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

De Pascalis R, Abrahams ID, Parnell WJ - Proc. Math. Phys. Eng. Sci. (2014)

Bottom Line: The approach outlined herein is shown to yield improved behaviour and offers a straightforward scheme for solving a wide range of models.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.

View Article: PubMed Central - PubMed

Affiliation: School of Mathematics , University of Manchester , Oxford Road, Manchester M13 9PL, UK.

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.

No MeSH data available.


Related in: MedlinePlus

Plot of the dimensionless stress history T/μ (a) and the resultant stretch λ (b), from the Yeoh model predictions (4.14) (dotted) and that from Mooney–Rivlin predictions (4.19) (dashed). The solid curve is the neo-Hookean limit α=0 (or γ=1/2).
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RSPA20140058F2: Plot of the dimensionless stress history T/μ (a) and the resultant stretch λ (b), from the Yeoh model predictions (4.14) (dotted) and that from Mooney–Rivlin predictions (4.19) (dashed). The solid curve is the neo-Hookean limit α=0 (or γ=1/2).

Mentions: An example is illustrated in figure 2, with the imposed stress history shown on the left graph. The one-term Prony series relaxation function (4.21), with constant values as given in equation (4.22), is again employed. The resultant stretch is given in figure 2b for the Yeoh strain energy function (4.14) (dotted curves with α=1,2), and for the Mooney–Rivlin strain energy function (dashed curves with α=1,2). As before, the solid curve is the neo-Hookean prediction (α=0,γ=1/2) and it can be seen that increasing α in the Yeoh model leads to material hardening, while decreasing γ leads to softening of the Mooney–Rivlin material.Figure 2.


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

De Pascalis R, Abrahams ID, Parnell WJ - Proc. Math. Phys. Eng. Sci. (2014)

Plot of the dimensionless stress history T/μ (a) and the resultant stretch λ (b), from the Yeoh model predictions (4.14) (dotted) and that from Mooney–Rivlin predictions (4.19) (dashed). The solid curve is the neo-Hookean limit α=0 (or γ=1/2).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4042724&req=5

RSPA20140058F2: Plot of the dimensionless stress history T/μ (a) and the resultant stretch λ (b), from the Yeoh model predictions (4.14) (dotted) and that from Mooney–Rivlin predictions (4.19) (dashed). The solid curve is the neo-Hookean limit α=0 (or γ=1/2).
Mentions: An example is illustrated in figure 2, with the imposed stress history shown on the left graph. The one-term Prony series relaxation function (4.21), with constant values as given in equation (4.22), is again employed. The resultant stretch is given in figure 2b for the Yeoh strain energy function (4.14) (dotted curves with α=1,2), and for the Mooney–Rivlin strain energy function (dashed curves with α=1,2). As before, the solid curve is the neo-Hookean prediction (α=0,γ=1/2) and it can be seen that increasing α in the Yeoh model leads to material hardening, while decreasing γ leads to softening of the Mooney–Rivlin material.Figure 2.

Bottom Line: The approach outlined herein is shown to yield improved behaviour and offers a straightforward scheme for solving a wide range of models.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.

View Article: PubMed Central - PubMed

Affiliation: School of Mathematics , University of Manchester , Oxford Road, Manchester M13 9PL, UK.

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.

No MeSH data available.


Related in: MedlinePlus