53 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
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
Writhe formulas and antipodal points in plectonemic DNA configurations
The linking and writhing numbers are key quantities when characterizing the
structure of a piece of supercoiled DNA. Defined as double integrals over the
shape of the double-helix, these numbers are not always straightforward to
compute, though a simplified formula exists. We examine the range of
applicability of this widely-used simplified formula, and show that it cannot
be employed for plectonemic DNA. We show that inapplicability is due to a
hypothesis of Fuller theorem that is not met. The hypothesis seems to have been
overlooked in many works.Comment: 20 pages, 7 figures, 47 reference
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