A family of herringbone patterns in thin films

Upon cooling, a thin metal film deposited on compliant elastomer substrate undergoes equi-biaxial compression and begins to buckle at a critical stress. As further cooling occurs, a highly ordered herringbone pattern self-assembles. The preference for the herringbone pattern over other potential modes is demonstrated based on minimum energy arguments. Control of the pre-buckling in-plane stress components may be one way to influence the pattern formation, possibly giving rise to a family of unbalanced herringbone modes that links one-dimensional modes with the balanced herringbone mode.