Frictional contact of soft polymeric shells

Abstract

The classical Hertzian contact model establishes a monotonic correlation between contact force and area. Here, we showed that the interplay between local friction and structural instability can deliberately lead to unconventional contact behavior when a soft elastic shell comes into contact with a flat surface. The deviation from Hertzian contact first arises from bending within the contact area, followed by the second transition induced by buckling, resulting in a notable decrease in the contact area despite increased contact force. Friction delays both transitions and introduces hysteresis during unloading. However, a high amount of friction suppresses both buckling and dissipation. Different contact regimes are discussed in terms of rolling and sliding mechanisms, providing insights for tailoring contact behaviors in soft shells.

Figures (4)

• Figure 1: (a) Bulk hemisphere made of PDMS in contact with a PLA plate. The contact area is circular and grows with normal load with an exponent of 2/3, following Hertzian contact solution (red line in subfig. c). (b) PDMS hemispherical shell in dry contact with a PLA plate (solid blue line in subfig. c.). (c) Presents the variation of contact area ($\bar{A}=2 A/(\pi R^2)$) as a function of normal load ($\bar{F}=F R/(E h^{3})$) for bulk and shell. First, a smooth deviation from Hertzian contact can be observed (inset). As indentation progresses, the contact morphology transitions from circular to annular, causing a sudden drop in the contact area (marked by a double arrow).
• Figure 2: The evolution of (a) normalized force $\bar{F}$, (b) contact area $\bar{A}$, and (c) maximum contact pressure multiplied by $10^3$ for clarity, ($\bar{p} =P_{max}/E$) as a function of indentation ($\bar{d}=d/R$) for different CoF. Black diamond and red triangle symbols in (a) present, respectively, the experimental data under dry and lubricated conditions. Solid lines represent simulation results for $\mu =0$ (blue), $0.48$ (red), $1.0$ (black), and $2.2$ (green). The inset in (a) presents the dissipated energy during unloading $W$, highlighting a parabolic correlation with CoF. The inset in (b) reveals two transitional points, 1) the deviation of force-area relation from the Hertzian solution (the orange dash line) due to bending, and 2) a sudden drop in contact area due to shell buckling.
• Figure 3: (a) In-situ snapshots of shell profile indented by a PLA plate, under dry contact ($\mu=1.0$) at different stages of indentation, corresponding to points $p_0$-$p_5$, marked in Fig. \ref{['fig:Fig1']}a. The profiles obtained from the simulation are superimposed with red solid lines for comparison. (b) and (c) present, respectively, the corresponding contact morphology and the contact pressure distribution ($p(x)/E$), obtained from simulations multiplied by $10^3$ for clarity. Inset numbers in (b) present the total contact area. The evolution of contact area and pressure distribution, as well as the indentation force and shell profile for different CoFs can be seen in supplementary movies SuppInf).
• Figure 4: The evolution of contact size and location in the loading and unloading phases for different CoF. The indentation on the y axes is normalized by the maximum indentation. The contact size represents the radius of a circular contact in the Hertzian regime and the width of an annular contact area in the intermediate and post-buckling regimes. Letters H, I, and B denote Hertzian, intermediate, and post-buckling regimes respectively. Red dash lines mark the transition point between the Hertzian and intermediate regimes. The shaded areas highlight the elastic unloading at the onset of unloading for cases of $\mu = 0.48$ and $1.0$.