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Different contact regimes between a spherical lens and a periodicallypatterned substrate are observed, when they are pressed against each other. Topcontact occurs when only the highest substrate sections touch the lens, whereasmixed contact implies that both the highest and the lowest substrate sectionscome into contact with the lens. In this paper, we study how the patterndensity of the substrate, along with its physical properties and those of thelens, determine the transition from top contact to mixed contact. Experimentsand numerical simulations had been performed, as complementary approaches toobtain data, and a theoretical analysis has been developed to gain insight onthe effect of the physical parameters on the contact transition. As a result, aphase diagram is presented, in terms of the load and the contact radius, thatcombines the observations of the three approaches (experimental, numerical, andtheoretical), unveiling the boundaries of three contact regimes: (1)deterministic-driven contact, (2) top contact, and (3) mixed contact.

physical review. e

Effect of the density of pillar-patterned substrates on the contact  mechanics: Transition from top to mixed contact with a detailed  pressure-field description