On the elastic fibre pull-out problem: asymptotic and numerical results

  • N. Phan-Thien
  • G. Pantelis
  • M. B. Bush
Original Papers
Received:

Summary

In this paper we present some asymptotic results for the pull out of a nearly-rigid fibre from an elastic matrix. The asymptotic results are accurate toO(ε2), whereε=(ln 2l/R)−1, if the fibre is pull-out from a semi-infinite matrix, and toO(h2/l2) if the fibre is pull-out from a matrix contained in a cylindrical container of radiush. Here R andl are the fibre radius and length, respectively. An interpolation formula is suggested which yields correct asymptotic behaviour at bothh/l=0 andh/l → ∞. These asymptotic results are confirmed by numerical methods to at least an aspect ratio ofl/R≧9. We also report some numerical confirmation of a previous approximate result for the pull out of a rigid fibre with an enlarged spherical end.

Keywords

Aspect Ratio Asymptotic Behaviour Mathematical Method Elastic Fibre Asymptotic Result 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Zusammenfassung

In der vorliegenden Arbeit geben wir einige asymptotische Ergebnisse für das Ausziehen einer beinahe starren Faser aus einer elastischen Matrix. Die asymptotischen Resultate sind aufO(ε2) genau, woε=(ln 2l/R)−1 bedeutet, falls die Faser aus einer halbunendlichen Matrix ausgezogen wird. Sie sind aufO(h2/l2) genau, falls die Faser aus einer Matrix ausgezogen wird, welche einen Zylinder vom Radiush füllt. Eine Interpolationsformel, die das richtige asymptotische Verhalten fürh/l=0 undh/l → ∞ aufweist, wird vorgeschlagen. Diese asymptotischen Ergebnisse werden durch numerische Methoden mindestens bis geometrische Verhältnisse vonl/R≧9 bestätigt. Wir berichten ebenfalls über eine gewisse numerische Bestätigung eines früheren approximativen Resultats für das Ausziehen einer starren Faser mit einem vergrößerten sphärischen Kopf.

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Copyright information

© Birkhäuser Verlag Basel 1982

Authors and Affiliations

  • N. Phan-Thien
    • 1
  • G. Pantelis
    • 1
  • M. B. Bush
    • 1
  1. 1.Dept. of Mechanical EngineeringUniversity of SydneySydneyAustralia

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