Coherency stresses in multilayers

The determination of the elastic state of coherently matched layers is important in a wide range of domains, including epitaxial films on a substrate with different crystal structures, deformation of a lamella welded on a substrate and lamellar crystals. It is shown that the elastic state of coherently matched multilayers depends on two coupled field quantities: the stress (or equivalently the elastic strain) and the curvature. A general method is derived to determine these fields and the contribution of curvature on stress relaxation is emphasized. Detailed applications are given for the case of stress-free dilatation and pure shear.