We propose a topological data analysis framework for the study of damage evolution in anisotropic composite materials based on scalar filtrations defined on cubical complexes. Two complementary anisotropic filtrations are constructed from the structure tensor: a fibre-oriented filtration f1, capturing directional coherence, and a crack-oriented filtration f2, sensitive to isotropic and weakly oriented structures. Zero-dimensional persistent homology is analysed through merge trees built from the superlevel-set filtration via the transformation g=1−f, providing a hierarchical representation of connected components. Higher-order connectivity is described using skeleton-based Reeb-like graphs. From these constructions, we derive spatial and global descriptors, including a topological danger map and a Topological Damage Complexity Index (TDCI) based on one-dimensional persistent homology. The behaviour of the TDCI is examined with respect to variations in its parameters and to image perturbations, showing consistent trends across the considered configurations. The results highlight complementary structural behaviours captured by the two filtrations and show a coherent correspondence with observed patterns. Overall, the proposed framework provides a mathematically grounded description of structural organisation. It is intended as an exploratory approach, and further work is needed to clarify its relationship with the underlying physical damage mechanisms.
Canot et al. (Wed,) studied this question.