Homogenization of a periodic elastic structure saturated with a Maxwell fluid

In this paper, the dynamics of an elastic porous medium saturated with a Maxwell fluid is investigated. Maxwell fluid belongs to the class of viscoelastic fluids whose deformation rate tensor is proportional to the sum of the stress tensor and its time derivative. The porous medium is governed by the equations of linear elasticity. A homogenized model of the structure is derived by employing the two-scale convergence technique. The model describes a new material which possesses two kinds of memory. The first memory is inherited from the Maxwell fluid, the second one is standard for the homogenization of non-stationary problems.