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

TL;DR

This paper introduces a statistical method to identify process zones in heterogeneous materials by spectral analysis and greedy algorithms, enabling better reduced order modeling of localized fracture phenomena.

Contribution

It presents a novel statistical approach for defining process zones and constructing low-dimensional subspaces in heterogeneous materials, enhancing fracture analysis.

Findings

Effective identification of process zones using spectral analysis.

Development of a greedy algorithm for subspace selection.

Validation of reduced space as a basis for reduced order models.

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.