Investigation of cortical bone post-yield behavior in nano-indentation test using ALE finite element method

Nano-indentation test is one of the most common method to study the material post-yielding behavior providing a suitable material model. Nowadays, this test is also used to investigate the pressure-dependent behavior and other mechanical behaviors of bone. Different material models such as Johnson-Cook, von-Mises, Drucker-Prager, and Hill models have been presented to consider the anisotropy, pressure dependency, strain rate, and temperature dependency of cortical bovine bones similar to human bone in tension and compression.In the present study, using the Arbitrary Eulerian-Lagrangian (ALE) finite element method in Abaqus software with appropriate contact conditions, the material flow and the results of bone pile-up was well predicted with an error of less than 1%. Also, suitable parameters of the extended Drucker-Prager model for predicting post-yielding bovine cortical bone behavior were presented such that the force-displacement curve of test, showed less than 5% deviation from the experimental results. The friction angle 46°, and zero-degree dilation angle along with the frictional contact conditions between the tool and the bone with a coefficient of 0.3 provided the best parameters to predict post-yielding behavior. It was also shown that changing the angle of dilation from zero to 10 degrees can increase the maximum force applied to the bone up to 40%.