Abstract
The ability to measure bone tissue material properties plays a major role in diagnosis of diseases and material modeling. Bone’s response to loading is complex and shows a viscous contribution to stiffness, yield and failure. It is also ductile and damaging and exhibits plastic hardening until failure. When performing mechanical tests on bone tissue, these constitutive effects are difficult to quantify, as only their combination is visible in resulting stress–strain data. In this study, a methodology for the identification of stiffness, damping, yield stress and hardening coefficients of bone from a single cyclic tensile test is proposed. The method is based on a two-layer elasto-visco-plastic rheological model that is capable of reproducing the specimens’ pre- and postyield response. The model’s structure enables for capturing the viscously induced increase in stiffness, yield, and ultimate stress and for a direct computation of the loss tangent. Material parameters are obtained in an inverse approach by optimizing the model response to fit the experimental data. The proposed approach is demonstrated by identifying material properties of individual bone trabeculae that were tested under wet conditions. The mechanical tests were conducted according to an already published methodology for tensile experiments on single trabeculae. As a result, long-term and instantaneous Young’s moduli were obtained, which were on average 3.64 GPa and 5.61 GPa, respectively. The found yield stress of 16.89 MPa was lower than previous studies suggest, while the loss tangent of 0.04 is in good agreement. In general, the two-layer model was able to reproduce the cyclic mechanical test data of single trabeculae with an root-mean-square error of 2.91 ± 1.77 MPa. The results show that inverse rheological modeling can be of great advantage when multiple constitutive contributions shall be quantified based on a single mechanical measurement.
Highlights
Mechanical testing is the gold standard for obtaining bone tissue material properties on the macroscopic and mesoscopic length scale in experimental biomechanics
We propose a two-layer elasto-visco-plastic rheological model for reproducing the uniaxial behavior of small length-scale bone samples
A two-layer elasto-visco-plastic rheological model is presented, capable of reproducing the stress response of single trabeculae subjected to uniaxial cyclic loading
Summary
Mechanical testing is the gold standard for obtaining bone tissue material properties on the macroscopic and mesoscopic length scale in experimental biomechanics. Material properties like stiffness and strength condense the material response to applied stress or strain into descriptive values. These values allow for easy comparison of sample groups (young vs old or healthy vs pathological, etc.) and are used as an input for constitutive material models. Bone is a living tissue that is subjected to continuous adaptations. Mechanical testing requires usually to extract bone samples from the living environment or utilizes donor tissue where remodeling and metabolic processes have stopped. Mechanical testing generally provides only a still image of the continuous tissue alterations that take place in the living organism
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