An improved relation for the effective elastic compliance of a film/substrate system during indentation by a flat cylindrical punch

Measurement of the mechanical properties of thin films on substrates by load and depth sensing indentation methods such as nanoindentation often requires accurate descriptions for the effective elastic compliance of the film/substrate system. Here, a simple modification of the commonly used solution derived by Gao et al. [H. Gao, C.H. Chiu, J. Lee, Int. J. Solids Struct. (1992) 2471] is presented, that significantly improves its accuracy and range of applicability, as demonstrated by comparison with finite element simulations.