title: Extraction of process zones and low-dimensional attractive subspaces in stochastic fracture mechanics.
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 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.
authors.affiliation: Cardiff University, School of Engineering Queen's Buildings, The Parade, Cardiff CF24 3AA, Wales, UK.
authors.forename: P
authors.initials: P
authors.lastname: Kerfriden
authors.affiliation: Cardiff University, School of Mathematics Senghennydd Road, Cardiff CF24 4AG, Wales, UK.
authors.forename: K M
authors.initials: KM
authors.lastname: Schmidt
authors.affiliation: Institute of Structural Mechanics, Bauhaus-University Weimar Marienstraße 15, 99423 Weimar, Germany.
authors.forename: T
authors.initials: T
authors.lastname: Rabczuk
authors.affiliation: Cardiff University, School of Engineering Queen's Buildings, The Parade, Cardiff CF24 3AA, Wales, UK.
authors.forename: S P A
authors.initials: SP
authors.lastname: Bordas
keywords: Cross-Validation; Particulate Composites; Process Zone; Proper Orthogonal Decomposition; Stochastic Fracture Mechanics