elastica

Is it possible to prevent the fall of a rod inside a sliding sleeve due to gravity?

By controlling the transverse oscillations of the constraint and revealing a novel self-tuning dynamic response, we provide a positive answer to this question in our paper:

May a double restabilization of the trivial path occurr at monotonically increasing compression force?

May movable constraints be exploited to attain target force–displacement curves?

Liu, M., Domino, L., & Vella, D.* (2020). Tapered elasticæ as a route for axisymmetric morphing structures. Soft Matter, 16(33), 7739-7750. 

How a mass falls when attached to a flexible element with varying length?
We provide the answer to this question in our paper: Armanini, Dal Corso, Misseroni, Bigoni (2019) Configurational forces and nonlinear structural dynamics.
Journal of the Mechanics and Physics of Solids.
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May a catastrophe machine be realized through an elastic continuous element?
We provide a positive answer to this question in our paper: Cazzolli, Misseroni, Dal Corso. Elastica catastrophe machine: theory, design and experiments. Journal of the Mechanics and Physics of Solids.

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We present a unified classical treatment of partially constrained elastic rods. Partial constraints often entail singularities in both shapes and reactions. Our approach encompasses both sleeve and adhesion problems, and provides simple and unambiguous derivations of counterintuitive results in the literature. Relationships between reaction forces and moments, geometry, and adhesion energies follow from the balance of energy during quasistatic motion. We also relate our approach to the configurational balance of material momentum and the concept of a driving traction.

What should be expected when an elastic rod is forced to slip inside a sliding sleeve and against an obstacle?

After buckling, configurational forces play a strong role, so that a force reversal is observed!

Enjoy the injection of an elastic rod at http://www.ing.unitn.it/~bigoni/injection.html

Complex structures consisting of intertwined, nominally vertical carbon nanotubes (CNTs) are called turfs. Under uniform compression experiments, CNT turfs exhibit irreversible collective buckling of a layer preceded by reorientation of CNT segments. Experimentally observed independence of the buckling stress and the buckling wavelength on the turf width suggests the existence of an intrinsic material length.