Elastic behavior of porous media with spherical nanovoids

• The modeling of the effective elastic properties of nanoporous media is studied.
• The case of the spherical nanovoids is investigated.
• The morphologically representative pattern-based approach is used.
• Existing models can be generalized to more complex microstructures.
• New bounds and estimates are derived and two particular cases are treated.

This study is devoted to the effective elastic properties of nanoporous media containing spherical nanovoids. Nanocomposites materials are strongly dependent on their nanometric characteristic lengths. This size effect cannot be directly modeled using the classical homogenization schemes based on the Eshelby inclusion problem. However recent studies have extended the continuum mechanics and well-known micromechanical models to the nanoscale. In this paper, it is shown that these models can be replaced in a unified framework using the morphologically representative pattern-based approach of Stolz and Zaoui (1991) and therefore can be generalized to more complex microstructures. Following this approach, new bounds and estimates are derived. Two particular cases are treated: (i) the case of an ellipsoidal spatial distribution of the voids, (ii) the case of a biporous material containing both spherical nanovoids and randomly oriented spheroidal microvoids. The second case is typical of the microstructure of the irradiated uranium dioxide (UO2). Thereby, the associated result could be used for determining the poro-elastic properties of these doubly voided materials.