From Pine Cones to Minimal Surfaces: The Geometry and Mechanics of Morphing Bilayers
type: CreativeWork
description: Ubiquitous to nature, is an inherent ability to program form to fulfill function. In thin biological structures, such as leaves and plants, growth coupled with their slenderness, allows for a wealth of complex geometries to emerge. Underpinning this sophisticated phenomena is a problem of mechanics, in which growth, or more specifically volume changes, impart inhomogeneous strain profiles which frustrate the structure and trigger deformations by way of buckling or wrinkling. Inspired by this, researchers have mathematically and physically characterised these phenomena, enabling 2D sheets to be programmed into 3D shapes and reconfigure between their different stable forms. This would have wide ranging applications in a variety of contexts such as robotics for instance, where smart actuators and mimicking live tissue is needed, or for deployable structures in aeronautics. A subset of this type of growth is that of bilayers, where the Uniform Curvature model has enabled researchers to successfully investigate problems of buckling and multistability. However, owing to the free edge, this model fails to capture higher order effects pertaining to a boundary layer phenomenon, in which moments must dissipate, and hence geometry vary beyond the quadratic terms near the boundary. Traditionally, researchers have neglected their effect in view of the bulk behaviour. However, the resulting linearly scaled Gauss for the stretching energy does not distinguish between planform geometries, and given recent findings concerning the influence of edge effects on preferred bending direction, the validity of the Uniform Curvature model has been put into question. By introducing a ’fictitious’ edge moment rotation, the energy function is reduced commensurately with the dissipation that occurs within this boundary layer. These reduction terms are a function of the curvatures and we obtain a system of algebraic equations. By consideration of the neutrally stable shell, we observe the alterin…
abstract: Ubiquitous to nature, is an inherent ability to program form to fulfill function. In thin biological structures, such as leaves and plants, growth coupled with their slenderness, allows for a wealth of complex geometries to emerge. Underpinning this sophisticated phenomena is a problem of mechanics, in which growth, or more specifically volume changes, impart inhomogeneous strain profiles which frustrate the structure and trigger deformations by way of buckling or wrinkling. Inspired by this, researchers have mathematically and physically characterised these phenomena, enabling 2D sheets to be programmed into 3D shapes and reconfigure between their different stable forms. This would have wide ranging applications in a variety of contexts such as robotics for instance, where smart actuators and mimicking live tissue is needed, or for deployable structures in aeronautics. A subset of this type of growth is that of bilayers, where the Uniform Curvature model has enabled researchers to successfully investigate problems of buckling and multistability. However, owing to the free edge, this model fails to capture higher order effects pertaining to a boundary layer phenomenon, in which moments must dissipate, and hence geometry vary beyond the quadratic terms near the boundary. Traditionally, researchers have neglected their effect in view of the bulk behaviour. However, the resulting linearly scaled Gauss for the stretching energy does not distinguish between planform geometries, and given recent findings concerning the influence of edge effects on preferred bending direction, the validity of the Uniform Curvature model has been put into question. By introducing a ’fictitious’ edge moment rotation, the energy function is reduced commensurately with the dissipation that occurs within this boundary layer. These reduction terms are a function of the curvatures and we obtain a system of algebraic equations. By consideration of the neutrally stable shell, we observe the alterin…
author: Salsby, Barney
language: eng
keywords: Boundary Layer Effects, Growth, Morphing Bilayers, Shell Structures
license: https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/67958eab-043c-4bcc-9f0f-99827887f2a1/download
license: https://www.rioxx.net/licenses/all-rights-reserved/
date published: 2024-02-01
date modified: 2026-07-22T22:23:57Z
provider: Cambridge University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Cambridge

PropertyValue
property ID: DOI
value: 10.17863/CAM.106220