The mechanical properties of a thin, planar material, perfused by an embedded flow network, can be changed locally and globally by the fluid transport and storage, resulting in small or large-scale deformation, such as out-of-plane buckling. Fluid absorption and storage eventually cause the material to locally swell. Different parts can hydrate and swell unevenly, prompting a differential expansion of the surface. In order to computationally study the hydraulically induced differential swelling and buckling of such a membrane, we develop a network model that describes both the membrane shape and fluid movement, coupling mechanics with hydrodynamics. We simulate the time-dependent fluid distribution in the flow network based on a spatially explicit resistor network model with local fluid-storage capacitance. The shape of the surface is modeled by a spring network produced by a tethered mesh discretization, in which local bond rest lengths are adjusted instantaneously according to associated local fluid content in the capacitors in a quasi-static way. We investigate the effects of various designs of the flow network, including overall hydraulic traits (resistance and capacitance) and hierarchical architecture (arrangement of major and minor veins), on the specific dynamics of membrane shape transformation. To quantify these effects, we explore the correlation between local Gaussian curvature and relative stored fluid content in each hierarchy by using linear regression, which reveals that stronger correlations could be induced by less densely connected major veins. This flow-controlled mechanism of shape transformation was inspired by the blooming of flowers through the unfolding of petals. It can potentially offer insights for other reversible motions observed in plants induced by differential turgor and water transport through the xylem vessels, as well as engineering applications.
Inference of the 3D pressure field exerted by a single cell from a thin membrane transverse deformation
Univ Toulouse, CNRS, LPT（图卢兹大学，法国国家科学研究中心，理论物理实验室）；Univ Toulouse, Inserm, CNRS, INFINITy（图卢兹大学，法国健康与医学研究院，法国国家科学研究中心，INFINITy）；Department of Dermatology, Medical University of Vienna（维也纳医科大学皮肤病学系）
Curvature Potential Formulation for Thin Elastic Sheets
Racah Institute of Physics, The Hebrew University of Jerusalem（拉卡物理研究所，耶路撒冷希伯来大学）；Engineering Mechanics Unit, Jawaharlal Nehru Center for Advanced Scientific Research（工程力学单元，贾瓦哈拉尔·尼赫鲁高级科学研究中心）；Einstein Institute of Mathematics, The Hebrew University of Jerusalem（爱因斯坦数学研究所，耶路撒冷希伯来大学）
