A Viscoelastic, Viscoplastic Model of Cortical Bone

Cortical bone, as the principal structural component of the human body, functions in both a load-bearing and protective capacity. As a material, cortical bone has been the subject of mechanical investigation and characterization for well over a century, and the time dependent nature of this material’s mechanical response to loading is well documented. To model this time-dependent behavior, many researchers have employed a Voigt viscoelastic element [1,3,5], but this approach lacks the ability to predict bone’s material response in all but the most basic of loading conditions and has been shown invalid for strain rates ranging over more than a few orders of magnitude [2]. Furthermore, use of a Voigt element ignores viscoplastic behavior of the material entirely. In response to these shortcomings, the present study proposes a simple but accurate rate-dependant model that captures both the viscoelastic and viscoplastic components of cortical bone’s stress-strain behavior and is shown to be valid over a range of strain rates from 0.0001 s -1 to 1500 s -1 .