Variational analysis of inextensible elastic curves

@article{Bevilacqua2022VariationalAO,
  title={Variational analysis of inextensible elastic curves},
  author={G. Bevilacqua and Luca Lussardi and Alfredo Marzocchi},
  journal={Proceedings of the Royal Society A},
  year={2022},
  volume={478}
}
We minimize elastic energies on framed curves which penalize both curvature and torsion. We also discuss critical points using the infinite dimensional version of the Lagrange multipliers’ method. Finally, some examples arising from the applications are discussed and also numerical experiments are presented. 

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References

SHOWING 1-10 OF 40 REFERENCES

Force and moment balance equations for geometric variational problems on curves.

TLDR
The Euler-Lagrange equations are presented as equilibrium equations for the internal force and moment of a functional defined on a curve in a three-dimensional space to promote the study of biofilaments and nanofilaments.

Dimensional Reduction of the Kirchhoff-Plateau Problem

We obtain the minimal energy solution of the Plateau problem with elastic boundary as a variational limit of the minima of the Kirchhoff-Plateau problems with a rod boundary when the cross-section of

ON THE KNOTTED ELASTIC CURVES

According to the Bernoulli-Euler theory of elastic rods the bending energy of the wire is proportional to the total squared curvature of , which we will denote by F( )= R k 2 ds. If the result of

Minimal elastic networks

We consider planar networks of three curves that meet at two junctions with prescribed equal angles, minimizing a combination of the elastic energy and the length functional. We prove existence and

Long time existence of solutions to an elastic flow of networks

Abstract The L2-gradient flow of the elastic energy of networks leads to a Willmore type evolution law with non-trivial nonlinear boundary conditions. We show local in time existence and uniqueness

Lagrangian Aspects of the Kirchhoff Elastic Rod

TLDR
Basic facts about (an integrable case of) Kirchhoff elastic rods are described here, which amplify the connection between the variational problem for rods and the soliton equation LIE.

Hamiltonians for curves

We examine the equilibrium conditions of a curve in space when a local energy penalty is associated with its extrinsic geometrical state characterized by its curvature and torsion. To do this we

A Corrected Sadowsky Functional for Inextensible Elastic Ribbons

The classical theory of ribbons, developed by Sadowsky and Wunderlich, has recently received renewed attention. Here, by means of Γ$\varGamma$-convergence, we re-examine the derivation of the limit

Knotted Elastic Curves in R3

One of the oldest topics in the calculus of variations is the study of the elastic rod which, according to Daniel Bernoulli's idealization, minimizes total squared curvature among curves of the same

Soap film spanning an elastic link

We study the equilibrium problem of a system consisting of several Kirchhoff rods linked in an arbitrary way and tied by a soap film, using techniques of the Calculus of Variations. We prove the