Physical networks for disordered metamaterials

Recent advances in high-resolution 3D imaging have provided unprecedented insights about the architecture of biological systems, revealing morphological and structural pat-terns that challenge conventional material design. In parallel, physical networks –graphs where nodes and links are space-filling objects subject to physical constraints– have emerged as a versatile framework to capture the morphological complexity found in real-world systems, offering data-driven strategies to design network metamaterials. In this talk, I will survey recent progress in the characterization of minimal models of physical networks, emphasizing how excluded volume interactions and geometric constraints give rise to correlated heterogeneities—such as morphological preferential attachment and bundling—in both structure and topology. Given their differences from classical disordered materials, these systems invite fundamental questions about how their distinctive structural features shape their mechanical behavior and adaptive response. I will conclude by outlining key open challenges and future directions for investigating the rheology and functioning of physical networks, aiming to trace new avenues for the design of mechanical metamaterials.