title: Soft beams: when capillarity induces axial compression.
abstract: 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 to 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 satisfies the classical Young-Dupré relation.
authors.affiliation: CNRS, UMR 7190, Institut Jean Le Rond d'Alembert, F-75005 Paris, France and UPMC Université Paris 06, UMR 7190, Institut Jean Le Rond d'Alembert, F-75005 Paris, France.
authors.forename: S
authors.initials: S
authors.lastname: Neukirch
authors.affiliation: CNRS, UMR 7190, Institut Jean Le Rond d'Alembert, F-75005 Paris, France and UPMC Université Paris 06, UMR 7190, Institut Jean Le Rond d'Alembert, F-75005 Paris, France.
authors.forename: A
authors.initials: A
authors.lastname: Antkowiak
authors.affiliation: CNRS, Ecole Polytechnique, UMR 7649, Laboratoire de Mécanique des Solides, F-91128 Palaiseau Cedex, France.
authors.forename: J-J
authors.initials: JJ
authors.lastname: Marigo