On nonlinear viscoelastic deformations - a reappraisal of Fung's quasilinear viscoelastic model

De Pascalis, Riccardo and Abrahams, I. David and Parnell, William J. (2014) On nonlinear viscoelastic deformations - a reappraisal of Fung's quasilinear viscoelastic model. submitted to Proceedings of the Royal Society A. (Submitted)

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Abstract

This article offers a reappraisal of Fung's method for quasilinear viscoelasticity. It is shown that a number of negative features exhibited in other works, commonly attributed to the Fung approach, are merely a consequence of the way it has been applied. The approach outlined herein is shown to yield improved behaviour, and offers a straightforward scheme for solving a wide range of models. Results from the new model are contrasted with those in the literature for the case of uniaxial elongation of a bar: for an imposed stretch of an incompressible bar, and for an imposed load. In the last case, a numerical solution to a Volterra integral equation is required to obtain the results. This is achieved by a high order discretisation scheme. Finally, the stretch of a compressible viscoelastic bar is determined for two distinct materials: Horgan-Murphy and Gent.

Item Type: Article
Uncontrolled Keywords: viscoelastic, quasilinear, Fung, Pipkin-Roger, Horgan-Murphy, Gent, hyperelastic, biological soft tissue, elastomer, strain energy function
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 74 Mechanics of deformable solids
Depositing User: Dr. Riccardo De Pascalis
Date Deposited: 08 Jan 2014
Last Modified: 20 Oct 2017 14:13
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2088

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