A partition of unity finite element method for obtaining elastic properties of continua with embedded thin fibres. Radtke, F.&nbsp;K.<nbsp>F., Simone, A., & Sluys, L.&nbsp;J. International Journal for Numerical Methods in Engineering, 84(6):708--732, 2010.
doi  abstract   bibtex   
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.
@article{ Radtke:PoUFibre2010,
  author = {F. K. F. Radtke and A. Simone and L. J. Sluys},
  title = {A partition of unity finite element method for obtaining elastic properties of continua with embedded
		  thin fibres},
  journal = {International Journal for Numerical Methods in Engineering},
  year = {2010},
  volume = {84},
  number = {6},
  pages = {708--732},
  kind = {journal paper (ISI)},
  doi = {http://dx.doi.org/10.1002/nme.2916},
  pdf = {J12 - A partition of unity finite element method for obtaining elastic properties of continua with
		  embedded thin fibres -- Radtke, Simone, Sluys - ijnme - 2010.pdf},
  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.}
}

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