No abstract

Homogenised finite element (FE) analyses are able to predict osteoporosis‐related bone fractures and become useful for clinical applications. The predictions of FE analyses depend on the apparent, heterogeneous, anisotropic, elastic, and yield material properties, which are typically determined by implicit micro‐FE (μFE) analyses of trabecular bone. The objective of this study is to explore an explicit μFE approach to determine the apparent post‐yield behaviour of trabecular bone, beyond the elastic and yield properties. The material behaviour of bone tissue was described by elasto‐plasticity with a von Mises yield criterion closed by a planar cap for positive hydrostatic stresses to distinguish the post‐yield behaviour in tension and compression. Two ultimate strains for tension and compression were calibrated to trigger element deletion and reproduce damage of trabecular bone. A convergence analysis was undertaken to assess the role of the mesh. Thirteen load cases using periodicity‐compatible mixed uniform boundary conditions were applied to three human trabecular bone samples of increasing volume fractions. The effect of densification in large strains was explored. The convergence study revealed a strong dependence of the apparent ultimate stresses and strains on element size. An apparent quadric strength surface for trabecular bone was successfully fitted in a normalised stress space. The effect of densification was reproduced and correlated well with former experimental results. This study demonstrates the potential of the explicit FE formulation and the element deletion technique to reproduce damage in trabecular bone using μFE analyses. The proper account of the mesh sensitivity remains challenging for practical computing times.

Stability of an implant is defined by its ability to undergo physiological loading-unloading cycles without showing excessive tissue damage and micromotions at the interface. Distinction is usually made between the immediate primary stability and the long-term, secondary stability resulting from the biological healing process. The aim of this research is to numerically investigate the effect of initial implantation press-fit, bone yielding, densification and friction at the interface on the primary stability of a simple bone-implant system subjected to loading-unloading cycles. In order to achieve this goal, human trabecular bone was modeled as a continuous, elasto-plastic tissue with damage and densification, which material constants depend on bone volume fraction and fabric. Implantation press-fit related damage in the bone was simulated by expanding the drilled hole to the outer contour of the implant. The bone-implant interface was then modeled with unilateral contact with friction. The implant was modeled as a rigid body and was subjected to increasing off-axis loading cycles. This modeling approach is able to capture the experimentally observed primary stability in terms of initial stiffness, ultimate force and progression of damage. In addition, it is able to quantify the micromotions around the implant relevant for bone healing and osseointegration. In conclusion, the computationally efficient modeling approach used in this study provides a realistic structural response of the bone-implant interface and represents a powerful tool to explore implant design, implantation press-fit and the resulting risk of implant failure under physiological loading.

No abstract

No abstract