Effective flow surface of a bi-porous material: constitutive modeling and numerical simulations

This work is devoted to the mechanical behavior of ductile porous materials with two populations of cavities of rather different sizes and shapes. A modeling of the effective plastic flow surface following [1] is briefly recalled and the results are compared to original numerical simulations using a computa-tional method based on augmented Lagrangians and Fast Fourier Transforms for composite materials (FFT Method, [2]). The starting point of this study is the modeling of the mechanical behavior of the highly irradiated ura-nium dioxide (UO2) studied by the French “Institut de Radioprotection et de Sûrete ́ Nucléaire ” (IRSN) to assess the behavior of fuel rods under accident conditions. UO2 is a porous material with a complex microstructure. This is a polycrystalline material with grain size of about 10 µm. When highly irradi-ated, its microstructure shows, as a first approximation, two populations of cavities of rather different sizes and shapes. At the smallest scale (microscopic scale), a first population of cavities, almost spher-ical in shape with a typical diameter of a few nanometers can be found in the interior of the grains (referred to as intragranular bubbles). At a larger scale (mesoscopic scale), a second population of cavities, roughly spheroidal in shape with typical size of a few microns, can be observed at the grai