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The interaction of a thin viscous film with an elastic sheet results incoupling of pressure and deformation, which can be utilized as an actuationmechanism for surface deformations in a wide range of applications, includingmicrofluidics, optics, and soft robotics. Implementation of such configurationsinherently takes place over finite domains and often requires somepre-stretching of the sheet. Under the assumptions of strong pre-stretching andsmall deformations of the lubricated elastic sheet, we use the linearizedReynolds and Foppl-von Karman equations to derive closed-form analyticalsolutions describing the deformation in a finite domain due to external forces,accounting for both bending and tension effects. We provide a closed-formsolution for the case of a square-shaped actuation region and present theeffect of pre-stretching on the dynamics of the deformation. We further presentthe dependence of the deformation magnitude and timescale on the spatialwavenumber, as well as the transition between stretching- and bending-dominantregimes. We also demonstrate the effect of spatial discretization of theforcing (representing practical actuation elements) on the achievableresolution of the deformation. Extending the problem to an axisymmetric domain,we investigate the effects arising from nonlinearity of the Reynolds andFoppl-von Karman equations and present the deformation behavior as it becomescomparable to the initial film thickness and dependent on the induced tension.These results set the theoretical foundation for implementation of microfluidicsoft actuators based on elastohydrodynanmics.

Elastohydrodynamics of a pre-stretched finite elastic sheet lubricated by a thin viscous film with application to microfluidic soft actuators