  The paper presents a new type of weakly nonlinear two-scale model of
controllable periodic porous piezoelectric structures saturated by Newtonian
fluids. The flow is propelled by peristaltic deformation of microchannels which
is induced due to piezoelectric segments embedded in the microstructure and
locally actuated by voltage waves. The homogenization is employed to derive a
macroscopic model of the poroelastic medium with effective parameters modified
by piezoelectric properties of the skeleton. To capture the peristaltic
pumping, the nonlinearity associated with deforming configuration must be
respected. In the macroscopic model, this nonlinearity is introduced through
homogenized coefficients depending on the deforming micro-configurations. For
this, linear expansions based on the sensitivity analysis of the homogenized
coefficients with respect to deformation induced by the macroscopic quantities
are employed. This enables to avoid the two-scale tight coupling of the macro-
and microproblems otherwise needed in nonlinear problems. The derived
reduced-order model is implemented and verified using direct numerical
simulations of the periodic heterogeneous medium. Numerical results demonstrate
the peristaltic driven fluid propulsion in response to the electric actuation
and the efficiency of the proposed treatment of the nonlinearity. The paper
shows new perspectives in homogenization-based computationally efficient
modelling of weakly nonlinear problems where continuum microstructures are
perturbed by coupled fields.
