The Effect of Time-Dependent Prestresses at the Bone-Screw Interface under Bending Load

The viscoelastic properties of bone significantly influence the mechanical stability of bone-screw complex. This study aims to evaluate the changes in stiffness of a bone-screw model under different bending displacements and pre-stress conditions over time. Using a finite element model, we applied bending displacements of 12,24, and $48 \mu \mathrm{~m}$ were applied to the head of the screw. The stiffness was predicted at time intervals of $1,61,121$, and 181 seconds to assess the impact of stress relaxation. The bone was modeled with viscoelastic properties, and the screw was considered rigid. The results showed a decrease in stiffness with increasing displacement. At $12 \mu \mathrm{~m}$, the initial stiffness was approximately $6.41 \mathrm{kN} / \mathrm{mm}$, decreasing slightly over time due to stress relaxation. At higher displacements (24 and $48 \mu \mathrm{~m}$), the stiffness reduction was more pronounced, especially in the absence of pre-stress, highlighting the significant role of initial thread engagement. Pre-stress conditions led to a stiffness increase of up to $\mathbf{7 0 \%}$ compared to the free-stressed state. The study demonstrates that both displacement and pre-stress significantly affect the stiffness of the bone-screw interface. Increased displacement reduces stiffness, while pre-stress raises it. Understanding these interactions is crucial for optimizing orthopedic implant design and surgical techniques to improve patient satisfaction and outcomes.