title: On nonlinear viscoelastic deformations: a reappraisal of Fung's quasi-linear viscoelastic model.
abstract: 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.
authors.affiliation: School of Mathematics , University of Manchester , Oxford Road, Manchester M13 9PL, UK.
authors.forename: Riccardo
authors.initials: R
authors.lastname: De Pascalis
authors.affiliation: School of Mathematics , University of Manchester , Oxford Road, Manchester M13 9PL, UK.
authors.forename: I David
authors.initials: ID
authors.lastname: Abrahams
authors.affiliation: School of Mathematics , University of Manchester , Oxford Road, Manchester M13 9PL, UK.
authors.forename: William J
authors.initials: WJ
authors.lastname: Parnell
keywords: Fung; biological soft tissue; hyperelastic; quasi-linear; strain energy function; viscoelastic