The effective mechanical properties of random porous media

Abstract The effective mechanical properties of homogeneous porous media can be theoretically determined by a multiple scale expansion. In such a scheme, the media are modelled as being spatially periodic. The elastic equations with appropriate boundary conditions are numerically solved on the unit cell to determine the macroscopic mechanical properties of the medium. Three types of unit cell were investigated: deterministic, fractal and random; the last type includes media derived from site percolation, random packings of spheres and a real sample of Fontainebleau sandstone. A systematic comparison is made with existing numerical data and with the predictions of various types of renormalization models.

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