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

Mehta, S. and Raju, Gangadharan and Kumar, S. and et al, . (2022) Instabilities in a compressible hyperelastic cylindrical channel under internal pressure and external constraints. International Journal of Non-Linear Mechanics, 144. pp. 1-12. ISSN 0020-7462

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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. © 2022 The Author(s)

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IITH Creators:
IITH CreatorsORCiD
Raju, Gangadharan
Item Type: Article
Additional Information: Prashant Saxena acknowledges the support of startup funds from the James Watt School of Engineering at the University of Glasgow, UK. The authors thank Prof Ray W Ogden for his valuable suggestions to improve the manuscript
Uncontrolled Keywords: Bifurcation, Compressible hyperelasticity, Cylindrical geometry, Stability analysis
Subjects: Physics > Mechanical and aerospace
Divisions: Department of Mechanical & Aerospace Engineering
Depositing User: . LibTrainee 2021
Date Deposited: 20 Jun 2022 08:49
Last Modified: 22 Jun 2022 08:41
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