Instabilities of soft films on compliant substrates

Instabilities in bilayered systems can generate a wide variety of patterns ranging from simple folds, wrinkles, and creases to complex checkerboards, hexagons, and herringbones. Physics-based theories traditionally model these systems as a thin film on a thick substrate under confined compression and assume that the film is orders of magnitude stiffer than the substrate. However, instability phenomena in soft films on soft substrates remain insufficiently understood. Here we show that soft bilayered systems are highly sensitive to the stiffness ratio, boundary conditions, and mode of compression. In a systematic analysis over a wide range of stiffness ratios, from 0.1<β<1000, for eight different compression modes including whole-domain compression, substrate prestretch, and film growth, we observe significantly different instability characteristics in the low-stiffness-contrast regime, for β<10. While systems with inverse stiffness ratios under whole-domain compression are unstable for a wide range of wrinkling modes, under film-only compression, the same systems display distinct wrinkling modes.Strikingly, these discrepancies disappear when using measures of effective strain, effective stiffness, and effective wavelength. Our study suggests that future instability studies should use these effective measures to standardize their findings. Our results have important applications in soft matter and living matter physics, where stiffness contrasts are low and small environmental changes can have large effects on morphogenesis, pattern tabselection, and the evolution of shape.