- Motivated by a review of advanced experimental techniques for the microstructure description, and by typical results involving fluctuations present in plasticity, damage, fracture, and flows phenomena in porous media, basic tools of applied probability and random processes are recalled.
- Probabilistic tools for the description random media and models together with their simulation are introduced.
- Physics and mechanics of random media are first presented from the standpoint of approximate solutions of partial differential equations with random coefficients. For example, linear electrostatics problems in random media are studied by means of a perturbation expansion of the random electric and displacement fields, while bounds on the effective permittivity and of elastic moduli are derived from variational principles. This approach of homogenization, which can be applied to other physical properties like the composition of permeability, or of the thermal conductivity, is illustrated by third order bounds.
- The use of numerical techniques (like Finite Elements), to provide an estimation of homogenized properties of random media from Monte Carlo type simulations is introduced. Bounds and numerical techniques are then extended to non linear behaviours, like the plasticity of polycrystals.
- Given the importance of reliability problems in a multitude of engineering applications, several fracture statistics models (brittle, ductile, fatigue) are worked out from a probabilistic approach.
Single week. Lectures (80%) and practical training on computers (20%).
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Niveau requis : Prerequisites: basic knowledge of probability theory, physics and solids mechanics.
Modalités d'évaluation : The students prepare a written project from data processed during the training sessions.
Dernière mise à jour : jeudi 7 février 2013