Extraction of process zones and low-dimensional attractive subspaces in stochastic fracture mechanics

Details Extraction of process zones and low-dimensional attractive subspaces in stochastic fracture mechanics Extraction of process zones and low-dimensional attractive subspaces in stochastic fracture mechanics

2012-03-12

arxiv.org/abs/1203.2487v2

Physics

Classical Physics

Submitted for publication in International Journal for Multiscale Computational Engineering

Scientific paper

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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