Homogenization of Dynamics Equations for a Medium Consisting of an Elastic Material and an Incompressible Oldroyd Fluid

The dynamics of a two-phase medium consisting of an isotropic elastic material and an incompressible viscoelastic Oldroyd fluid is investigated. For this medium, a mathematical model is derived that describes the dynamics of the corresponding effective medium. The resulting model contains a system of integro-differential equations with constant coefficients. The coefficients and kernels of the effective equations are found through solutions of auxiliary periodic problems defined on the unit cube. Their explicit analytical expressions for the case of a layered medium are calculated.