A two-scale model for an array of AFM’s cantilever in the static case

The primary objective of this paper is to present a simplified model for an array of Atomic Force Microscopes (AFMs) operating in static mode. Its derivation is based on the asymptotic theory of thin plates initiated by P. Ciarlet and P. Destuynder and on the two-scale convergence introduced by M. Lenczner which generalizes the theory of G. Nguetseng and G. Allaire. As an example, we investigate in full detail a particular configuration, which leads to a very simple model for the array. Aspects of the theory for this configuration are illustrated through simulation results. Finally the formulation of our theory of two-scale convergence is fully revisited. All the proofs are reformulated in a significantly simpler manner.