Mechanics of pressurized cellular sheets

TL;DR

This paper investigates how internal pressure in cellular sheets, like plant cells and synthetic structures, influences their mechanical stiffness and shape, revealing pressure-dependent bending behavior and potential applications in biomimetic actuators.

Contribution

It introduces a model explaining pressure-dependent bending stiffness in single-cell sheets, clarifying the mechanical role of turgor pressure and inspiring a biomimetic un-curling actuator.

Findings

Pressure increases sheet stiffness contrary to simple expectations.

Turgor pressure influences leaf shape and curling behavior.

Model explains turgor-driven shrinkage in plant cells.

Abstract

Everyday experience shows that cellular sheets are stiffened by the presence of a pressurized gas: from bicycle inner tubes to bubble wrap, the presence of an internal pressure increases the stiffness of otherwise floppy structures. The same is true of plants, with turgor pressure (due to the presence of water) taking the place of gas pressure; indeed, in the absence of water, many plants wilt. However, the mechanical basis of this stiffening is somewhat opaque: simple attempts to rationalize it suggest that the stiffness should be independent of the pressure, at odds with everyday experience. Here, we study the mechanics of sheets that are a single cell thick and show how a pressure-dependent bending stiffness may arise. Our model rationalizes observations of turgor-driven shrinkage in plant cells and also suggests that turgor is unlikely to provide significant structural support in many monolayer leaves, such as those found in mosses. However, for such systems, turgor does provide a way to control leaf shape, in accordance with observations of curling upon drying of moss leaves. Guided by our results, we also present a biomimetic actuator that un-curls upon pressurization.