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

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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.

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Authors and Affiliations

  1. Division of Physical Sciences and Engineering, Computational Solid Mechanics Laboratory (CSML), King Abdullah University of Science and Technology (KAUST), 4700 KAUST, Thuwal, 23955-6900, Kingdom of Saudi Arabia

    Kamran A. Khan & Tamer El-Sayed

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  1. Kamran A. Khan
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  2. Tamer El-Sayed
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Correspondence to Tamer El-Sayed.

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Khan, K.A., El-Sayed, T. A phenomenological constitutive model for the nonlinear viscoelastic responses of biodegradable polymers. Acta Mech 224, 287–305 (2013). https://doi.org/10.1007/s00707-012-0760-7

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  • DOI: https://doi.org/10.1007/s00707-012-0760-7

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