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

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.

References in corpus (3)

• Mechanical Characterization of Brain Tissue in Compression at Dynamic Strain Rates
• Mechanical characterization of brain tissue in simple shear at dynamic strain rates
• On the Abaqus FEA model of finite viscoelasticity

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• Incremental dynamics of prestressed viscoelastic solids and its applications in shear wave elastography
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• Foundations of viscoelasticity and application to soft tissues mechanics
• Computation of viscoelastic shear shock waves using finite volume schemes with artificial compressibility