Abstract
We consider the motion of an infinitely long, naturally curved, planar Elastica. The Elastica is flattened onto a rigid impenetrable substrate and held by its endpoints. When one of its endpoints is released, it is set off in a curling motion, which we seek to describe mathematically based on the non-linear equations of motions for planar elastic rods undergoing finite rotations. This problem is used to introduce the technique of matched asymptotic expansions. We derive a non-linear solution capturing the late dynamics, when a roll comprising many turns has formed: in this regime, the roll advances at an asymptotically constant velocity, whose selection we explain. This contribution presents an expanded version of the results published in Callan-Jones et al. (Phys. Rev. Lett. 2012).
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© 2015 CISM, Udine
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Audoly, B., Callan-Jones, A., Brun, PT. (2015). Dynamic curling of an Elastica: a nonlinear problem in elastodynamics solved by matched asymptotic expansions. In: Bigoni, D. (eds) Extremely Deformable Structures. CISM International Centre for Mechanical Sciences, vol 562. Springer, Vienna. https://doi.org/10.1007/978-3-7091-1877-1_3
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DOI: https://doi.org/10.1007/978-3-7091-1877-1_3
Publisher Name: Springer, Vienna
Print ISBN: 978-3-7091-1876-4
Online ISBN: 978-3-7091-1877-1
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