Anisotropic post-yield response of cancellous bone simulated by stress-strain curves of bulk equivalent structures

During the last decade, finite element (FE) modelling has become ubiquitous in understanding complex mechanobiological phenomena, e.g. bone-implant interactions. The extensive computational effort required to achieve biorealistic results when modelling the post-yield behaviour of microstructures like cancellous bone is a major limitation of these techniques. This study describes the anisotropic biomechanical response of cancellous bone through stress-strain curves of equivalent bulk geometries. A cancellous bone segment, reverse engineered by micro computed tomography, was subjected to uniaxial compression. The material's constitutive law, obtained by nano-indentations, was considered during the simulation of the experimental process. A homodimensionally bulk geometry was employed to determine equivalent properties, resulting in a similar anisotropic response to the trabecular structure. The experimental verification of our model sustained that the obtained stress-strain curves can adequately reflect the post-yield behaviour of the sample. The introduced approach facilitates the consideration of nonlinearity and anisotropy of the tissue, while reducing the geometrical complexity of the model to a minimum.