Elastic relationships in layered composite media with approximation for the case of thin films on a thick substrate

A general theory is presented for the elastic interactions in a composite plate of layers with different relaxed planar dimensions. Solutions are obtained for the case of equivalent elastic properties and for the case of different elastic properties among the layers. Approximations for the case of thin films on a substrate lead to the governing equations for stresses in multilayered thin-film systems. Finally, the experimental determination of the planar substrate strain, which is first order in the film/substrate thickness ratio, is presented as a rigorous test of the correctness of the theory.