AI-Revealed Transition From Density- to Connectivity-Controlled Mechanics in Hierarchical Porous Materials

Hierarchical porous architectures enable lightweight, damage-tolerant materials, yet their performance depends on how mechanical properties scale with density. Classical cellular-solid theory captures the density-controlled scaling law, but it remains unclear whether microscale defect topology drives its breakdown. Here, in situ synchrotron tomography, diffusion-based generative modeling, and micromechanical simulations are combined to reveal an AI-enabled, scale-dependent transition in stiffness-density scaling in trabecular bone with hierarchical porous structures. At the millimeter scale, the effective Young's modulus follows cellular-solid behavior, $E\propto {\left(\frac{BV}{TV}\right)}^2$ , where $\frac{BV}{TV}$ is defined as bone volume divided by total volume. At the lacunar (microscale) level, simulations on thousands of lacunar microstructures, augmented by statistically faithful AI-generated ensembles, exhibit a markedly steeper dependence, $E\propto {\left(\frac{BV}{TV}\right)}^{4-6}$ . This hypersensitivity arises from long-range interactions between void-induced stress fields that merge into system-spanning weak corridors, shifting load transfer from porosity control to matrix connectivity and promoting guided crack initiation and propagation. By preserving higher-order morphology while expanding microstructural sampling, AI generation enables ensemble-level quantification of this connectivity-controlled regime under data-limited imaging. These results establish a mechanism by which microscale defect topology can dominate stiffness in hierarchical porous materials.