Supervisors:
E. Cancès (CERMICS, Ecole des Ponts Paristech)
V. Ehrlacher (CERMICS, Ecole des Ponts Paristech)
F. Legoll (Laboratoire Navier, Ecole des Ponts Paristech) | frederic.legoll@enpc.fr | http://navier.enpc.fr/LEGOLL-Frederic
Keywords:
random materials, homogenization, parallel computation, domain decomposition.
The aim of this project is to develop an efficient and original numerical method to compute the effective elastic properties of random heterogeneous materials.
We focus on heterogeneous elastic materials containing small inclusions embedded in a matrix. We assume that these inclusions are randomly distributed in the material. The effective elastic properties of the material are then deterministic, and their computation by a full-field method requires the resolution of an auxiliary problem defined over the entire space. Classical methods consist in considering a large (but finite) statistical elementary volume, on which the auxiliary problem, complemented with appropriate boundary conditions (for instance, periodic boundary conditions), is solved.
In this project, we consider another type of auxiliary problem, defined over the whole space, where the statistical elementary volume is embedded in an exterior infinite homogeneous material. The new problem, which has initially been introduced in a completely different setting, can be seen as a generalization of the Eshelby problem. In some previous work, we have shown, in collaboration with Benjamin Stamm (Aachen university, Germany), how such auxiliary problems can be used to approximate the effective thermal conduction properties.
In this project, the candidate will extend the range of application of the method in order to (i) compute the effective properties of polydisperse materials, (ii) compute the effective mechanical properties of microstructured materials (only thermal problems have been considered until now), …