Objectifs :
• Gain a better understanding and prediction of the impact of multiscale and random nature of the microstructure of heterogeneous media
• Learn new methods for describing a modeling approach based on a combination of probabilistic concepts with methods of physics and mechanics
• Learn the numerical techniques (like fast Fourier Transform) to provide an estimation of homogenized properties of random media from Monte Carlo type simulations

Contenu :
1- Introduction and basic concepts
- Introduction to materials and porous media variability of physical and mechanical properties at different scales
- Advances in experimental techniques :available data at different scales
- Introduction to applied probability, probabilistic models and to simulation of random variables
2- Models and simulation of random media
- Morphological characterization of random sets and of random functions : size, repartition, connectivity
- Examples of models and simulations of point processes, of random sets
3-Homogeneization of random media (linear properties) : bound and numerical techniques
- Electrostatics of random media
- Estimation of the effective classical and Hashin-Shtrikman variational principles
- Basis of the homogeneization of periodic media
- Transport properties of random porous media
4- Homogeneization of random media (non linear properties)
- Introduction to non linear constitutive behaviours
- Introduction to the Elshelby’s problem of inclusions
- Plasticity of polycrystals
5- Fracture statistic, Computer aided design of materials
- Probalistic continuum models of brittle fracture

Commentaires :
Department Mathematics and Systems
Centre de Morphologie Mathématique (CMM)
Dr. François WILLOT
Email: francois.willot@mines-paristech.fr
http://www.cmm.mines-paristech.fr/

Dernière mise à jour : mardi 9 septembre 2014