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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.

SUBMITTER: Huynen A

PROVIDER: S-EPMC4950185 | biostudies-literature | 2016 Jun

REPOSITORIES: biostudies-literature

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Eulerian formulation of elastic rods.

Huynen Alexandre A Detournay Emmanuel E Denoël Vincent V

Proceedings. Mathematical, physical, and engineering sciences 20160601 2190

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 refer ...[more]

PMID: 27436960

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Eulerian formulation of elastic rods.

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Eulerian formulation of elastic rods.

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