The inflation of viscoelastic balloons and hollow viscera

De Pascalis, Riccardo and Parnell, William J. and Abrahams, I. David and Shearer, Tom and Daly, Donna M. (2018) The inflation of viscoelastic balloons and hollow viscera. Proceedings of the Royal Society A, 474. p. 20180102. ISSN 1364-5021

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Abstract

For the first time, the problem of the inflation of a thick-walled spherical shell is considered where the wall material is nonlinearly viscoelastic. We focus here specifically on the context where the wall has quasilinear viscoelastic constitutive behaviour. This problem is of fundamental importance in a wide range of applications but particularly in the context of biological systems such as hollow viscera including the lungs and bladder. Some canonical problems associated with the inflation and deflation of a thick walled nonlinear viscoelastic shell are described, noting that the solution of such problems, where pressures are imposed, requires the numerical solution to a nonlinear Volterra integral equation in space and time. Here a new technique to solve such equations is described. Furthermore, the limit of a thin-walled shell yields the scenario of a viscoelas-tic balloon. The associated nonlinear elastic problem of inflation of a balloon has been studied extensively but there is a paucity of studies considering the associated nonlinear viscoelastic problem. We show that, in contrast to the elastic scenario, the peak pressure associated with inflation of a neo-Hookean balloon is not independent of the shear modulus of the medium. This problem is also described in the context of intragastric balloons, which are now commonly used to treat obesity effectively.

Item Type: Article
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 74 Mechanics of deformable solids
Depositing User: Dr Tom Shearer
Date Deposited: 11 Nov 2018 09:18
Last Modified: 11 Nov 2018 09:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2671

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