60 research outputs found
Singular inextensible limit in the vibrations of post-buckled rods: Analytical derivation and role of boundary conditions
In-plane vibrations of an elastic rod clamped at both extremities are studied. The rod is modeled as an extensible planar Kirchhoff elastic rod under large displacements and rotations. Equilibrium configurations and vibrations around these configurations are computed analytically in the incipient post-buckling regime. Of particular interest is the variation of the first mode frequency as the load is increased through the buckling threshold. The loading type is found to have a crucial importance as the first mode frequency is shown to behave singularly in the zero thickness limit in the case of prescribed axial displacement, whereas a regular behavior is found in the case of prescribed axial load.This publication is based in part upon work supported by Award no. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST) (A.G.). A.G. is a Wolfson/Royal Society Merit Award holder. Support from the Royal Society, through the International Exchanges Scheme (Grant IE120203), is also acknowledge
Soft beams: when capillarity induces axial compression
We study the interaction of an elastic beam with a liquid drop in the case
where bending and extensional effects are both present. We use a variational
approach to derive equilibrium equations and constitutive relation for the
beam. This relation is shown to include a term due to surface energy in
addition of the classical Young's modulus term, leading to a modification of
Hooke's law. At the triple point where solid, liquid, and vapor phases meet we
find that the external force applied on the beam is parallel to the
liquid-vapor interface. Moreover, in the case where solid-vapor and
solid-liquid interface energies do not depend on the extension state of the
beam, we show that the extension in the beam is continuous at the triple point
and that the wetting angle satisfy the classical Young-Dupr\'e relation
Role of uncrosslinked chains in droplets dynamics on silicone elastomers
We report an unexpected behavior in wetting dynamics on soft silicone
substrates: the dynamics of aqueous droplets deposited on vertical plates of
such elastomers exhibits two successive speed regimes. This macroscopic
observation is found to be closely related to microscopic phenomena occurring
at the scale of the polymer network: we show that uncrosslinked chains found in
most widely used commercial silicone elastomers are responsible for this
surprising behavior. A direct visualization of the uncrosslinked oligomers
collected by water droplets is performed, evidencing that a capillarity-induced
phase separation occurs: uncrosslinked oligomers are extracted from the
silicone elastomer network by the water-glycerol mixture droplet. The sharp
speed change is shown to coincide with an abrupt transition in surface tension
of the droplets, when a critical surface concentration in uncrosslinked
oligomer chains is reached. We infer that a droplet shifts to a second regime
with a faster speed when it is completely covered with a homogeneous oil film
Modélisation numérique de rubans en éléments de haut degré
National audienceNous proposons un modèle numérique robuste et efficace pour calculer les états d’équilibre stable d’un ruban naturellement plat ou courbé. Notre discrétisation spatiale se base sur des éléments à courbure normale linéaire et torsion géodésique quadratique en l’abscisse curviligne, qui permettent une grande richesse de représentation cinématique tout en garantissant l’inextensibilité parfaite du ruban. Les équilibres stables sont calculés par minimisation des énergies de gravité et d’élasticité du ruban, sous contrainte de développabilité
Getting DNA twist rigidity from single molecule experiments
We use an elastic rod model with contact to study the extension versus
rotation diagrams of single supercoiled DNA molecules. We reproduce
quantitatively the supercoiling response of overtwisted DNA and, using
experimental data, we get an estimation of the effective supercoiling radius
and of the twist rigidity of B-DNA. We find that unlike the bending rigidity,
the twist rigidity of DNA seems to vary widely with the nature and
concentration of the salt buffer in which it is immerged
Piercing a liquid surface with an elastic rod: Buckling under capillary forces
Abstract When a thin elastic structure comes in contact with a liquid interface, capillary forces can be large enough to induce elastic deformations. This effect becomes particularly relevant at small scales where capillary forces are predominant, for example in microsystems (Micro-Electro-Mechanical Systems or microfluidic devices) under humid environments. In order to explore the interaction between capillarity and elasticity, we have developed a macroscopic model system in which an initially immersed vertical elastic rod is raised through a horizontal liquid surface. We follow a combined approach of experiments, theory and numerical simulations to study this system. In spite of its apparent simplicity, our experiment reveals a complex phase diagram, involving large hysteretic behaviour. We employ Kirchhoff equations for thin elastic rods and use path-following methods from which we obtain a variety of equilibrium states and associated transitions that are in excellent qualitative and quantitative agreement with those observed experimentally
- …