On the stability of internally pressurized thick-walled spherical and cylindrical shells made of functionally graded incompressible hyperelastic material

Anani, Yavar; Rahimi, G. H.

doi:10.1590/1679-78254322

Cited by 7 publications

(1 citation statement)

References 30 publications

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“…Recently, Sang et al (2016) performed the stability analysis of incompressible rubber tube under internal pressure using Gent's strain energy function. Anani and Rahimi (2018) discussed the stability analysis of functionally graded incompressible thick-walled cylindrical and spherical shells using extended version of Ogden's strain energy function. The wall thickness has a significant influence on the stability of cylinder subjected to internal/external pressure.…”

Section: Introductionmentioning

confidence: 99%

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

Mehta,

Raju,

Kumar

et al. 2021

Preprint

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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 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 would be useful for designing transforming material architectures such as soft robotics and soft metamaterials.

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Section: Introductionmentioning

confidence: 99%