Viscous-elastic-plastic behavior of bone using Berkovich nanoindentation

Abstract

A series viscous-elastic-plastic (VEP) indentation model was expanded to include analysis of the common trapezoidal testing condition, consisting of constant loading—and unloading—rates with an intervening creep hold period. This full VEP model was applied to analyze nanoindentation test of three polymers and five different types of bone. The full VEP solution allows for direct determination of the viscous term as calculated from the creep hold, while the elastic and plastic material parameters were determined from a non-linear curve-fit of the unloading displacement-time data. Additionally, the use of the trapezoidal loading procedure permitted analysis of the unloading load-displacement data with traditional Oliver-Pharr analysis; the material properties from this analysis compared well with those obtained with VEP analysis. Using the full VEP solution and fitted material constants the loading and creep hold displacement-time curves were simulated and matched well to both polymer and bone experimental data. The full VEP solution shows great promise in for obtaining material parameters for many viscoelastic materials such as hydrated bone, polymers, and other biological tissues.