*2.3. Loads and Boundary Conditions*

Boundary conditions and contact interactions were defined in ABAQUS/CAE software (Dassault Systems Simulia Corp., Johnston, RI, USA).

The solution of the task in ABAQUS included two steps: screw tightening and standing. The region of the contact interaction and boundary conditions were unchanged between the steps. The model had contact interactions with friction in the following pairs: the implant and pelvic bone and the acetabular liner and the artificial femoral head. The coefficient of friction was equal to 0.2 for the titanium–bone pair and 0.15 for the polyethylene–titanium pair. The screw heads and threads are bonded with implant and bone correspondingly, so these contact pairs are considered as linear contacts without friction and separation.

The first step was to bring together the implant and the pelvic bone with the screws. Therefore, a special compressive screw force was applied to each screw. The calculations were conducted with four values of screw forces: 100, 500, 1000, and 1500 N. The upper surface of the sacrum is fully constrained.

The second step simulated the walking cycle as a slow, quasistatic process. The reaction forces corresponding to the patient's weight were applied to the reference points in the centres of the acetabular cups (Figure 5). The reaction force was obtained from the HIP98 software available from the OrthoLoad open resource (https://orthoload.com/testloads/data-collection-hip98/, accessed on 1 October 2021). The software generates the biomechanical forces based on the special database, which was developed within study [25] using special instrumented implants. *Materials* **2021**, *14*, x FOR PEER REVIEW 9 of 24

**Figure 5.** Boundary conditions and applied forces: (**a**) model with boundary conditions and loads including screw pretension and reaction forces applied to the centres of the left and right joints; (**b**) reaction force curves for walking simulation measured as a percentage of body weight (BW). **Figure 5.** Boundary conditions and applied forces: (**a**) model with boundary conditions and loads including screw pretension and reaction forces applied to the centres of the left and right joints; (**b**) reaction force curves for walking simulation measured as a percentage of body weight (BW).

*2.4. Model Validation*  The FE method requires strict validation of the model because an inaccurate model may lead to incorrect and unreliable results [9–11]. Comprehensive experimental validation of the FE model of the reconstructed pelvis is not carried out before the surgery because a definite forecast of the bone stress state is required before performing surgery. At the beginning of the second loading step, where the walking process was simulated, the length of the screws was fixed, which occurs at the end of the pretension phase. A detailed strength analysis was further performed for screw force values of 500 N and 1000 N. The general kinematic boundary conditions remained unchanged from the previous step of the considered computer simulation.

However, the evaluation of the general adequacy of the model was carried out in accordance with several parameters. First, the FE mesh was assessed based on several

The preliminary frequency analysis proved that the reconstructed pelvis assembly

Another validation based on the displacement distribution (Figure 6) showed that the values obtained in the current study were within range close to the ranges described in papers [1,10,29]. The results of the analysis of the stress and strain fields were also close to previous results [1,2,10], proving the principal qualitative and quantitative conform-

element size, type, and shape. Second, the physical and mechanical characteristics of materials ensuring model accuracy were obtained from reliable sources [9,12,14,16,18,19]. Kinematic boundary conditions for the model and contact regions were applied and approved by the medical studies described in other articles [11,26,27]. The loading scheme, which was used in current research and based on the loading of the structure with the hip joint force acting as a reaction force, was the same as used previously [28]. It

allowed us to describe the stress-strain state in a more accurate way.

ance.

was joint and adjusted correctly, and all the connections were set up properly.
