UC Santa Barbara

Inferring mechanical interactions from the spatial organization of discrete damage events is a fundamental inverse problem in the mechanics of heterogeneous materials. This work develops a statistical framework for extracting load-transfer interactions from three-dimensional fiber fracture data in unidirectional fiber-reinforced composites. Conventional micromechanical models typically assume global load sharing (GLS), implying statistically independent fiber fracture events, whereas growing experimental evidence suggests that load redistribution can become localized, producing spatially autocorrelated fracture. To distinguish these effects, classical second-order spatial statistics are extended by decomposing pairwise separations into transverse and axial components, reflecting the directional asymmetry of stress redistribution in fiber composites. Analytical solutions are derived for two canonical GLS models that establish a mechanics-based null hypothesis for mechanical independence. Unlike conventional approaches based on complete spatial randomness, this null hypothesis explicitly accounts for both the underlying fiber arrangement and the observed axial break intensity profile, allowing arbitrary fracture distributions to be analyzed without assuming a particular axial form. A normalized fiber interaction statistic is then introduced to remove these contributions, enabling direct assessment of mechanically induced coupling between neighboring fibers and meaningful comparison among datasets with different fiber arrangements and break distributions. Monte Carlo simulations quantify estimator variability and demonstrate that localized interactions can be detected with high statistical power even when only a modest fraction of fiber breaks are mechanically coupled. The resulting framework provides a rigorous methodology for interpreting volumetric fracture data and establishes a quantitative bridge between experimentally observed spatial damage patterns and micromechanical load-sharing models. Although demonstrated for fiber fracture in unidirectional composites, the underlying methodology is broadly applicable to heterogeneous materials in which damage evolves through discrete spatial events.