  The processing of thin-structured materials in a fluidic environment, from
nearly inextensible but flexible graphene sheets to highly extensible polymer
films, arises in many applications. So far, little is known about the dynamics
of such thin sheets freely suspended in fluid. In this work, we study the
dynamics of freely suspended soft sheets in uniaxial extensional flow. Elastic
sheets are modeled with a continuum model that accounts for in-plane
deformation and out-of-plane bending, and the fluid motion is computed using
the method of regularized Stokeslets. We explore two types of sheets: "stiff"
sheets that strongly resist bending deformations and always stay flat, and
"flexible" sheets with both in-plane and out-of plane deformability that can
wrinkle. For stiff sheets, we observe a coil-stretch-like transition, similar
to what has been observed for long-chain linear polymers under extension as
well as elastic sheets under planar extension: in a certain range of capillary
number (flow strength relative to in-plane deformability), the sheets exhibit
either a compact or a highly stretched conformation, depending on deformation
history. For flexible sheets, sheets with sufficiently small bending stiffness
wrinkle to form various conformations. Here, the compact-stretched bistability
still occurs, but is strongly modified by the wrinkling instability: a
highly-stretched planar state can become unstable and wrinkle, after which it
may dramatically shrink in length due to hydrodynamic screening associated with
wrinkling. Therefore, wrinkling renders a shift in the bistability regime. In
addition, we can predict and understand the nonlinear long-term dynamics for
some parameter regimes with linear stability analysis of the flat steady
states.
