|Course title||Physics and Mechanics of Random Media|
|Course address||60 boulevard Saint-Michel, 75272 Paris cedex 06|
|Minimum year of study||4th year|
|Minimum level of English||Good|
|Minimum level of French||Poor|
|Key words||random structures, variability, simulations, homogenization, upscaling, elasticity, fracture statistics, reliability, computer aided design of materials|
|Professor responsible||François Willot, Centre de Morphologie Mathématique, ENSMP|
|Participating professors||M. Bornert, B. Figliuzzi, C. Lantuejoul, B. Noetinger, Yves-Patrick Pellegrini, Anne-Françoise Gourgues-Lorenzon, F. Willot|
|Number of places||Minimum: 5, Maximum: 25, Reserved for local students: 0|
|Objectives||Many solid media and materials (composites, granular media, metals, biomaterials, porous media, soils, rocks, etc.) encountered in materials sciences, geophysics, environmental sciences, energetics, hydrogeology,... display microstructures and structures of several length scales, showing often a non-deterministic disorder. A better understanding and prediction of the resulting multiscale and random nature of materials' mesoscopic and/or macroscopic properties requires a modeling approach based on a combination of probabilistic concepts with methods of physics and mechanics. The course, which aims to provide an introduction to this subject, will be given in a self-contained series of lectures and training sessions on computers.|
|Programme to be followed||
The main topics of the course are as follows :
- - Transport in random media. Fracture Statistics models.
The courses detail the construction of models, their main properties, and their use from experimental data by means of examples of application.
A large part of the course is based on training by means of softwares Micromorph and Morph'Hom developed in CMM.
Structure of the course : Five full days in a single week. Lectures (70 %) and practical training on PC computers (30 %).
The daily course programme can be consulted some ten days prior to the course, please see : www.ensmp.fr (under the link , Ingénieurs civils)
|Prerequisites|| Basic knowledge in probability theory. Physics and Mechanics of solids
|Course exam||The students prepare a written project from data processed durig the training session