Shape transformation of thin membrane induced by flow-controlled differential expansion

A thin, planar material irrigated by a flow network can be swollen locally by fluid transport in the network and subsequent fluid absorption, resulting in spatial variation of material properties and large-scale deformation like out-of-plane buckling. This flow-controlled mechanism of shape change is proposed for plant motions such as flower blooming and petal expansion. Facilitated by the xylem vascular system, petal segments are hydrated at different rates and swell unequally due to the uneven distribution of dynamically and spatially varying water content. Inspired by the process, we develop a network model that couples fluid movement (hydrodynamics) with membrane shape (mechanics) to computationally study the hydraulically induced differential swelling and buckling. We simulate the fluid dynamics using a spatially explicit model with local fluid-storage capacitance, and the mechanical network using a spring system on discretized surface, where bonds are adjusted quasi-statically by fluid distribution. We investigate the effects of network size, spatial hierarchical organization of major/minor veins, and hydraulic resistance/capacitance on shape transformation, which includes saddle shapes with negative Gaussian curvature.