Using a scale-bridging technique to determine the effect of elastic properties on stress distribution around the femoral stem of an artificial hip joint with a simplified geometry

Abstract

A scale-bridging technique was used to investigate the effect of the elastic properties of beta-Ti alloys on the stress distribution around the femoral stem of an artificial hip joint with a simplified geometry when under an external loading. The anisotropic elastic constants of single-crystalline beta-Ti alloys (TN1: Ti-18.75 at% Nb, TN2: Ti-37.5 at% Nb, and TN3: Ti-43.75 at% Nb) were calculated using an ab-initio technique that was based on density functional theory calculation. The single-crystalline elastic constants calculated via the ab-initio technique were used to calculate the elastic constants of polycrystal beta-Ti alloys using an elastic selfconsistent scheme. Finite element analysis based on the elastic constants of polycrystalline beta-Ti alloys for a femoral stem was conducted to calculate the above-mentioned stress distribution. The model system consisting of a TN1 alloy exhibited a relatively high level of von Mises stress on the surface of cancellous and cortical bones compared to model systems consisting of TN2, TN3 alloys and commercial biomaterials (Ti-6Al-4V alloy and 316STS). The thickness of the cancellous bone between the femoral stem and the cortical bone affected the stress concentration on the surface of the cortical bone.