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

Pierre Kerfriden (1) , Karl Michael Schmidt (2) , Timon Rabczuk (3) , Stephane Pierre-Alain Bordas (1)

1 School of Engineering [Cardiff]
2 School of Mathematics [Cardiff]
3 ISM - Institute of Structural Mechanics [Weimar]

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.

Mots clés: Fracture Mechanics; Particulate Composites; Process Zone; Proper Orthogonal Decomposition; Cross-Validation

Domaines: Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]

Pierre Kerfriden, Karl Michael Schmidt, Timon Rabczuk, Stephane Pierre-Alain Bordas. Statistical extraction of process zones and representative subspaces in fracture of random composites. 2012. ⟨hal-00678260⟩