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Published October 2018 | Submitted
Journal Article Open

A diffuse interface model for the analysis of propagating bulges in cylindrical balloons

Abstract

With the aim to characterize the formation and propagation of bulges in cylindrical rubber balloons, we carry out an expansion of the nonlinear axisymmetric membrane model assuming slow axial variations. We obtain a diffuse interface model similar to that introduced by van der Waals in the context of liquid–vapour phase transitions. This provides a quantitative basis to the well-known analogy between propagating bulges and phase transitions. The diffuse interface model is amenable to numerical as well as analytical solutions, including linear and nonlinear bifurcation analyses. Comparisons to the original membrane model reveal that the diffuse interface model captures the bulging phenomenon very accurately, even for well-localized phase boundaries.

Additional Information

© 2018 The Author(s). Published by the Royal Society. Received: 30 May 2018; Accepted: 12 September 2018. We would like to thank John Hutchinson for drawing our attention to the absence of a strain gradient model for the analysis of bulging in balloons, and for providing useful feedback on the manuscript. Data accessibility: This work does not have any experimental data. Authors' contributions: Both authors have equally contributed to all aspects of the work. We declare we have no competing interests. There has been no dedicated funding for this work.

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August 19, 2023
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