# A Tunable Self-Offloading Module for Plantar Pressure Regulation in Diabetic Patients
## 3 Modeling and Simulation  
This section presents the numerical modeling and simulation of the proposed device. The COMSOL multiphysics software was used for the numerical modeling. For device to be able to be restored to default State 1, the head should be non-magnetic. Otherwise, it would lead to mainly three problems: first, it may interact with the magnetic environment/loading, leading to a deviation from the targeted behavior. Secondly, it would add up additional magnetic bonding in the direction of the loading (Figure 1d), which would reduce the blocking threshold limit of the device.  
The size and magnetic strength of the permanent magnet were chosen based on the bonding strength required (the threshold PP). In this work, we aimed to achieve a bonding strength of up to 800 kPa. A ring magnet with a height of 5 mm, outer diameter of 10 mm, and internal diameter of 4 mm was chosen for this work. This magnet is axially magnetized and gives high axial bonding strength. For the mentioned size, the material properties were chosen based on the availability from the different magnet suppliers and are listed in Table 1.  
Therefore, these physics were coupled in the current analysis. The magnetic flux coming (Figure 2) from the ring permanent magnet was modeled as the remnant magnetic  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Recoil Permeability & 1.05 \\ Effective Remament Flux Density (Norm) & 2.15 \\ Young Modulus (GPa) & 350 \\ Poisson’s Ratio & 0.35 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Properties of the chosen magnet.  
flux, while the mechanics involved as the application of the load was modeled using solid mechanics. A complete quasistatic situation was considered in the above analysis. The distance \(g\) between the fixed magnet and the mobile magnetic support defines the bonding force between them. For piston length \(L\) (the distance between the head and mobile magnetic support; see Figure 2), the free spacing between the head and magnet fixation \(d\), and a fixed magnetic height \(b\), then \(g\) can be given by Equation (1).  
\[g=L-(d+b) \tag{1}\]  
For the above simulation, a \(g\) of 40 \(\upmu\)m was used (given by Equation (1)), as it better suited the meshing and boundary conditions, while playing with this distance \(g\), an offline tunability in terms of threshold pressure limit can be achieved. From Equation (1), with the increase in \(d\) (both \(L\) and \(b\) are fixed), \(g\) decreases; therefore, more \(d\) would lead to a stronger magnetic bonding and, so, a high threshold pressure. As, from the practical side, it is easier to measure \(d\) than \(g\), we directly refer to \(d\) for the tunability. In the COMSOL environment, an input displacement of 1.5 mm was given to the head of the device, and the corresponding impact was measured. From the PP redistribution requirement, 1.5-3 mm of the head/mobile part displacement can be considered sufficient based on the flexibility of human foot skin. Figure 3d presents the corresponding pressure limit obtained from the input displacement of 1.5 mm against different spacings \(d\) (1.7-2.7 mm). In Figure 1d, the bottom screw allows the adjustment in spacing, therefore enabling the tunability feature. For a given device, Figure 3b shows that, with the spacing (between the head and fixed end) increment, the threshold pressure limit can be tuned from 69 kPa to 800 kPa. This validates the proof of concept of the pressure tunability.  
Figure 2: Simulated device with magnetic field strength (T). **(a)** Initial configuration: State 1 (**b**); partial opening: State 2; **(c)** complete opening: State 3.