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Related Experiment Video

Updated: Mar 17, 2026

Ultrasonic Fatigue Testing in the Tension-Compression Mode

Ultrasonic Fatigue Testing in the Tension-Compression Mode

Published on: March 7, 2018

Eulerian formulation of elastic rods.

Alexandre Huynen¹, Emmanuel Detournay², Vincent Denoël³

¹Division 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.

Proceedings. Mathematical, Physical, and Engineering Sciences

|July 21, 2016

Summary

This summary is machine-generated.

This study presents a new method for modeling elastic rods constrained by tubular surfaces. The approach simplifies complex contact detection and boundary problems for engineering and medical applications.

Keywords:

Eulerian formulation elastic rod self-feeding

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Area of Science:

Mechanics of Materials
Computational Engineering
Biomechanical Engineering

Background:

Elastic rods frequently deform within tubular constraints in biological, medical, and engineering fields.
Existing models face challenges in efficiently handling these complex contact and boundary conditions.

Purpose of the Study:

To develop an efficient computational framework for analyzing the deformation of elastic rods within generic tubular constraints.
To simplify the mathematical treatment of contact and boundary value problems associated with constrained rod mechanics.

Main Methods:

Reformulation of elastic rod deflection equations within an Eulerian framework for tubular constraints.
Description of rod configuration relative to a reference curve (spine) of the constraint.
Application of a segmentation strategy to divide the problem into manageable rod segments.

Main Results:

Trivialized detection of new contacts between the rod and the tubular surface.
Transformation of free boundary problems into standard two-point boundary-value problems.
Elimination of isoperimetric constraints arising from segment extremity conditions.

Conclusions:

The proposed Eulerian reformulation offers an efficient and robust method for simulating constrained elastic rod behavior.
This approach significantly simplifies the analysis of complex mechanical systems involving tubular constraints.
The findings have broad applicability in fields requiring precise modeling of deformable structures within confined spaces.