Molecular Dynamics Study of Contact Mechanics: Contact Area and Interfacial Separation from Small to Full Contact

We report a molecular dynamics study of the contact between a rigid solid with a randomly rough surface and an elastic block with a flat surface. We study the contact area and the interfacial separation from small contact (low load) to full contact (high load). For small load the contact area varies linearly with the load and the interfacial separation depends logarithmically on the load. For high load the contact area approaches the nominal contact area (i.e., complete contact), and the interfacial separation approaches zero. The present results may be very important for soft solids, e.g., rubber, or for very smooth surfaces, where complete contact can be reached at moderate high loads without plastic deformation of the solids.

Figure 1

The pressure distribution for $\zeta =4$ for three different nominal pressure, (a) $p/E^{*}\approx 0.013$, (b) $p/E^{*}\approx 0.113$, (c) $p/E^{*}\approx 0.218$. The pressure probability distribution becomes broader with increasing the squeezing pressure. Properly choosing the correction factor (see Fig. 2) makes the numerical results in good agreement with Persson’s contact mechanics theory.

Figure 2

(a) Correction factor $r$ as a function of the contact area ratio $A/A_0$. The points are simulation results, which have been fitted by the function $f(x)=a+b{x}^2+c{x}^3+d{x}^4$ under the condition $d=1-a-b-c$ (solid line). The corresponding coefficients $a$, $b$, $c$ are 0.51, 2.5, $-3.3$, respectively. (b) The contact area ratio $A/A_0$ as a function of squeezing pressure normalized by effective elastic modulus.

Figure 3

An elastic block squeezed against a rigid rough substrate. The natural logarithm of the normalized average pressure $\log (p/E^{*})$, as a function of normalized interfacial separation $\overline{u}/h_{\mathrm{rms}}$ on different magnifications $\zeta =4$ and $\zeta =216$.

Figure 4

The relation between the natural logarithm of the squeezing pressure $p$ (normalized by $E^{*}$) and the interfacial separation $\overline{u}$ (normalized by the root-mean-square roughness amplitude $h_{\mathrm{rms}}$) for an elastic solid squeezed against a rigid surface. The theory curve (solid line) has been calculated using the theory presented in Ref. 18 with $\gamma =0.42$.

Figure 5

Probability distribution of interfacial separation under different pressure (a) $p/E^{*}\approx 0.002$, (b) $p/E^{*}\approx 0.013$, (c) $p/E^{*}\approx 0.113$, at low and high magnifications, respectively. For low pressure, the interfacial separation probability distribution on low and high magnification is similar for $u>5\AA$. This result is expected since mainly the long-wavelength, large amplitude roughness will determine the separation between the surfaces when the separation is large.