STATISTICAL EXTRACTION OF PROCESS ZONES AND REPRESENTATIVE SUBSPACES IN FRACTURE OF RANDOM COMPOSITES | Zendy

Pierre Kerfriden | Zendy; Karl Michael Schmidt | Zendy; Timon Rabczuk | Zendy; Stéphane Bordas | Zendy

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STATISTICAL EXTRACTION OF PROCESS ZONES AND REPRESENTATIVE SUBSPACES IN FRACTURE OF RANDOM COMPOSITES

Author(s) -

Pierre Kerfriden,

Karl Michael Schmidt,

Timon Rabczuk,

Stéphane Bordas

Publication year - 2013

Publication title -

international journal for multiscale computational engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.43

H-Index - 28

eISSN - 1940-4352

pISSN - 1543-1649

DOI - 10.1615/intjmultcompeng.2013005939

Subject(s) - linear subspace , subspace topology , process (computing) , basis (linear algebra) , algorithm , stochastic process , computer science , space (punctuation) , mathematical optimization , mathematics , geometry , artificial intelligence , statistics , operating system

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 pre-computed 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 localised phenomena, we show that the reduced space generated by the method is a valid basis for the construction of a reduced order model.

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