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

Kerfriden, Pierre ORCID: https://orcid.org/0000-0002-7749-3996, Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024, Rabczuk, T. and Bordas, Stephane Pierre Alain ORCID: https://orcid.org/0000-0001-8634-7002 2013. Statistical extraction of process zones and representative subspaces in fracture of random composites. International Journal for Multiscale Computational Engineering 11 (3) , pp. 253-287. 10.1615/IntJMultCompEng.2013005939

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Abstract

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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Engineering
Subjects:	T Technology > TA Engineering (General). Civil engineering (General)
Uncontrolled Keywords:	fracture of particulate composites, process zone, adaptive proper orthogonal decomposition, domain decomposition, cross-validation, greedy algorithm
Publisher:	Begell House
ISSN:	1543-1649
Funders:	EU FP7, European Research Council (ERC), Royal Academy of Engineering, Leverhulme Trust
Last Modified:	11 Mar 2023 02:13
URI:	https://orca.cardiff.ac.uk/id/eprint/51172

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