Scaling law for the onset of the surface wrinkling of multilayer tubes

TL;DR

This paper develops a theoretical model to predict the critical bending conditions that induce surface wrinkling in multilayer tubes, such as carbon nanotubes, revealing an inverse relationship between critical curvature and bending moment.

Contribution

It introduces a simple analytical model for determining the onset of wrinkling in multilayer tubes under bending, applicable across different layer counts and core sizes.

Findings

Critical curvature and bending moment are inversely proportional.

The model applies to various multilayer tubes, including carbon nanotubes.

Wrinkling occurs when bending exceeds a critical threshold.

Abstract

Surface wrinkling is an instability mode that is often observed in a wide variety of multilayer tubes under bending deformation. When the degree of applied bending exceeds a critical value, wrinkles appear at the intrados of the tube and release a large amount of in-plane strain energy stored by bending deformation. In the present work, we propose a simple theoretical model for evaluating the critical curvature and critical bending moment for the occurrence of wrinkling in multilayer tubes and apply the model to carbon nanotubes in a case study. Results indicate an inverse proportional relationship between the two critical properties, which holds true regardless of the number of layers and the size of the hollow core.