Publisher's Note: Loading-unloading hysteresis loop of randomly rough adhesive contacts [Phys. Rev. E 92, 062404 (2015)]

Figure 6

The true contact area $A/A_0$ as a function of the dimensionless quantity $m_2^{-1/2}\tilde{\sigma }$ for two different Hurst exponents $H=0.8(m_2=2.7\times {10}^{-3}), H=0.9(m_2=1.5\times {10}^{-3})$, and for three different values of energy of adhesion, $\gamma =0.01\mathrm{J}/{\mathrm{m}}^2$ (black curves), $\gamma =0.04\mathrm{J}/{\mathrm{m}}^2$ (blue curves), and $\gamma =0.07\mathrm{J}/{\mathrm{m}}^2$ (red curves). As predicted by the theories, there is a marginal influence of the fractal dimension on the true contact area at small loads under loading conditions. The influence of $D_f$ becomes important during unloading. This leads to the formation of a hysteresis loading-unloading loop, which is strongly affected by the adhesion energy $\gamma$.

Figure 7

The dimensionless load $\tilde{\sigma }=2\sigma /\left(E^{*}{q}_0{h}_{\max }\right)$ (a) and the quantity $A/A_0$ (b) as a function of the nondimensional penetration $\tilde{\mathrm{\Delta }}$, for two different Hurst exponents $H=0.8(m_2=2.7\times {10}^{-3}), H=0.9(m_2=1.5\times {10}^{-3})$, and for three different values of energy of adhesion, $\gamma =0.01\mathrm{J}/{\mathrm{m}}^2$ (black curves), $\gamma =0.04\mathrm{J}/{\mathrm{m}}^2$ (blue curves), and $\gamma =0.07\mathrm{J}/{\mathrm{m}}^2$ (red curves).