Recent advances in 3D printing technologies open new possibilities in design of porous metamaterials intended for various engineering applications, including soft robotics, or tissue engineering. We consider fluid filled elastic scaffolds with embedded piezoelectric (PZ) segments extended by external electric circuits (EEC) providing a control handle. Homogenization of such structures under small deformation leads to a kind of Biot type media extended due to the electromechanical coupling. We have in mind secondary effects arising due the equilibrium and conservation laws imposed in the deformed configuration. This naturally induces the hypoelastic behaviour of the solid. Moreover, soft elastic surface of the pore provides a strong heterogeneity which yields local ``microproblems'' accounting for the fluid-structure interaction (FSI) including the dynamic effects of the flow in deforming pores. Since the nonlinear advection term of the acceleration is non-negligible, two time scales are considered and an appropriate time scaling of the fast-slow dynamics is introduced in a proportion to the spatial scaling. In addition, propagating acoustic waves (due to the PZ actuators) lead to the acoustic streaming effect in the fluid also characterized by two temporal scales. The nonlinearity associated with deforming configuration is respected by deformation-dependent homogenized coefficients involved in the macroscopic problem. To reduce the computational efficiency, the sensitivity analysis of the homogenized coefficients (HC) with respect to deformation induced by the macroscopic quantities is employed. This enables to introduce a convenient approximation scheme for the HCs and, by the consequence, to avoid the two-scale tight coupling of the macro- and microproblems otherwise needed in nonlinear problems using the ``FE-square'' method. The electromechanical interactions due to the EEC modify the dynamic impedance of the medium and introduces interesting features of the metamaterial; namely the associated nonlocal effects when distant actuation and sensing spots are linked.