Statistical extraction of process zones and representative subspaces in fracture of random composites

P. Kerfriden, K. M. Schmidt, Timon Rabczuk, S. P A Bordas

Research output: Contribution to journalArticle

15 Citations (Scopus)


We propose to identify process zones in heterogeneous materials by tailored statistical tools. The process zone is redefined as the part of the structure where the random process cannot be correctly approximated in a low-dimensional deterministic space. Such a low-dimensional space is obtained by a spectral analysis performed on precomputed solution samples. A greedy algorithm is proposed to identify both process zone and low-dimensional representative subspace for the solution in the complementary region. In addition to the novelty of the tools proposed in this paper for the analysis of localized phenomena, we show that the reduced space generated by the method is a valid basis for the construction of a reduced-order model.

Original languageEnglish
Pages (from-to)253-287
Number of pages35
JournalInternational Journal for Multiscale Computational Engineering
Issue number3
Publication statusPublished - 2013 May 10
Externally publishedYes



  • Adaptive proper orthogonal decomposition
  • Cross-validation
  • Domain decomposition
  • Fracture of particulate composites
  • Greedy algorithm
  • Process zone

ASJC Scopus subject areas

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

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