Efficient analysis of dense fiber reinforcement using a reduced embedded formulation

M. Goudarzi*, H.J.M. Geijselaers, R. Akkerman

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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In this paper we alleviate limitations of the conventional embedded reinforcement formulation for applications with dense fiber contents. We demonstrate that by condensing the fiber degrees of freedom during the assembly stage, the condition number of the resultant stiffness matrix is effectively reduced and the use of iterative solvers is facilitated even without preconditioning. Numerical benchmarks consisting of very large numbers of high aspect ratio discrete fibers are performed, and major advantages are reported in terms of the computational efficiency of the solution method. We apply the solution method to a set of examples in the modeling of the fiber reinforced composites, specifically the estimation of the homogenized mechanical properties of the discontinuous fiber composites and modeling of the compression molding process. In the latter case, a specimen containing more than 2 million discrete fibers is analyzed.

Original languageEnglish
Pages (from-to)1-15
Number of pages15
JournalComputational mechanics
Early online date11 Sep 2020
Publication statusPublished - Jan 2021


  • UT-Hybrid-D
  • Effective material properties
  • Embedded reinforcement
  • Fiber reinforced composite
  • Finite element method
  • Compression molding


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