De Pascalis, R., Parnell, W.J., Abrahams, I.D. et al. (3 more authors) (2018) The inflation of viscoelastic balloons and hollow viscera. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 474 (2218). 20180102. ISSN 1364-5021
Abstract
For the first time, the problem of the inflation of a nonlinear viscoelastic thick-walled spherical shell is considered. Specifically, the wall has quasilinear viscoelastic constitutive behaviour, which is of fundamental importance in a wide range of applications, particularly in the context of biological systems such as hollow viscera, including the lungs and bladder. Experiments are performed to demonstrate the efficacy of the model in fitting relaxation tests associated with the volumetric inflation of murine bladders. While the associated nonlinear elastic problem of inflation of a balloon has been studied extensively, there is a paucity of studies considering the equivalent nonlinear viscoelastic case. We show that, in contrast to the elastic scenario, the peak pressure associated with the inflation of a neo-Hookean balloon is not independent of the shear modulus of the medium. Moreover, a novel numerical technique is described in order to solve the nonlinear Volterra integral equation in space and time originating from the fundamental problem of inflation and deflation of a thick-walled nonlinear viscoelastic shell under imposed pressure.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. |
Keywords: | quasilinear viscoelasticity; Fung; nonlinear Volterra integral equations; balloons; bladder; biological soft tissue |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Biosciences (Sheffield) > Department of Biomedical Science (Sheffield) |
Funding Information: | Funder Grant number EUROPEAN COMMISSION - FP6/FP7 TRUST - 238541 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 25 Feb 2020 15:23 |
Last Modified: | 25 Feb 2020 15:23 |
Status: | Published |
Publisher: | The Royal Society |
Refereed: | Yes |
Identification Number: | 10.1098/rspa.2018.0102 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:156147 |