On nonlinear viscoelastic deformations: a reappraisal of Fung's quasi-linear viscoelastic model

This paper offers a reappraisal of Fung's model for quasi-linear 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...

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Bibliographic Details
Published in:Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2014-06, Vol.470 (2166), p.20140058-20140058
Main Authors: De Pascalis, Riccardo, Abrahams, I. David, Parnell, William J.
Format: Article
Language:English
Subjects:
Biological Soft Tissue
Fung
Hyperelastic
Quasi-Linear
Strain Energy Function
Viscoelastic
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Summary:This paper offers a reappraisal of Fung's model for quasi-linear 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 latter case, a numerical solution to a Volterra integral equation is required to obtain the results. This is achieved by a high-order discretization scheme. Finally, the stretch of a compressible viscoelastic bar is determined for two distinct materials: Horgan-Murphy and Gent.
ISSN:1364-5021
1471-2946
DOI:10.1098/rspa.2014.0058