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

Outline

3 ECTS / 30 h

 Courses : 15 h

 Exercises : 15 h

 Practice : 0 h

Team

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

Objectives

To give a review of damage models for different materials (metal and alloys, concrete and glass, composites, elastomers) and different applucations (e.g. rupture under monotoni loading conditions, fatigue, dynamic fragmentation). To give the fundamentals for the numerical implementation of constitutive damage models.

Targets

This course of advanced modeling prepares engineers and young researchers for future design methods based on Damage mechanics concepts. Fields : aircraft and space industry, energy industry, car industry, civil engineering.

Bibliography

Mechanics of Solid Materials, J. Lemaitre, Cambridge University Press, 1990 A Course on Damage Mechanics, J. Lemaitre, Springler-Verlag,1992 Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittles Failures, J. Lemaitre and R. Desmorat, Springer, 2005 Mécanique non linéaire des matériaux, J. Besson, G. Cailletaud, J.-L. Chaboche, S. Forest, Hermès-Lavoisier, 2001

Content

• A - Probabilistic description
  1. Probabilistic description of the degradation and failure of britlle and quasi-brittle materials.
  2. Analysis of the transition between single and multiple fragmentation.
  3. Introduction to Poisson point processes. Weibull model.
• B - Phenomenological model in the thermodynamiccs framework
  1. Marigo and Mazars damage models.
  2. Lemaitre type damage models : effective stress concept, stored energy damage threshold, damage evolution laws, isotropy/induced anisotropy (damage tensors).
  3. Different behavior in tension and in compression.
  4. Micro-defect closure effect or quasi-unilateral conditions.
  5. General thermodynamics framework for hysteresis, fatigue and damage
• C - Gurson Type models
  1. GTN model for ductile failure
  2. Gurson-Rousselier-Lemaitre unified thermodynamics approach
• D - Localization and instabilities
  1. Bifurcation analysis. Perturbation analysis. Regularisation and non local models
• Written examination