A phenomenological constitutive model for the nonlinear viscoelastic responses of biodegradable polymers

Type
Article

Authors
Khan, Kamran
El Sayed, Tamer S.

KAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Physical Science and Engineering (PSE) Division

Online Publication Date
2012-11-09

Print Publication Date
2013-02

Date
2012-11-09

Abstract
We formulate a constitutive framework for biodegradable polymers that accounts for nonlinear viscous behavior under regimes with large deformation. The generalized Maxwell model is used to represent the degraded viscoelastic response of a polymer. The large-deformation, time-dependent behavior of viscoelastic solids is described using an Ogden-type hyperviscoelastic model. A deformation-induced degradation mechanism is assumed in which a scalar field depicts the local state of the degradation, which is responsible for the changes in the material's properties. The degradation process introduces another timescale (the intrinsic material clock) and an entropy production mechanism. Examples of the degradation of a polymer under various loading conditions, including creep, relaxation and cyclic loading, are presented. Results from parametric studies to determine the effects of various parameters on the process of degradation are reported. Finally, degradation of an annular cylinder subjected to pressure is also presented to mimic the effects of viscoelastic arterial walls (the outer cylinder) on the degradation response of a biodegradable stent (the inner cylinder). A general contact analysis is performed. As the stiffness of the biodegradable stent decreases, stress reduction in the stented viscoelastic arterial wall is observed. The integration of the proposed constitutive model with finite element software could help a designer to predict the time-dependent response of a biodegradable stent exhibiting finite deformation and under complex mechanical loading conditions. © 2012 Springer-Verlag Wien.

Citation
Khan, K. A., & El-Sayed, T. (2012). A phenomenological constitutive model for the nonlinear viscoelastic responses of biodegradable polymers. Acta Mechanica, 224(2), 287–305. doi:10.1007/s00707-012-0760-7

Acknowledgements
This work was funded by the KAUST baseline fund. The authors would like to thank Dr. Amir Siddiq for the valuable discussions on integrating constitutive models into ABAQUS. The authors would also like to thank the Research Computing team and KAUST IT for their technical support.

Publisher
Springer Nature

Journal
Acta Mechanica

DOI
10.1007/s00707-012-0760-7

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