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The conformation of a long linear polymer dissolved in fluid and exposed toan extensional flow is well-known to exhibit a "coil-stretch" transition, whichfor sufficiently long chains can lead to bistability. The present work reportscomputations indicating that an analogous "compact-stretched" transition arisesin the dynamics of a thin elastic sheet. Sheets of nominally circular, squareor rectangular shape are simulated in planar and biaxial flows using a finiteelement method for the sheet conformations and a regularized Stokeslet methodfor the fluid flow. If a neo-Hookean constitutive model is used for the sheetelasticity, the sheets will stretch without bound once a critical extensionrate, as characterized nondimensionally by a capillary number, is exceeded.Nonlinear elasticity, represented with the Yeoh model, arrests the stretching,leading to a highly-stretched steady state once the critical capillary numberis exceeded. For all shapes and in both planar and biaxial extension, aparameter regime exists in which both weakly stretched (compact) and stronglystretched states can be found, depending on initial conditions. I.e. thisparameter regime displays bistability. As in the long-chain polymer case, thebistable behavior arises from the hydrodynamic interaction between distantelements of the sheet, and vanishes if these interactions are artificiallyscreened by use of a Brinkman model for the fluid motion. While the sheets cantransiently display wrinkled shapes, all final shapes in planar and biaxialextension are planar.

Coil-stretch-like transition of elastic sheets in extensional flows