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A new approach to the contact to coated elastic materials is presented. A relatively simple numerical algorithm based on an exact integral formulation of the elastic contact of an axisymmetric indenter to a coated substrate is detailed. It provides contact force and penetration as a function of the contact radius. Computations were carried out for substrate to layer moduli ratios ranging from 10 −2 to 10 2 and various indenter shapes. Computed equivalent moduli showed good agreement with thedoi:10.1557/jmr.2004.19.2.600 fatcat:7ekymzst5re6tdihqjxuanytum