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Research Papers

Development of a Flow Evolution Network Model for the Stress–Strain Behavior of Poly(L-lactide)

[+] Author and Article Information
Maureen L. Dreher

Division of Applied Mechanics,
Office of Science and Engineering Laboratories,
Center for Devices and Radiological Health,
U.S. Food and Drug Administration,
10903 New Hampshire Avenue,
Silver Spring, MD 20993
e-mail: maureen.dreher@fda.hhs.gov

Srinidhi Nagaraja

Division of Applied Mechanics,
Office of Science and Engineering Laboratories,
Center for Devices and Radiological Health,
U.S. Food and Drug Administration,
10903 New Hampshire Avenue,
Silver Spring, MD 20993
e-mail: srinidhi.nagaraja@fda.hhs.gov

Jorgen Bergstrom

Veryst Engineering,
47A Kearney Road,
Needham Heights, MA 02494
e-mail: jbergstrom@veryst.com

Danika Hayman

Veryst Engineering,
47A Kearney Road,
Needham Heights, MA 02494
e-mail: dhayman@veryst.com

1Corresponding author.

Manuscript received July 25, 2016; final manuscript received June 2, 2017; published online July 7, 2017. Assoc. Editor: Sean S. Kohles.This work is in part a work of the U.S. Government. ASME disclaims all interest in the U.S. Government's contributions.

J Biomech Eng 139(9), 091002 (Jul 07, 2017) (9 pages) Paper No: BIO-16-1315; doi: 10.1115/1.4037071 History: Received July 25, 2016; Revised June 02, 2017

Computational modeling is critical to medical device development and has grown in its utility for predicting device performance. Additionally, there is an increasing trend to use absorbable polymers for the manufacturing of medical devices. However, computational modeling of absorbable devices is hampered by a lack of appropriate constitutive models that capture their viscoelasticity and postyield behavior. The objective of this study was to develop a constitutive model that incorporated viscoplasticity for a common medical absorbable polymer. Microtensile bars of poly(L-lactide) (PLLA) were studied experimentally to evaluate their monotonic, cyclic, unloading, and relaxation behavior as well as rate dependencies under physiological conditions. The data were then fit to a viscoplastic flow evolution network (FEN) constitutive model. PLLA exhibited rate-dependent stress–strain behavior with significant postyield softening and stress relaxation. The FEN model was able to capture these relevant mechanical behaviors well with high accuracy. In addition, the suitability of the FEN model for predicting the stress–strain behavior of PLLA medical devices was investigated using finite element (FE) simulations of nonstandard geometries. The nonstandard geometries chosen were representative of generic PLLA cardiovascular stent subunits. These finite element simulations demonstrated that modeling PLLA using the FEN constitutive relationship accurately reproduced the specimen’s force–displacement curve, and therefore, is a suitable relationship to use when simulating stress distribution in PLLA medical devices. This study demonstrates the utility of an advanced constitutive model that incorporates viscoplasticity for simulating PLLA mechanical behavior.

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Figures

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Fig. 1

Injection molded PLLA sheets with 0.5 mm thickness were laser cut to either a microtensile bar geometry with a gauge length of 3.81 mm and a width of 1.28 mm or a generic stent subunit

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Fig. 2

Rheological representation of the flow evolution network. One parallel network is shown, but the model itself may utilize multiple parallel networks if indicated by the experimental data.

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Fig. 3

(a) Representative stress–strain curves from microtensile specimens subjected to monotonic loading at three different rates. Strains were measured using DIC and are reported as Lagrangian strain values. Stress was calculated from the instantaneous force measurement and the original cross-sectional area. (b) Computational fits of experimental representative data to the FEN model where strain is calculated based on crosshead motion. For comparison, (c) calibration of the experimental data to a rate-dependent elastic–plastic model and (d) to a Neo-Hookean model with a three-term Prony series.

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Fig. 4

Comparison of experimental data for PLLA undergoing monotonic testing at 5%/s (a) and undergoing stress relaxation testing with a short relaxation time in (b) for specimens tested under room temperature, air conditions as compared to those tested under physiologic conditions of 37 °C fluid bath

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Fig. 5

Comparisons of FEN model predictions as compared to experimental data for yield point testing at 5%/s (a) and 10%/s (b) and for cyclic yield testing (c). Experimental data are shown as individual points and model predictions are shown as a solid line.

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Fig. 6

Comparisons of FEN model predictions for stress relaxation as compared to experimental data. Stress relaxation experiments with a long relaxation time appear in (a) while those with a short relaxation time appear in (b). Experimental data are shown as individual points and model predictions are shown as a solid line.

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Fig. 7

Predicted Von Mises Stress in the PLLA stent subunit at 1 mm of axial displacement (a), 4 mm of displacement (b), and 7 mm of displacement (c)

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Fig. 8

Comparison of experimental measurements for the force–displacement curve with FEA predictions for PLLA model stent subunits undergoing tensile displacement under physiologic conditions

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