Micro-Scale Numerical Model of Bovine Cortical Bone: Analysis of Plasticity Localization

Evolution of damage and fracture in a bone is affected by its microstructure. A non-uniform distribution of osteons in a cortical bone tissue results in a localization of deformation processes. Such localization can affect bone performance under external load and initiate fracture. In this paper, a two-dimensional numerical (finite-element) model for osteonal bovine cortical bone was developed with account for its microstructure. The topology of a transverse-radial cross section of a bovine cortical bone was captured with optical microscopy. The elastic-plastic data for the microstructural features of the cross section was obtained with a use of the nanoindentation technique. Both the topology and nanoindentation data were used as input to the model formulated with the Abaqus finite-element software. The area, directly reflecting micro-scale information, was embedded into the region with homogenised properties of the cortical bone. Different scenarios of the loading were tried: (i) tension in transverse direction, (ii) tension in radial direction and (iii) tension in both directions. The calculated stress and strain fields for various cases of loading demonstrate different patterns due to implementation of microstructural features in the finite-element model. There are obvious signs of localization of the plastic regions at the micro-structure level that can be considered as fracture precursors. The suggested approach emphasizes the importance of microstructural features in development of bone failure.