Reliability analysis for cementless hip prosthesis using a new optimized formulation of yield stress against elasticity modulus relationship

• We develop a new formulation between the yield stress and Young’s modulus of bone.
• We validate the optimized formulation for cortical and trabecular bone.
• We integrate the reliability analysis into artificially hip replacement design.

Using classical design optimization methods for implant-bone studies does not completely guarantee a safety and satisfactory performance, due in part to the randomness of bone properties and loading. Here, the material properties of the different bone layers are considered as uncertain parameters. So their corresponding yield stress values will not be deterministic, that leads to integrate variable limitations into the optimization process. Here there is a strong need to find a reliable mathematical relationship between yield stress and material properties of the different bone layers. In this work, a new optimized formulation for yield stress against elasticity modulus relationship is first developed. This model is based on some experimental results. A validation of the proposed formulation is next carried out to show its accuracy for both bone layers (cortical and cancellous). A probabilistic sensitivity analysis is then carried out to show the role of each input parameter with respect to the limit state function. The new optimized formulation is next integrated into a reliability analysis problem in order to assess the reliability level of the stem–bone study where we deal with variable boundary limitations. An illustrative application is considered as a bi-dimensional example (contains only two variables) in order to present the results in an illustrative 2D space. Finally, a multi-variable problem considering several daily loading cases on a hip prosthesis shows the applicability of the proposed strategy.