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.

测量骨组织材料特性的能力在疾病诊断和材料建模中发挥着重要作用。骨骼对载荷的响应很复杂，并且显示出对刚度、屈服和失效的粘性贡献。它还具有延展性和破坏性，并表现出塑性硬化直至失效。当对骨组织进行机械测试时，这些本构效应很难量化，因为在最终的应力应变数据中只能看到它们的组合。在这项研究中，提出了一种通过单循环拉伸试验来识别骨骼的刚度、阻尼、屈服应力和硬化系数的方法。该方法基于两层弹粘塑性流变模型，能够再现样本的屈服前和屈服后响应。该模型的结构能够捕获粘性引起的刚度、屈服和极限应力的增加，并直接计算损耗角正切。通过优化模型响应以拟合实验数据，以逆向方法获得材料参数。通过识别在潮湿条件下测试的单个骨小梁的材料特性来证明所提出的方法。机械测试是根据已发表的单小梁拉伸实验方法进行的。结果，获得了长期和瞬时杨氏模量，平均分别为3.64 GPa和5.61 GPa。发现的屈服应力为 16.89 MPa，低于之前的研究结果，而损耗角正切为 0.04，两者吻合良好。总的来说，两层模型能够重现单小梁的循环力学测试数据，均方根误差为2.91±1.77 MPa。 结果表明，当基于单个机械测量来量化多个本构贡献时，逆流变模型具有很大的优势。