Variational analysis of inextensible elastic curves

  title={Variational analysis of inextensible elastic curves},
  author={G. Bevilacqua and Luca Lussardi and Alfredo Marzocchi},
  journal={Proceedings of the Royal Society A},
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. 

Figures and Tables from this paper

Elastic membranes spanning deformable boundaries
We perform a variational analysis of an elastic membrane spanning a curve which may sustain bending and torsion. First, we deal with parametrized curves and linear elastic membranes proving the
The Kirchho -Plateau problem and its generalizations
The Kirchho -Plateau problem concerns the equilibrium shapes of a system in which a flexible filament in the form of a closed loop is spanned by a liquid film, with the filament being modeled as a


Force and moment balance equations for geometric variational problems on curves.
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
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
Semilinear Elliptic Equations for Beginners: Existence Results via the Variational Approach
Introduction and basic results.- Minimization techniques: compact problems.- Minimization techniques: lack of compactness.- Introduction to minimax methods.- Index of the main assumptions
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
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