  We present a molecular dynamics study of the contact between a rigid solid
with a randomly rough surface and an elastic block with a flat surface. The
numerical calculations mainly focus on 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 numerical results have been
compared with analytical theory and experimental results. They are in good
agreement with each other. The present findings 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.
