Elastic stress driven morphological instabilities in thin films have been studied extensively: see Jesson et al, J. Elect. Mat., 26, 9, pp., 1039-1047 (1997), for example, for a nice micrograph of rippling in Si-Ge system and a schematic of the explanation for the rippling. In the case of multilayer films, it is also well known that there could be  post-growth morphological changes, and the layer geometry as well as the number of layers play a crucial role apart from the elastic constants in these changes; see the studies on a Gadolinia-Silica system by Sahoo et al for example -- Appl. Surf. Sci., 252, pp. 1520-1537 (2005). In addition, there is also experimental evidence to show that in the case of multilayer films, there could be strong interactions between different layers of films:  see the studies on Si/Ge multilayers by B Rahmati et al, Appl. Phys. A, 62, pp. 575-579 (1996), for example.  Finally, Sridhar et al (Acta Mater., 45, 7, pp. 2715-2733 (1997)), using a linear stability analysis, showed that in embedded single and multilayer films, there could be two dominant modes of break-up, namely, symmetric and anti-symmetric.

The linear stability analyses of the type used by Sridhar et al, however, are not ideal for a detailed quantitative study of the effect of elastic interactions and volume fraction; further, such analyses are also not meant for the study of long term evolution and final break-up of thin films. In a paper of ours (Chirranjeevi et al--submitted to Acta Materialia), we study elastic stress driven morphological instabilities and consequent break-up of thin film assemblies using a phase field model.