Course 5 : Thermo-elastoplastic behaviour : modelling, identification (2nd part).
• Exercise 5 : 1D elasto-plasticity.

6th session

• Course 6 : Thermo-elastoplastic behaviour : modelling, thermodynamics, identification (3rd part).
• Exercise 6 : 1D elasto-viscoplasticity.

7th session

• Course 7 : Thermo-elastoviscoplastic behaviour : phenomenology, mechanisms, modelling, identification.
• Exercise 7 : Elastoplasticity under non-proportionnal loading.

8th session

• Course 8 : Continuous damage.
• Exercise 8 : Tangential operator.

9th session

• Course 9 : Thermodynamics of fracture.
• Exercise 9 : Damage (uniaxial case).

10th session

• Course 10 : Introduction to porous media.
• Exercise 10 : Introduction to porous media.

Evaluation

Written examination.