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

Abstract

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.