  We carry out a statistically meaningful study on self-affine rough surfaces
in elastic frictionless non-adhesive contact. We study the evolution of the
true contact area under increasing squeezing pressure. Rough surfaces are
squeezed from zero up to full contact, which enables us to compare the
numerical results both with asperity based models at light pressures and with
Persson's contact model for the entire range of pressures. Through the contact
perimeter we estimate the error bounds inherent to contact area calculation in
discrete problems.
  A large number of roughness realizations enables us to compute reliably the
derivative of the contact area with respect to the pressure. In contrast to
Persson's model and in agreement with asperity based models, we demonstrate
that at light pressures it is a decreasing convex function. The nonlinearity of
the contact area evolution, preserved for the entire range of pressures, is
especially strong close to infinitesimal contact. This fact makes difficult an
accurate investigation of contact at light pressure and prevents the evaluation
of the proportionality coefficient, which is predicted by analytical models. A
good agreement of numerical results with Persson's model is obtained for the
shape of the area-pressure curve especially near full contact. We investigate
the effects of the cutoff wavenumbers in surface spectrum onto the contact area
evolution. Nayak's parameter is one of the central characteristics of
roughness, it also plays an important role in rough contact mechanics, but its
effect is significantly weaker than predicted by asperity based models. We give
a detailed derivation of a new phenomenological contact evolution law; also we
derive formulae that link Nayak's parameter and density of asperities with
Hurst exponent and cutoffs wavenumbers.
