Instabilities in a compressible hyperelastic cylindrical channel under internal pressure and external constraints

Mehta, S., Raju, G., Kumar, S. and Saxena, P. (2022) Instabilities in a compressible hyperelastic cylindrical channel under internal pressure and external constraints. International Journal of Non-Linear Mechanics, 144, 104031. (doi: 10.1016/j.ijnonlinmec.2022.104031)

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Abstract

Pressurised cylindrical channels made of soft materials are ubiquitous in biological systems, soft robotics and metamaterial designs. In this paper, we study large deformation and subsequent instability of a thick-walled and compressible hyperelastic cylinder under internal pressure and external constraints. The applied pressure can lead to elastic bifurcations along the axial or circumferential direction. Perturbation theory is used to derive the partial differential equations that govern the bifurcation behaviour of the cylindrical channel. Two cases of boundary conditions on the outer surface of the cylinder, namely, free and constrained are studied to understand their influence on the instability behaviour. The derived equations are solved numerically using the compound matrix method to evaluate the critical pressure for instability. The effects of the wall-thickness of the cylinder and the compressibility of the material on the critical pressure is investigated for both the boundary conditions. The results reveal that for an isotropic material, the bifurcation occurs along the axial direction of the cylinder at lower critical pressure compared to circumferential direction for all cases considered herein. Finally, the tuneability of the bifurcation behaviour of transversely isotropic cylinder is demonstrated by considering reinforcements along the cylinder’s axis, triggering bifurcation in the circumferential direction in certain cases. The findings of the study indicate that the instability-induced pattern formation will be useful for designing shape changing material systems such as soft robotics and soft metamaterials.

Item Type:Articles
Additional Information:Prashant Saxena acknowledges the support of startup funds from the James Watt School of Engineering at the University of Glasgow.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Saxena, Dr Prashant and Kumar, Professor Shanmugam
Authors: Mehta, S., Raju, G., Kumar, S., and Saxena, P.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
College of Science and Engineering > School of Engineering > Systems Power and Energy
Journal Name:International Journal of Non-Linear Mechanics
Publisher:Elsevier
ISSN:0020-7462
ISSN (Online):1878-5638
Published Online:06 April 2022
Copyright Holders:Copyright © 2022 The Author(s)
First Published:First published in International Journal of Non-Linear Mechanics 144: 104031
Publisher Policy:Reproduced under a Creative Commons Licence

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