Homogenization of materials having inclusions surrounded by layers modeled by the extended finite element method

E. Gal, E. Suday, H. Waisman

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


We study the homogenization of materials having three phases: matrix, inclusions, and inclusion coatings. To model the inclusions and their coatings we investigate two weakly discontinuous enrichment functions within the extended finite element method (XFEM) framework described by a single level set function. In both formulations the inclusion and coating shapes are independent of each other. The first approach, denoted as a V-type enrichment, combines several weak discontinuities by stacking the corresponding inclusion and coating enriched degrees of freedom in a single node (one on top of the other) while the second, denoted as a zigzag-type enrichment, only adds one additional degree of freedom per each direction. The XFEM approach is extremely efficient and avoids excessive remeshing compared to standard FEM, in particular when the coatings are very thin as in the case of aggregates surrounded by the interface transition zone (ITZ) in concrete materials. Comprehensive verification studies are presented including two-dimensional continuum problems and homogenization of concrete. Herein we mainly focus on the microscopic material response via homogenization of the unit cell. Nonetheless, once the homogenized material properties are obtained, the application to a full multiscale analysis is straightforward. While both enrichment types are different possible extensions to XFEM applied to such three-phase materials, both methods seem to work well and provide significant reduction in degrees of freedom and computation time as compared to standard FEM.

Original languageEnglish
Pages (from-to)239-252
Number of pages14
JournalInternational Journal for Multiscale Computational Engineering
Issue number3
StatePublished - 10 May 2013


  • Coatings
  • Homogenization
  • Inclusions
  • Level set
  • Multiscale
  • Three-phase materials
  • XFEM

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computational Mechanics
  • Computer Networks and Communications


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