The main objective of this thesis is to obtain a better understanding of adhesive contacts and their frictional behaviour. Both natural and man-made surfaces are rough over a wide range of length scales. Tribological studies of rough surfaces need to account for the interactions between these asperities. In this work a sim- ple atomistically–inspired macro-scale model is developed to study smooth and rough contacts between elastically deformable bodies where adhesion and fric- tion are simultaneously active at the interface. A full description of the model is presented in Chapter 2. There, the Green’s function molecular dynamics (GFMD) technique is extended to explicitly de- scribe the two solids in contact and their mixed-mode interface interactions. The interactions between surfaces are described through a coupled cohesive-zone model implemented in the GFMD technique. The extended GFMD technique includes an incremental iterative scheme, which is necessary to capture the con- tact area evolution when tangential tractions develop at the interface between the solids under loading.

Various contact mechanics theories have been developed in recent years. The most popular are the statistical asperity theories of the type of Greenwood and Williamson and Persson’s theory, which treats self affine rough surfaces. The latter theory includes roughness at all length scales as well as long range elastic interactions. However, it is exact only at full contact conditions, which are often met by rubbers but not by metals. With metals in mind, we here use Green’s function molecular dynamics (GFMD) simulations to assess the validity of Persson’s theory at small loads, therefore small contact areas. GFMD is a boundary-value method which allows for ultra fine discretization of rough surfaces since it is computationally very efficient, and treats interfacial contact using interatomic potentials. To date, the GFMD method was only used in 3-D for modelling the normal loading of rough elastic semi-infinite incompressible (Poisson's ratio = 0.5) solids. In this work we extend GFMD in order to model both normal and tangential loading of rough solids with finite height and generic elastic properties. GFMD is then used to numerically calculate the proportionality constant κ between the area of real contact ar and nominal pressure p for the contact between a compressible linear elastic solid and a rough rigid punch. The numerically calculated value of the proportionality constant k is then extrapolated to the thermodynamic, fractal and continuum (TFC) limit. Results are then compared with that of the other analytical models.