  The two-scale computational homogenization method is proposed for modelling
of locally periodic fluid-saturated media subjected a to large deformation
induced by quasistatic loading. The periodic heterogeneities are relevant to
the mesoscopic scale at which a double porous medium constituted by
hyperelastic skeleton and an incompressible viscous fluid is featured by large
contrasts in the permeability. Within the Eulerian framework related to the
current deformed configuration, the two-scale homogenization approach is
applied to a linearized model discretized in time, being associated with an
incremental formulation. For this, the equilibrium equation and the mass
conservation expressed in the spatial configuration are differentiated using
the material derivative with respect to a convection velocity field. The
homogenization procedure of the linearized equations provides effective
(homogenized) material properties are computed to constitute the incremental
macroscopic problem. The coupled algorithm for the multiscale problem is
implemented using the finite element method. Illustrative 2D numerical
simulations of a poroelastic medium are presented including a simple validation
test.
