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# QLV (Quasi Linear Viscoelasticity) vs Linear Viscoelasticity

Can anyone explain what is main difference between Linear Viscoelasticity vs qlv (Quasi linear Viscoelasticity) proposed by Fung. As far as I understand stress relaxation function and elastic response functions separated and given in convolution form which provides "strain rate independent" results in qlv application.

Is linear viscoelastic description is strain dependent?

To understand difference, I have generated simple stress relaxation experiment using Abaqus where different strain rates are applied into same model (kept constant a while) which has material property of viscoelastic (Prony ) + hyperelastic (Mooney-Rivlin).

I have used same model but only changed material property hyperelastic to elastic + viscoelastic with different strain rates applied again.

In overall I have see no difference (characteristics of the stress relaxation curve) between two models (visco+hyper VS visco+elastic) .

How can I design a such a experimental model to be able to understand difference between linear viscoelasticity vs quasi linear viscoelasticity in Abaqus?

Is it qlv behaviour if I have use prony series approximation for viscoelastic part and hyperelasticity for elastic part in Abaqus material defination?

I hope,I have expressed myself clear enough...

## QLV (Quasi Linear Viscoelasticity) vs Linear Viscoelasticity

Hi,

How much is your strain? 5% or more?

If the strain is forced more than 5% (

finite strain), your linear elastic analysis would be incorrect due to finite element formulation itself not by viscoelastic formulation.In my opinion, the QLV is intended to capture

finite strainregime without considering dependency of stress level (nonlinear viscoelastic).## Quasi-linear viscoelasticity

This is merely a separation between strain effects and time effects: a better terminology is "separable nonlinear viscoelasticity" which is a simplification of generalized nonlinear viscoelasticity. The original idea pre-dates Fung by quite a bit, it appears in the 1950s textile literature, primarily from Leaderman. The relaxation function, which is a function of both strain and time for a nonlinearly viscoelastic material, is split into two components, one a function of time and one a function of strain, and they are multiplied. They are then used in a Boltzmann hereditary integral formulation just as for linear viscoelasticity (when the relaxation function is only a function of time). But as noted, if your strains are small, the effect might not be noticeable; similarly if you are looking at strain-rate dependence but don't have strain rates that differ enough or differ but are outside the active range of the material time constants you also would not necessarily see an obvious effect. The test for a QLV type material behavior experimentally is if the relaxation responses for two different peak displacements normalize to the same shape; in my work on collagenous tissues I have rarely found this to be the case as the materials do not follow this separability rule and are truly nonlinearly viscoelastic.

References:

Oyen ML, Cook RF, Stylianopoulos T, Barocas VH, Calvin SE, and Landers DL, Uniaxial and Biaxial Mechanical Behavior of Human Amnion. Journal of Materials Research, 20 (2005) 2902-9.

Oyen ML, A model for nonlinear viscoelastic mechanical responses of collagenous soft tissues, in Mechanical Behavior of Biological and Biomimetic Materials, edited by Andrew J. Bushby, Virginia L. Ferguson, Ching-Chang Ko, Michelle L. Oyen (Mater. Res. Soc. Symp. Proc. 898E, Warrendale, PA, 2005) L05-16.1-6.

## other tissues that exhibit non-separable non-QLV behavior

Thanks for the link on amnion.

Many tissues exhibit non-separable behavior that cannot be modeled by QLV.

Articles on non-separable behavior in tendon and ligament as well as citations of other research are provided on

http://silver.neep.wisc.edu/~lakes/Biom.html

One reason that QLV has persisted so long is that many people obtain one stress strain curve that shows nonlinearity, and one creep or relaxation curve that shows viscoelasticity. Such a protocol is insufficient to discriminate among nonlinear models. It is expedient to do multiple creep tests at different stress or multiple relaxation tests at different strain, over a sufficient range of stress or strain. Recovery tests are also helpful in that regard.

## a new idea on viscoelasticity model

Please find details in the following paper

A viscoelasticity model for polymers: Time, temperature, and hydrostatic pressure dependent Young's modulus and Poisson's ratio across transition temperatures and pressures