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

C Lestringant (1) , B. Audoly (2, 3)

1 D-MAVT - Department of Mechanical and Process Engineering [Zürich]
2 LMS - Laboratoire de mécanique des solides
3 EAS - Division of Engineering and Applied Science [Pasadena]

With the aim to characterize the formation and propagation of bulges in cylindrical rubber balloons, we carry out an expansion of the non-linear 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-vapor 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 non-linear 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.

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des structures [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Physique mathématique [math-ph]; Mécanique des solides [physics.class-ph]

C Lestringant, B. Audoly. A diffuse interface model for the analysis of propagating bulges in cylindrical balloons. Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences, 2018, 474, pp.20180333. ⟨10.1098/rspa.2018.0333⟩. ⟨hal-01898162⟩