# ABAQUS ( viscoelastic material model)

Does any one know how to implement other viscoelastic material models, like Burgers' model, in ABAQUS? To my knowledge only Prony series can be used to model visoelastic materials in ABAQUS/standard.

thanks,

Milliyon

## Comments

### Re: Prony series

A one-dimensional Burgers model is a Kelvin-Voigt model + Maxwell model in series.  A Prony series (which is essentially a generalized Maxwell model) can be generated for any of these models and more complex materials by first finding the frequency/time dependent elastic constants and then fitting a curve.   In some of the simpler cases an analytical Prony series can also be found.

For a better understanding of the issues involved you can look at Application of Prony Series to Linear Viscoelasticity by Soussou et al., 1970 or in these Lecture notes at Brown.

A very readable paper on the matter is Methods of interconversion between linear viscoelastic material functions. Part I-a numerical method based on Prony series by Park and Schapery, 1999, IJSS, 36, 1653-1675.

### *Hysteresis material model in ABAQUS/Standard

You can check out this material model in ABAQUS/Std. It is an implementation of a nonlinear viscoelastic model for filled elastomers proposed by Bergstrom and Boyce.

### Prony/Hysteresis models

Biswajit and Amit

Thank you guys for the reply. I am doing modeling in asphalt and the reason I choose Burgers model is because it captures permanent strain/deformation using the maxwell-dashpot element sitting in series with Kelvin-Voigit model. I have all the parameters for the model obtained from experimental data fitting but dont know how to implement that in ABAQUS. In the case of Prony series(generalised Maxwell model), permanent deformation can't be captured; once the load is removed from the model the strain goes back to zero( because of the single parallel spring element in the model).

First I should  go through all the resources you and Amit mentioned and I will get back to you guys again if I need more help.

Thanks a lot,

Milliyon

### permanent deformation

In some sense the difference between viscoelasticity and any form of plasticity is that in viscoelasticity, by definition, there is no permanent deformation (although there is dissipation). Hence, you may also want to consider rate-dependent plasticity models.

### Other viscoelastic material models

Recently we have implemented a simple visco-elastic-plastic material model in ABAQUS to simulate indentation on polymers. The work can be found in C.Y. Zhang, Y.W. Zhang, K.Y. Zeng, L. Shen, Characterization of mechanical properties of polymers by nanoindentation tests. Phil. Mag. 86 (28): 4487-4506 (2006).

### Viscoelastic paper

The most readable Prony series implementation to me is

Kaliske, M. and Rothert, H., ‘Formulation and
implementation of three-dimensional viscoelasticity at small and finite
strains’, Computational Mechanics 19, 1997, 228--239

'Permanent deformation' can be modelled by having a very small time constant on one of the elements.