Three-dimensional finite element analysis of the effects of anisotropy on bone mechanical properties measured by nanoindentation

A three-dimensional finite element analysis (FEA) model with elastic-plastic anisotropy was built to investigate the effects of anisotropy on nanoindentation measurements for cortical bone. The FEA model has demonstrated a capability to capture the cortical bone material response under the indentation process. By comparison with the contact area obtained from monitoring the contact profile in FEA simulations, the Oliver-Pharr method was found to underpredict or overpredict the contact area due to the effects of anisotropy. The amount of error (less than 10% for cortical bone) depended on the indentation orientation. The indentation modulus results obtained from FEA simulations at different surface orientations showed a trend similar to experimental results and were also similar to moduli calculated from a mathematical model. The Oliver-Pharr method has been shown to be useful for providing first-order approximations in the analysis of anisotropic mechanical properties of cortical bone, although the indentation modulus is influenced by anisotropy.

A generalized Drucker–Prager viscoplastic yield surface model for asphalt concrete

A generalized Drucker–Prager (GD–P) viscoplastic yield surface model was developed and validated for asphalt concrete. The GD–P model was formulated based on fabric tensor modified stresses to consider the material inherent anisotropy. A smooth and convex octahedral yield surface function was developed in the GD–P model to characterize the full range of the internal friction angles from 0° to 90°. In contrast, the existing Extended Drucker–Prager (ED–P) was demonstrated to be applicable only for a material that has an internal friction angle less than 22°. Laboratory tests were performed to evaluate the anisotropic effect and to validate the GD–P model. Results indicated that (1) the yield stresses of an isotropic yield surface model are greater in compression and less in extension than that of an anisotropic model, which can result in an under-prediction of the viscoplastic deformation; and (2) the yield stresses predicted by the GD–P model matched well with the experimental results of the octahedral shear strength tests at different normal and confining stresses. By contrast, the ED–P model over-predicted the octahedral yield stresses, which can lead to an under-prediction of the permanent deformation. In summary, the rutting depth of an asphalt pavement would be underestimated without considering anisotropy and convexity of the yield surface for asphalt concrete. The proposed GD–P model was demonstrated to be capable of overcoming these limitations of the existing yield surface models for the asphalt concrete.