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Localised bifurcation in soft cylindrical tubes under axial stretching and surface tension

Fu

Localised bifurcation in soft cylindrical tubes under axial stretching and surface tension Thumbnail


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Abstract

We investigate localised bulging or necking in an incompressible, hyperelastic cylindrical tube under axial stretching and surface tension. Three cases are considered in which the tube is subjected to different constraints. In case 1 the inner and outer surfaces are traction-free and under surface tension, whilst in cases 2 and 3 the inner and outer surfaces (respectively) are fixed to prevent radial displacement and surface tension. However, each free surface in these latter two cases is still under surface tension. We first state the analytical bifurcation conditions for localisation and then validate them numerically whilst determining whether localisation is preferred over bifurcation into periodic modes. It is shown that bifurcation into a localised solution is unattainable in case 1 but possible and favourable in cases 2 and 3. In contrast, in case 1 any bifurcation must necessarily take the form of a periodic mode with a non-zero wave number. Our results are validated using Finite Element Method (FEM) simulations.

Citation

Fu. (2021). Localised bifurcation in soft cylindrical tubes under axial stretching and surface tension. International Journal of Solids and Structures, 23- 33. https://doi.org/10.1016/j.ijsolstr.2021.02.007

Acceptance Date Feb 8, 2021
Publication Date Feb 20, 2021
Journal International Journal of Solids and Structures
Print ISSN 0020-7683
Publisher Elsevier
Pages 23- 33
DOI https://doi.org/10.1016/j.ijsolstr.2021.02.007
Keywords Soft tube; Non-linear elasticity; Surface tension; Bifurcation; Localisation
Publisher URL https://www.sciencedirect.com/science/article/pii/S0020768321000615?via%3Dihub

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