The inflation of viscoelastic balloons and hollow viscera

Riccardo De Pascalis, William Parnell, I. David Abrahams, Tom Shearer, Donna Daly, David Grundy

    Research output: Contribution to journalArticlepeer-review

    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.
    Original languageEnglish
    JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
    Volume474
    Issue number2218
    Early online date24 Oct 2018
    DOIs
    Publication statusPublished - Oct 2018

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