Open Access

ARTICLE

A Nonlinear Viscoelastic Finite Element Model of Polyethylene

by P.C. Chen∗ ,†^†, C.W. Colwell†^†, D.D. D’Lima† ‡^†

∗ Scripps, La Jolla, CA, USA
† UCSD, La Jolla, CA, USA
‡ This paper is a tribute to Prof. Pin Tong in honor of his 72th birthday, and edited by Dr. David Lam.

Molecular & Cellular Biomechanics 2011, 8(2), 135-148. https://doi.org/10.3970/mcb.2011.008.135

Abstract

A nonlinear viscoelastic finite element model of ultra-high molecular weight polyethylene (UHMWPE) was developed in this study. Eight cylindrical specimens were machined from ram extruded UHMWPE bar stock (GUR 1020) and tested under constant compression at 7% strain for 100 sec. The stress strain data during the initial ramp up to 7% strain was utilized to model the "instantaneous" stress-strain response using a Mooney-Rivlin material model. The viscoelastic behavior was modeled using the time-dependent relaxation in stress seen after the initial maximum stress was achieved using a stored energy formulation. A cylindrical model of similar dimensions was created using a finite element analysis software program. The cylinder was made up of hexahedral elements, which were given the material properties utilizing the "instantaneous" stress-strain curve and the energy-relaxation curve obtained from the experimental data. The cylinder was compressed between two flat rigid bodies that simulated the fixtures of the testing machine. Experimental stress-relaxation, creep and dynamic testing data were then used to validate the model. The mean error for predicted versus experimental data for stress relaxation at different strain levels was 4.2%. The mean error for the creep test was 7% and for dynamic test was 5.4%. Finally, dynamic loading in a hip arthroplasty was modeled and validated experimentally with an error of 8%. This study establishes a working finite element material model of UHMWPE that can be utilized to simulate a variety of postoperative arthroplasty conditions.

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