title: Eulerian formulation of elastic rods.
abstract: In numerous biological, medical and engineering applications, elastic rods are constrained to deform inside or around tube-like surfaces. To solve efficiently this class of problems, the equations governing the deflection of elastic rods are reformulated within the Eulerian framework of this generic tubular constraint defined as a perfectly stiff normal ringed surface. This reformulation hinges on describing the rod-deformed configuration by means of its relative position with respect to a reference curve, defined as the axis or spine curve of the constraint, and on restating the rod local equilibrium in terms of the curvilinear coordinate parametrizing this curve. Associated with a segmentation strategy, which partitions the global problem into a sequence of rod segments either in continuous contact with the constraint or free of contact (except for their extremities), this re-parametrization not only trivializes the detection of new contacts but also transforms these free boundary problems into classic two-points boundary-value problems and suppresses the isoperimetric constraints resulting from the imposition of the rod position at the extremities of each rod segment.
authors.affiliation: Division of Structural Engineering, Department of Architecture, Geology, Environment and Constructions, University of Liège, Liège, Belgium; Department of Civil, Environmental and Geo-Engineering, University of Minnesota, Minneapolis, MN, USA; F.R.I.A., F.R.S.-FNRS, National Fund for Scientific Research, Brussels, Belgium.
authors.forename: Alexandre
authors.identifier: 0000-0001-9771-6926
authors.initials: A
authors.lastname: Huynen
authors.affiliation: Department of Civil, Environmental and Geo-Engineering , University of Minnesota , Minneapolis, MN, USA.
authors.forename: Emmanuel
authors.initials: E
authors.lastname: Detournay
authors.affiliation: Division of Structural Engineering, Department of Architecture, Geology, Environment and Constructions , University of Liège , Liège, Belgium.
authors.forename: Vincent
authors.initials: V
authors.lastname: Denoël
keywords: Eulerian formulation; elastic rod; self-feeding