## 2 Materials and Methods
### Interfragmentary Movement Analysis (IFM)  
The stabilizing power of the plate-screws configurations were assessed according to the [PERSON]'s theory [34], which states that the presence of suitable axial and transversal strains at fracture gap could be advantageous for bone healing through the formation of  
\begin{table}
\begin{tabular}{c c} \hline
**Components Pair** & **Static Friction Coeff.** \\ \hline Femur simulacre—Cartilage & 0.02 [24; 25] \\ Plate—Bone & 0.37 [24] \\ Plate—Screw & 0.10 [26] \\ Bone—Bone & 0.40 [24] \\ \hline \end{tabular}
\end{table}
Table 4: Static friction coefficients considered for each components pair.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Material** & **Elastic Modulus E (MPa)** & **Poisson’s Ratio \(\
u\)** & **Density \(\delta\) (Kg/m\({}^{3}\))** \\ \hline Cortical bone [22] & 16,700 & 0.300 & 1600 \\ Cancellous bone [22] & 1000 & 0.055 & 640 \\ Screws and plate [23] & 193,000 & 0.290 & 8000 \\ \hline \end{tabular}
\end{table}
Table 3: Components material properties.  
the bone callus. To compute the fracture gap strains, two local coordinate systems for the transverse fracture (in blue) and for the vertical component of T-shaped fracture (in red) were considered (Figure 5).  
According to these local coordinate systems, the z-direction describes the compression and traction at the fracture region, conversely x- and y-directions represent movements that would bring misalignments of the bone stumps on the fracture plane.  
To implement the gap analysis along the fractures brim, 22 equidistant couples of points crossing the fracture gap have been selected for the transverse fracture and 15 for the vertical component of T-shaped fracture; the same couples of points have been used for each model within the same fracture type (Figure 5). The incremental distances of each couple were measured and strains were then computed. The axial strain \(\varepsilon_{axial}\) has been obtained as the percentage variation in length along z direction over the respective mean fracture gap (GAP):  
\[\varepsilon_{axial}=\varepsilon_{z}=\frac{\Delta z}{GAP}\cdot 100, \tag{1}\]  
while for the shear strain, \(\varepsilon_{shear}\), a strain magnitude was computed in order to obtain a unique value representing the fracture plane:  
\[\varepsilon_{shear}=\sqrt{\varepsilon_{x}^{2}+\varepsilon_{y}^{2}}=\sqrt{ \left(\frac{\Delta x}{GAP}\cdot 100\right)^{2}+\left(\frac{\Delta y}{GAP} \cdot 100\right)^{2}}, \tag{2}\]  
where \(\Delta x\), \(\Delta y\) and \(\Delta z\) are the maximum distance increment between each couple of points along the respective axis and according to the specific local reference system, and \(GAP\) is the mean fracture gap amplitude.  
The so obtained strains have been classified in specific ranges (Table 5). For the axial strain, an optimal range, based on the limits defined by [PERSON]'s theory [34; 35; 36] and other studies [37; 38; 39; 40], was selected. Conversely, the shear strain optimal range was defined based on the hypothesis that blocking sliding motions in the fracture plane would guarantee fracture extremities alignment during healing. An additional acceptable range was adopted for results visualization purposes to discriminate values that tends to optimal behaviors to those highly unacceptable for bone healing.  
Figure 5: Reference systems and points couples selection in the transverse fracture (**left**) and in the T-shaped fracture (**right**). Note that the same blue reference system was applied for both the transverse fracture and the transverse component of the T-shaped fracture, while the red reference system was only applied for the vertical component of the T-shaped fracture. For both local reference systems, the z direction describes the compression and traction at the fracture region.