DEFORMABLE POROUS-MEDIA WITH DOUBLE POROSITY - QUASI-STATICS .2. MEMORY EFFECTS

As in our previous paper, we investigate the macroscopic quasi-static description of a porous medium with a double porosity constituted by pores and fractures. For this purpose, we use a homogenization technique. As expected, the macroscopic description is sensitive to the ratios between the different scales, l/l' and l'/l'' where l, l', l'' are characteristic lengths of the pores, the fractures, and the macroscopic medium, respectively. In the first paper, we investigated the case l'/l'' = O(l2/l'2) much less than 1 (case 1) which exhibits a coupling between the flows through the pores and the fractures. In the present paper, we deal with the other homogenizable cases. The case 3 where l/l'= O(l'2/l''2) much less than 1 gives a macroscopic description similar to that of a single porosity medium. The main result, however, is the case 2, where l/l' = O(l'/l'') much less than 1, which exhibits memory effects. These are due to the seepage through the micropores.