## 2 Materials and Methods
### Finite Element Analyses  
The finite element models of the intact and treated clavicles were developed using ANSYS Workbench 19.2 (ANSYS, Inc., Canonsburg, PA, USA). The materials used for the fixation devices and bones were assumed to be linearly elastic isotropic. The ligaments and muscles were developed using tension-only spring elements. The stiffness for a muscle was calculated by a formula K = (E \(\times\) A)/L, where K is the stiffness, E is the Young's modulus, A is the cross-sectional area, and L is the length of a muscle. The insertion points of the ligaments and muscles followed the guidance of an orthopaedic surgeon. All material properties of the finite element models were obtained from previous studies [24, 25, 26, 27, 28] and are listed in Table 1. Owing to the complicated and irregular geometries  
Figure 1: Simplified single-clavicle models. Figure 2: Complete human upper-body models. of the implants and bones, the numerical models were free-meshed using 20-node solid elements of SOLID 186 (Figure 3). The element size of the finite element models was determined by conducting a convergent study, and the element size was 0.5 mm for the implants, 2 mm for the clavicle, 8 mm for the skull, and 4 mm for the others. A frictionless contact interface was defined between the fractured fragments. For the plate fixations, the following interfaces were assumed to be bonded: the screw head and the plate, and the screws and the bone. Additionally, a contact interface between the plate and the bone was considered. For the nail fixation, a contact interface between the nail and the bone was considered. However, the interface between the proximal clavicle and the proximal nail was assumed to be bonded. Under the loading and boundary conditions of the single-clavicle model, a bending force of 200 N [21; 29], a compression force of 200 N [21; 29], and a combination of the bending and compression forces were applied to the distal clavicle. Moreover, the proximal clavicle was fully constrained (Figure 4A). For the human upper-body skeleton model, a load of 200 N was applied to the distal humerus of the right arm, and the surfaces of the sternum, fifth rib, fifth thoracic vertebra, and cranium were fully restricted (Figure 4B). During the post-processing, the maximum displacement of the clavicle, the maximum von Mises stress of the clavicle, and the maximum von Mises stress of the fixation devices were calculated to investigate each fixation strategy. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Materials** & **Young’s Modulus (MPa)** & **Poisson’s Ratio** & **Area (mm\({}^{2}\))** \\ \hline Skeleton & & & \\ Skull & 10,000 & 0.29 & - \\ Teeth & 18,600 & 0.31 & - \\ Clavile (Cortical bone) & 10,000 & 0.29 & - \\ Clavile (Cancellous bone) & 100 & 0.29 & - \\ Scapular & 16,000 & 0.3 & - \\ Rib & 4520 & 0.375 & - \\ Sternum & 9680 & 0.3 & - \\ Coastal cartilages & 24.5 & 0.4 & - \\ Spine column (Cortical bone) & 10,000 & 0.25 & - \\ Spine column (Cancellous bone) & 450 & 0.25 & - \\ Spine column (Posterior elements) & 3500 & 0.3 & - \\ Spine column (Annulus fibrosis) & 4.2 & 0.45 & - \\ Spine column (Nucleus pulposus) & 1 & 0.499 & - \\ \hline
**Implants** & & & \\ \hline Plates/Nail/Screws (Titanium alloy) & 114,000 & 0.3 & - \\ \hline
**Muscles** & & & \\ Sternocleidomastoid muscle & 0.5 & - & 246 \\ Trapezius muscle & 0.5 & - & 126 \\ Deltoid muscle & 0.5 & - & 1817 \\ Levator scapulae muscle & 0.5 & - & 126 \\ Supraspinatus muscle & 0.5 & - & 572 \\ Infraspinatus muscle & 0.5 & - & 1374 \\ Pectoralis major muscle & 0.5 & - & 1334 \\ Subscapularis muscle & 0.5 & - & 1630 \\ \hline
**Ligaments** & Stiffness (N/mm) & & \\ \hline Anterior sternolavicular ligament & 50 & - & - \\ Posterior sternolavicular ligament & 50 & - & - \\ Interclavicular ligament & 50 & - & - \\ Costolacivicular ligament & 50 & - & - \\ Superior acromiodavicular ligament & 30 & - & - \\ Inferior acromiodavicular ligament & 30 & - & - \\ Coracoclavicular ligament & 30 & - & - \\ \hline \hline \end{tabular}
\end{table}