## 2 Approaches
### Modelling of Lumbar Belt's Pressure  
As a first approximation, the lumbar belt acts on the body by delivering a pressure \(p\) proportional to the belt tension (\(T_{1}\) or \(T_{2}\), 1 and 2 referring to the weft or warp direction) and to the local curvature defined by its radius (\(R_{1}\) or \(R_{2}\)), as expressed by Laplace's law:  
\[p=\frac{T_{1}}{R_{1}}+\frac{T_{2}}{R_{2}}\,T_{1},T_{2}\geq 0\,R_{1},R_{2}>0 \tag{1}\]  
Then, the pressure depends on the body's curvature, the belt geometry and stiffness, and the level of stretch applied by the user. Last, the belt placement on the body has to be carefully addressed. The body shape is extracted from the FE model, thereby calculating the curvature locally.  
Belt stiffness is obtained using a tensile test according to the European standard EN ISO 13934-1:1999 with an Instron 3343 Universal testing machine. Belts are stretched 3  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Subject Type** & **Waist (mm)** & **Bust (mm)** & **Height of Trunk (mm)** \\ \hline Tall-Large & 1182.8 & 1088.9 & 726.5 \\ \hline Tall-Thin & 868.6 & 885.1 & 724.2 \\ \hline Small-Large & 1182.8 & 1089.3 & 617.4 \\ \hline Small-Thin & 868.9 & 885.2 & 618.9 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Morphological characteristics of four chosen subjects.  
Figure 1: Schematic lumbar belt according to the French Healthcare system recommendation. 1: Textile (assembly of band or cut fabric), 2: fastening system, 3: rigid whalebones, 4: soft whalebones, and 5: additional straps (optional).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Belt Type** & \
\begin{tabular}{c} **Global Stiffness of** \\ **the Belt (N/m)** \\ \end{tabular} & **Textile Architecture** &
\begin{tabular}{c} **Presence of** \\ **Additional Straps** \\ \end{tabular} \\ \hline A & 3244 & Assembly of band & Yes \\ \hline B & 1489 & Assembly of band & No \\ \hline C & 2054 & Assembly of band & No \\ \hline D & 3070 & Assembly of band & Yes \\ \hline E & 2651 & Cut fabric & No \\ \hline F & 3146 & Cut fabric & Yes \\ \hline G & 4250 & Cut fabric & Yes \\ \hline H & 3459 & Cut fabric & Yes \\ \hline \hline \end{tabular}
\end{table}
Table 2: Typical characteristics of selected lumbar belts for the study.  
times up to 20% of strain, as recommended by the manufacturer. Since the patient closes the belt in a loosening phase, the stiffness is taken as the tangential slope of the strain/lineic force curve during unloading at 20% strain. This procedure is explained in more detail in [PERSON] et al. [18].  
The belt is stretched around the body in a way, as the mean stretch is 20%, by overlapping the two ends on the abdomen, mimicking real life. Even if the mean stretch value is 20%, local variations are taken into account by comparing the body diameter to the belt size. Considering the local equilibrium on a belt slice--seen as a beam--the mean stretch of each slice varies with the section. If the belt is made of fabric, the section varies along the belt and so does the mean stretch; if the belt is made of elastic bands, the section is constant, even if the width varies, and so the mean stretch of a section remains constant.  
This approach is a simplification of a more complex situation by considering only the unidirectional loading of the belt without any transverse or shear effects. Since the material is highly anisotropic, with the shear stiffness being significantly lower than the tensile stiffness, and since there is no transverse loading, this assumption is reasonable and avoids the high complexity of solving the coupled belt/body interaction.