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We report on the elastic contact between a spherical lens and a patternedsubstrate, composed of an hexagonal lattice of cylindrical pillars. The stressfield and the size of the contact area are obtained by means of numericalmethods (discrete Green's function superposition and iterative bisection-likemethods). For small indentations, a transition from a Hertzian to aBoussinesq-Cerruti-like behavior is observed when the surface fraction of thesubstrate that is covered by pillars is increased. In particular, we present amaster curve defined by two dimensionless parameters, which allows to predictthe stress at the center of contact region in terms of the surface fractionoccupied 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 contactbetween the lens and a single elastic pillar, which takes into account thepillar geometry and the elastic properties of the two bodies, is presented.

Stress concentration in periodically rough hertzian contact: Hertz to soft-flat-punch transition