A partition of unity finite element method for obtaining elastic properties of continua with embedded thin fibres

Authors

  • F. K. F. Radtke,

    1. Faculty of Civil Engineering and Geosciences, Delft University of Technology, P.O. Box 5048, 2600 GA Delft, The Netherlands
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  • A. Simone,

    Corresponding author
    1. Faculty of Civil Engineering and Geosciences, Delft University of Technology, P.O. Box 5048, 2600 GA Delft, The Netherlands
    • Faculty of Civil Engineering and Geosciences, Delft University of Technology, P.O. Box 5048, 2600 GA Delft, The Netherlands
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  • L. J. Sluys

    1. Faculty of Civil Engineering and Geosciences, Delft University of Technology, P.O. Box 5048, 2600 GA Delft, The Netherlands
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  • This article was published online on [20 April 2010]. An error was subsequently identified. This notice is included in the online and print versions to indicate that have been corrected [2 September 2010].

Abstract

The numerical analysis of large numbers of arbitrarily distributed discrete thin fibres embedded in a continuum is a computationally demanding process. In this contribution, we propose an approach based on the partition of unity property of finite element shape functions that can handle discrete thin fibres in a continuum matrix without meshing them. This is made possible by a special enrichment function that represents the action of each individual fibre on the matrix. Our approach allows to model fibre-reinforced materials considering matrix, fibres and interfaces between matrix and fibres individually, each with its own elastic constitutive law. Copyright © 2010 John Wiley & Sons, Ltd.

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