Calibration of a constitutive model for the post-yield behaviour of cortical bone

In this work, the post-yield behaviour of cortical bone is investigated using finite element modelling, nanoindentation and atomic force microscopy. Based on recent investigations, it is proposed that, since pressure dependent deformation mechanisms may contribute to yielding in bone, constitutive models attempting to capture its post-yield behaviour should also incorporate pressure dependence. Nanoindentation testing is performed using a spheroconical indenter tip, and subsequent atomic force microscopy at the indented site shows that bone does not exhibit surface pile-up. By simulating the nanoindentation test, it is found that a Mises based constitutive law cannot simultaneously capture the deformations and load-displacement curve produced during nanoindentation. However, an extended Drucker-Prager model can capture the post-yield behaviour of bone accurately, since it accounts for pressure dependent yield. This suggests that frictional mechanisms are central to the post-yield behaviour of bone. In this work, the extended Drucker-Prager model is calibrated and validated using further simulations.