Morphing active networks.

Abstract

Biological networks like leaf venation exhibit remarkable morphing capabilities that enable organisms to adapt and thrive in their environments. However, the underlying mechanisms that govern the morphing of such networks, especially when the network itself actively grows and imposes constraints, remain poorly understood. The inherent complexity of interconnected topological elements poses significant challenges for both theoretical modeling and experimental investigation. Here we develop an active Cosserat rod model capturing growth-induced network morphing, validated through polydimethylsiloxane swelling experiments and four-dimensional printing. By examining cellular lattices with varying geometries, we reveal how symmetry and chirality can be systematically programmed through network architecture. Using bioinspired venation patterns with tunable pinned sites, we demonstrate that the network functions as a mechanically constraining framework: Its geometry dictates the spatial distribution of growth-induced deformation, with model predictions matching biological observations. We further achieve precise control of nonuniform morphing, including chirality, bidirectional curvature, and edge rippling, through engineered inhomogeneous growth. Our findings uncover how network geometry and active growth can program three-dimensional shape transformations, offering a design strategy for morphing matter, soft robotics, and deployable structures.