Effective elastic properties of bi-nanoporous materials
Résumé
This work is devoted to the theoretical modeling of the overall elastic properties of random nanoporous materials.
Focussing on irradiated uranium dioxide (UO2) material-type studied by the French ”Institut de Radioprotection
et de Sˆuret´e Nucl´eaire” to investigate the response of fuel rods under accident conditions, we consider
nanomaterials exhibiting two populations of cavities at two different scales: 1/ small scale cavities almost spherical
in shape (radius r) with a typical diameter of a few nanometers, 2/ larger scale cavities roughly ellipsoidal in
shape (major axis b and shape ratio w) with a typical size of a few microns. Recent molecular dynamics results [1]
show the existence of a non-neglectible surface effect on the effective elastic behavior for uranium dioxide at the
smallest scale, particularly when the surface/volume ratio is drastically increasing.
Analytical micromechanical [2, 3] models concerning materials with an isotropic distribution of nano-sized
spherical inclusions are extended here to the case of materials with two populations of voids. The spatial distribution
is assumed to be generally ellipsoidal which is more general than the case of spherical and ellipsoidal
cavities randomly distributed in space and in orientation. The proposed model follows the general framework of
the so-called ’morphologically representative pattern approach’ [4] and is called Mori-Tanaka-Generalized (MTG)
model. This model is compared to existing models (with or without surface effects). Particularly, the present model
allows a generalization of the Ponte Casta˜neda and Willis (PCW) model [5] to the case of porous media with surface
effects.