Surface elasticity and area incompressibility regulate fiber beading instability

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2025-04-26

Date

2023-04-26

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Source Title

Journal of the Mechanics and Physics of Solids

Print ISSN

0022-5096

Electronic ISSN

1873-4782

Publisher

Elsevier

Volume

176

Issue

Pages

105298-1 - 105298-15

Language

English

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Abstract

A continuum body endowed with an energetic surface can exhibit different mechanical behavior than its bulk counterpart. Soft polymeric cylinders under surface effects become unstable and form surface undulations referred to as the elastic Plateau–Rayleigh (PR) instability, exclusively driven by competing surface and bulk properties. However, the impact of surface elasticity and area compressibility, along with bulk compressibility, on the PR instability of soft solids remains unexplored. Here we develop a theoretical, finite deformations framework to capture the onset of the PR instability in highly deformable solids with surface tension, surface elasticity, and surface compressibility, while retaining the compressibility of the bulk as a material parameter. In addition to the well-known elastocapillary number, surface compressibility and a dimensionless parameter related to the surface modulus are found to govern the instability behavior. The results of the theoretical framework are analyzed for an exhaustive list of bulk and surface parameters and loading scenarios, and it is found that increasing surface elasticity and surface incompressibility preclude PR instability. Theoretical results are compared with high-fidelity numerical simulation results from surface-enhanced isogeometric finite element analysis and an excellent agreement is observed across a broad range of material parameters and large deformation levels. Our results demonstrate how surface effects can be used to (i) render stable soft structures and prevent PR instability when it occurs as an unwanted by-product of manufacturing techniques or (ii) tune the instability behavior for possible applications involving polymer fibers.

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