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A partition of unity finite element method for obtaining elastic properties of continua with embedded thin fibres
Author(s) -
Radtke F. K. F.,
Simone A.,
Sluys L. J.
Publication year - 2010
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2916
Subject(s) - finite element method , partition of unity , partition (number theory) , matrix (chemical analysis) , constitutive equation , mathematical analysis , mathematics , computer science , materials science , structural engineering , composite material , engineering , combinatorics
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.