  We report on the elastic contact between a spherical lens and a patterned
substrate, composed of an hexagonal lattice of cylindrical pillars. The stress
field and the size of the contact area are obtained by means of numerical
methods (discrete Green's function superposition and iterative bisection-like
methods). For small indentations, a transition from a Hertzian to a
Boussinesq-Cerruti-like behavior is observed when the surface fraction of the
substrate that is covered by pillars is increased. In particular, we present a
master curve defined by two dimensionless parameters, which allows to predict
the stress at the center of contact region in terms of the surface fraction
occupied by pillars. The transition between the limiting contact regimes,
Hertzian and Boussinesq-Cerruti-like, is well described by a rational function.
Additionally, a simple model to describe the Boussines-Cerruti-like contact
between the lens and a single elastic pillar, which takes into account the
pillar geometry and the elastic properties of the two bodies, is presented.
