Preventing stress singularities in peri-implant bone - a finite element analysis using a graded bone model

In finite element analysis bone is often treated as two-layered material that has a discontinuity between the cortical and cancellous bone, which leads to a singularity and incorrect stresses. The goal of this study was to eliminate this singularity and to create a more realistic representation of bone which also considers the transition zone between cortical and cancellous bone as observed in natural bone. This was achieved by modelling bone as a graded material and inserting node-specific values for Young's modulus in the finite element simulation, whereas the transition zone thickness was derived from a CT scan. The modelling was performed semi-automatically, and the maximum principal stresses of the new approach were compared to those of a conventional approach. The new approach was found to effectively avoid singularities and provides more accurate predictions of stress in areas of the bone transition zone. As the approach is automatable and causes rather small overhead it is recommended for use in future work, when the problem at hand requires evaluating stresses close to the former singularity.