Slender elastic structures that interact with surrounding fluids are common in many biological and engineering settings. Motivated by these applications, we investigate the dynamics of a thin elastic sheet that is initially held in a laterally compressed configuration within a quiescent fluid, and then released from rest. As the sheet tries to recover its minimum energetic shape, its motion is governed by a subtle balance between elasticity, inertia, and fluid resistance. We begin by focusing on the early-time behavior and derive an analytical model in the inviscid limit, capable of predicting the oscillation frequency around the first buckling mode of the sheet and the growth rate near the unstable second mode. These predictions are in close agreement with numerical simulations of the more complex viscous formulation of the fluid, and show strong dependence on the sheet-to-fluid inertia ratio. At later times we analyze the sheet's transition from the second to the first buckling mode. We find that the inviscid model continues to track the system's evolution with good accuracy. In particular, we identify a logarithmic scaling for the transition time, which is also well supported by our numerical results. Altogether, our findings suggest that even in viscous environments, inviscid models can offer valuable insight into transient elastohydrodynamic processes.

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• Buckling
• Flow-structure interactions