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We characterize the thermodynamical equilibrium states of axisymmetric Euler-Beltrami flows. They have the form of coherent structures presenting one or several cells. We find the relevant control parameters and derive the corresponding…

This paper deals with the introduction of a decomposition of the deformations of curved thin beams, with section of order $\delta$, which takes into account the specific geometry of such beams. A deformation $v$ is split into an elementary…

Numerical Analysis · Mathematics 2011-09-13 Dominique Blanchard , Georges Griso

The behavior of an elastic curve bound to a surface will reflect the geometry of its environment. This may occur in an obvious way: the curve may deform freely along directions tangent to the surface, but not along the surface normal.…

Soft Condensed Matter · Physics 2014-08-18 Jemal Guven , Dulce María Valencia , Pablo Vázquez-Montejo

We study the initial-boundary value problem for an Euler-Bernoulli beam model with discontinuous bending stiffness laying on a viscoelastic foundation and subjected to an axial force and an external load both of Dirac-type. The…

Analysis of PDEs · Mathematics 2011-02-11 Günther Hörmann , Sanja Konjik , Ljubica Oparnica

We develop a Nitsche finite element method for a model of Euler--Bernoulli beams with axial stiffness embedded in a two--dimensional elastic bulk domain. The beams have their own displacement fields, and the elastic subdomains created by…

Numerical Analysis · Mathematics 2022-03-02 Peter Hansbo , Mats G. Larson

A short historical account of the curves related to the two-dimensional floating bodies of equilibrium and the bicycle problem is given. Bor, Levi, Perline and Tabachnikov found, quite a number had already been described as Elastica by…

Classical Physics · Physics 2020-03-04 Franz Wegner

We study a planar thin brittle beam subject to elastic deformations and cracks described in terms of a nonlinear Griffith energy functional acting on $SBV$ deformations of the beam. In particular we consider the case in which elastic bulk…

Analysis of PDEs · Mathematics 2016-02-25 Bernd Schmidt

We provide an extension to previous analysis of the localised beading instability of soft slender tubes under surface tension and axial stretching. The primary questions pondered here are: under what loading conditions, if any, can…

Soft Condensed Matter · Physics 2021-01-13 Dominic Emery , Yibin Fu

We consider the problem of minimizing Euler's elastica energy for simple closed curves confined to the unit disk. We approximate a simple closed curve by the zero level set of a function with values +1 on the inside and -1 on the outside of…

Analysis of PDEs · Mathematics 2010-05-21 Patrick W. Dondl , Luca Mugnai , Matthias Röger

An exact transformation method is introduced that reduces the governing equations of a continuum structure coupled to strong nonlinearities to a low dimensional equation with memory. The method is general and well suited to problems with…

Dynamical Systems · Mathematics 2014-03-05 Robert Szalai

Nonlinear bending phenomena of thin elastic structures arise in various modern and classical applications. Characterizing low energy states of elastic rods has been investigated by Bernoulli in 1738 and related models are used to determine…

Numerical Analysis · Mathematics 2024-12-20 Sören Bartels

Buckling plays a critical role in the transport and dynamics of elastic microfilaments in Stokesian fluids. However, previous work has only considered filaments with homogeneous structural properties. Filament backbone stiffness can be…

Soft Condensed Matter · Physics 2023-01-20 Thomas Nguyen , Harishankar Manikantan

We consider non-stationary localized oscillations of an infinite Bernoulli-Euler beam. The beam lies on the Winkler foundation with a point inhomogeneity (a concentrated spring with negative time-varying stiffness). In such a system with…

Classical Physics · Physics 2018-10-26 E. V. Shishkina , S. N. Gavrilov , Yu. A. Mochalova

In this third and final paper of a series, elastic properties of numerically simulated isotropic packings of spherical beads assembled by different procedures and subjected to a varying confining pressure P are investigated. In addition P,…

Disordered Systems and Neural Networks · Physics 2016-09-08 Ivana Agnolin , Jean-Noël Roux

We investigate buckling of soft elastic capsules under negative pressure or for reduced capsule volume. Based on nonlinear shell theory and the assumption of a hyperelastic capsule membrane, shape equations for axisymmetric and initially…

Soft Condensed Matter · Physics 2011-12-01 Sebastian Knoche , Jan Kierfeld

Fiber-reinforcement is a universal feature of many biological tissues. It involves the interplay between fiber stiffness, fiber orientation, and the elastic properties of the matrix, influencing pattern formation and evolution in layered…

Soft Condensed Matter · Physics 2025-04-29 Yang Liu , Rui-Cheng Liu , Wanyu Ma , Alain Goriely

The flow past a bullet-shaped blunt body moving in a pipe is investigated through global linear stability analysis (LSA) and direct numerical simulation (DNS). A cartography of the bifurcation curves is provided thanks to LSA, covering the…

Fluid Dynamics · Physics 2022-09-21 P. Bonnefis , D. Fabre , C. Airiau

The Euler--Plateau problem, proposed by \cite{gm}, concerns a soap film spanning a flexible loop. The shapes of the film and the loop are determined by the interactions between the two components. In the present work, the Euler--Plateau…

Soft Condensed Matter · Physics 2013-07-15 Yi-chao Chen , Eliot Fried

For curves of prescribed length embedded into the unit disc in two dimensions, we obtain scaling results for the minimal elastic energy as the length just exceeds $2\pi$ and in the large length limit. In the small excess length case, we…

Differential Geometry · Mathematics 2020-10-02 Stephan Wojtowytsch

Spatially confined rigid membranes reorganize their morphology in response to the imposed constraints. A crumpled elastic sheet presents a complex pattern of random folds focusing the deformation energy while compressing a membrane resting…