The peristaltic flow is induced by deforming wall of a channel. The study of this phenomenon is of a great importance in physiology and biomechanics, however, as a driving mechanism of fluid transport, it presents and important and challenging issue in the design of smart ``bio-inspired'' materials. We consider locally periodic porous structures saturated by a Newtonian fluid. The peristaltic deformation wave of the microchannels can be induced by acoustic propagating waves, or by a convenient local control of piezoelectric segments. In this paper we report several issues related to the homogenization framework with the aim to construct a computationally efficient two-scale metamaterial model. We consider relatively small deformation which enables to use the linear kinematic framework. The poro-piezoelectric model derived in [1] is extended for the viscous fluid flow while respecting the inertia effects in both the phases. Using the homogenization based on the classic asymptotic analysis, cell problems (at the microlevel) are obtained which provide characteristic responses of the microstructures with respect to macroscopic strains, fluid pressure and electric potentials. These responses are needed to compute the effective (homogenized) parameters of the macroscopic problem which depend on the microconfiguration. The numerical studies demonstrate that such a linear model cannot capture the desired pumping effect of the homogenized continuum. For this, it is necessary to account for the nonlinearity associated with deformation-dependent microconfigurations. To avoid hurdles associated with such a fully nonlinear two-scale model, we apply a linearization procedure based on the sensitivity analysis of the local characteristic responses with respect to the deformation induced by the macroscopic quantities. In this way, by virtue of the methodology introduced in [2], we get first-order expansions of all the homogenized coefficients. The dynamic effects lead to the macroscopic flow model in a convolution form. For this option, a special treatment of the deformation-dependent dynamic permeability is needed. Numerical examples illustrate efficiency of the proposed computational approach.