How Thickness Affects the Area–Pressure Relation in Line Contacts

It has been demonstrated that in Hertzian and randomly rough surface contact problems, linearity between relative contact area \(a_{\mathrm{r}}\) and reduced pressure \(p^* \equiv p/(E^*{\bar{g}}_{{\mathrm{c}}})\) holds if the root mean square gradient \({\bar{g}}_{{\mathrm{c}}}\) is evaluated over the actual contact area. In this study, using Green’s function molecular dynamics (GFMD), we show that for (1+1) dimensional contact simulations, the factor \(\kappa =a_{{\mathrm{r}}}/p^*\) cannot remain constant and scales linearly with the reduced thickness \({\tilde{d}} \equiv d/a_{{\mathrm{r}}}\) in the limit of small \({\tilde{d}}\), where d is the thickness of elastic body. This linearity not only exists in contacts with smooth indenter with harmonic height profiles, but also in contacts with randomly rough surfaces. The asymptotic curves for both large and small \({\tilde{d}}\) are presented and validated with numerical simulations based on GFMD.