Three-dimensional compositional elastic field in cubic anisotropic solid films on compliant substrates

A two-dimensional Laplace transform technique is used to find an analytical solution for the three-dimensional elastic field in solid films attached to a compliant substrate. The stress field arises from the misfit between the film and substrate and also from the non-uniform composition field in the film itself. Both the film and substrate are assumed to have cubic symmetry. The solution method can also be applied to materials with general orthotropic symmetry.