# Viscoelastic Finite Line Contact of Thin Bonded Layered Solids of Low Elastic Modulus
## 4 Experimental Results  
Table 1 lists the averaged sensor output voltage for the various sensors under the applied indentation load of 3.9 N. Note that the various values in each column show the relaxed value of the output voltage with time (as whole multiples of the HFCP relaxation time, \(\tau\) = 0.9 s). These values are converted to equivalent contact pressures, using the appropriate calibration lines in Figure 3, and plotted along the appropriate axes shown in Figure 1b. The footprint area is slightly larger than the cross-sectional area of the flat indenter. This is because under the indentation load, the material of the soft protective silicone rubber layers is pulled into the contact area. The contact area also gradually increases in dimensions with relaxation. The footprint area is obtained from the impression made by the \"engineering blue\" gel on the epithelial layer of the silicone rubber under all the indentation loads and at different multiples of the relaxation time of HFCP. Table 2 lists the contact area for various values of load and at different relaxation time multiples. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Time (s)** & **Element 1** & **Element 2** & **Element 3** & **Element 4** & **Element 5** \\ \hline \(\tau\) & 9.305 & 8.793 & 8.213 & 8.238 & 8.113 \\ \hline \(2\tau\) & 9.02 & 8.573 & 7.699 & 7.925 & 7.854 \\ \hline \(3\tau\) & 8.34 & 7.987 & 7.03 & 7.24 & 6.975 \\ \hline \(5\tau\) & 7.995 & 7.693 & 6.75 & 6.78 & 6.575 \\ \hline \(10\tau\) & 7.15 & 7.04 & 5.89 & 6.17 & 5.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The sensing elements output voltage. \begin{table}
\begin{tabular}{c c} \hline \hline
**Relaxation Time (s)** & **Contact Area (mm\({}^{2}\))** \\ \hline \(\tau\) & 51.785 \\ \hline \(2\tau\) & 52.104 \\ \hline \(3\tau\) & 52.553 \\ \hline \(5\tau\) & 52.939 \\ \hline \(10\tau\) & 54.015 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Measured contact area under different loads. Figure 3: The calibration curves for the normal load of 3.9 N.  
The voltage output per sensing site has a maximum of 10 volts, corresponding to no contact condition. When a sensing site is directly contacted, the change in the conductance of HFCP results in a corresponding drop in the voltage output. There is a linear relationship between pressure and voltage output. This depends upon the relaxation time of HFCP as can be observed in Figure 3.  
Figure 4 shows the pressure distribution along the \(x\)-axis (shown in Figure 1b) for an applied contact load of 3.9 N. The pressure profiles in the figure are axisymmetric about the vertical pressure axis (i.e., half the distribution is shown in the figure). The pressure spike at the edge of the contact is caused by the stress concentration there. This is because of a sharp change in the axial profile of the indenter. This effect is observed in finite line contacts, for example in the contact of unblended rollers against a semi-infinite elastic solid [6; 10; 11]. The same is true for the contact of a flat indenter (punch) against an elastic half-space [6]. Finite difference or finite element solutions show a finite pressure in the vicinity of the edge of the contact, which can be as much as several times the central region of the pressure distribution. The magnitude of the pressure spike is largest under the instantaneous application of a load, corresponding to the initial instantaneous elastic response of the layer. This instantaneous pressure distribution is difficult to record experimentally for materials with low relaxation times, such as the HFCP polymer. Therefore, the results are presented at \(t=\tau\) and its higher multiples. Relaxation characteristics of the polymer result in a drop in the magnitude of pressure spike with time. This is clearly observed in Figure 4. The central portion of the pressure distribution is approximately equal to the average (i.e., Pascal) pressure of \(P=\frac{W}{A}\).