Indentation experiments and simulation of ovine bone using a viscoelastic-plastic damage model
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Simon Turner and Jennifer MacLeay Department of Clinical Sciences, College of Veterinary Medicine & Biomedical Sciences, Colorado State University, Fort Collins, Colorado 80523
Glen L. Niebur and Timothy C. Ovaerta) Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, Indiana 46556 (Received 5 May 2011; accepted 4 October 2011)
Indentation methods have been widely used to study bone at the micro- and nanoscales. It has been shown that bone exhibits viscoelastic behavior with permanent deformation during indentation. At the same time, damage due to microcracks is induced due to the stresses beneath the indenter tip. In this work, a simplified viscoelastic-plastic damage model was developed to more closely simulate indentation creep data, and the effect of the model parameters on the indentation curve was investigated. Experimentally, baseline and 2-year postovariectomized (OVX-2) ovine (sheep) bone samples were prepared and indented. The damage model was then applied via finite element analysis to simulate the bone indentation data. The mechanical properties of yielding, viscosity, and damage parameter were obtained from the simulations. The results suggest that damage develops more quickly for OVX-2 samples under the same indentation load conditions as the baseline data. I. INTRODUCTION
Indentation techniques have become a standard method to assess the mechanical properties of numerous materials.1,2 In recent years, nanoindentation of bone has been used to extract the mechanical behavior at the level of osteons,3,4 or even lamellae.5 Different procedures during the indentation test can be used for different testing purposes. A conventional test provides the hardness of materials by measuring the size of the residual indentation impression. The load and indentation depth can also be recorded to form an indentation curve, which reveals information regarding mechanical properties. There are many material models for bone, reflecting its anisotropic structure.6 On large scales and small strain levels, bone can be modeled as viscoelastic,4,5,7,8 viscoelastic-plastic,9 or elastic-plastic damage.10 At reduced (micron) scales, cortical bone consists of osteons embedded in interstitial bone,3 while trabecular bone consists of structures similar to rods or plates. Continuum models on the micron scale can represent the overall behavior during indentation, regardless of the anisotropic microstructure and interactions within the microstructure. However, at the nanoscale, indentation becomes much more localized, where the structure of interest can be collagen and the mineral crystals that bond it together.11 a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2011.357 368
J. Mater. Res., Vol. 27, No. 1, Jan 14, 2012
http://journals.cambridge.org
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Under a fluorescent light microscope, tiny microcracks can be observed in cortical bone and breaking of trabeculae can be observed in trabecular bone, which have been implicated in physiolog
