Trabecular bone is a honeycomb-like load-bearing structure located within many whole bones of the human body, including sites commonly associated with osteoporotic fracture such as spinal vertebrae and the hip joint. The bone tissue that makes up the trabecular network contains active bone cells that are constantly working to repair and remodel the bone material over time. The product of this cellular activity influences the mechanical properties of trabecular bone, specifically the formation and propagation of microdamage and microfracture. At the same time, the stress and strain states within the tissue help to direct how the cells function. Thus it is valuable to characterise the mechanics of trabecular bone tissue in understanding the behaviour of bone in health and disease. While the elastic properties of bone tissue have been thoroughly examined and reported in the literature, its post-yield behaviour remains unclear, especially that of trabecular bone.
This study characterised the mechanical response of trabecular bone, of both bovine and human origin, using nanoindentation combined with Atomic Force Microscopy (AFM) to map the residual deformation. Tissue features of bone mineral content and trabecular orientation, as well as the effect of desktop micro-computed tomography (μCT) were examined to identify their role in the response of bone to nanoindentation loading. Finally, Finite Element Analysis (FEA) was used to evaluate the application of von Mises plasticity, with perfect plasticity and strain hardening, and Drucker-Prager yield criteria, in capturing the plastic deformation characteristics of trabecular bone tissue.
The overall aim of this thesis was to investigate and model the mechanical behaviour of trabecular bone with focus on the post-yield response of the material at the nanoscale. This was subsequently broken down into an experimental component, with mechanical testing to induce considerable plastic deformation within the bone tissue, and FEA to explore constitutive material models to capture post-yield behaviour.
Nanoindentation was selected as the mechanical characterisation tool for trabecular bone tissue of both bovine and human origin, and combining this with Atomic Force Microscopy (AFM) enabled residual deformation to be mapped. Testing was performed using a high load single indent loading profile and a novel incremental loading protocol.
The results showed that increased bone mineral content was associated with a stiffer response of the local tissue to loading and reduced dissipation of energy during the nanoindentation event. Trabecular orientation, with respect to the primary loading direction within the body and indented normal to the axis of a trabecula, was not found to influence the material‟s response to nanoindentation.
No pile-up of material was observed surrounding the indent, nor any discrete fracture or cracking of the tissue associated with the indenter, even to loads as high as 150 mN. These novel data are valuable in the development of constitutive material behaviour governing the post-yield response.
In addition, the effect of commonly used desktop micro-Computed Tomography (µCT) was examined to identify its effect on the response of bone to nanoindentation loading. In bone tissue from an 86-year-old donor, the radiation was found to reduce the indent depth and energy involved in the response to loading.
Constitutive material models with relations to govern the plastic behaviour of the material were evaluated using FEA. A 3D FE model of one sixth of the boneindenter interaction (due to six-fold symmetry) and an equivalent axisymmetric FE model were developed for the bone nanoindentation problem. To maintain a manageable scope, time-dependent and fracture behaviour was excluded from the material modelling. Isotropic linear elasticity was assumed to implement plasticity models using ABAQUS/Std FE software. Following classic metal plasticity, the von Mises yield surface, initially with perfect plasticity and subsequently with isotropic and kinematic strain hardening, was evaluated. Consistent with the literature, the von Mises model was found to inadequately capture the response of the tissue to loading and the energy involved in the nanoindentation event, as well as predicting excessive pile-up of material around the indentation site. While the addition of strain hardening suppressed the pile-up height prediction, an improved solution was achieved by turning to plasticity theory in soil mechanics.
The Drucker-Prager yield surface with and without dilation was assessed. The pressure-dependent yield and available modifications that this yield criterion offers are advantageous in capturing the post-yield behaviour of trabecular bone tissue. Although it did not model the experimental observations perfectly, the Drucker-Prager yield criterion is a good plasticity model to capture the deformation characteristics of trabecular bone tissue to nanoindentation loading.
The significant and novel contributions of this thesis are the introduction of the high load incremental loading protocol to characterise the plastic behaviour of trabecular bone tissue, and its application in generating novel data for the development of constitutive material relations incorporating plasticity. These experimental and modelling tools can be modified to examine bone tissue from trauma and disease. Further, the models may contribute to understanding the role of stress and strains in biological activity within bone tissue.