The Primary Bilayer Ruga-Phase Diagram II: Irreversibility in Ruga Evolution

When an elastic thin-film/substrate bilayer is cyclically compressed with a large plane-strain stroke, various surface morphologies develop either reversibly or irreversibly with cyclic hysteresis. Here, we examine the cyclic morphology evolution with extensive finite-element analyses and present a generic irreversibility map on the primary bilayer Ruga-phase diagram (PB-RPD). The term “PB” refers to a system of a film on a substrate, both of which are incompressible neo-Hookean, while the term “Ruga-phase” refers to the classification of corrugated surface morphologies. Our generic map reveals two configurational irreversibility types of Ruga-phases during a loading and unloading cycle. One, localization irreversibility, is caused by unstable crease localization and the other, modal irreversibility, by unstable mode transitions of wrinkle-Ruga configurations. While the instability of crease localization depends mainly on smoothness of the creasing surface or interface, the instability of Ruga-mode transition is sensitive to film/substrate stiffness ratio, film/substrate strain mismatch (εps), and material viscosity of the bilayer. For small strain mismatches (εps ≲ 0.5), PB Ruga structures are ordered; otherwise, for large strain mismatches, the Ruga structures can evolve to ridge configurations. For evolution of ordered Ruga phases, the configurational irreversibility leads to shake-down or divergence of cyclic hysteresis. Underlying mechanisms of the cyclic hysteresis are found to be the unstable Ruga-phase transitions of mode-period multiplications in the loading cycle, followed by either mode “locking” or primary-period “switching” in the unloading cycle. In addition, we found that the primary-period switching is promoted by the strain mismatch and material viscosity. These results indicate that various Ruga configurations can be excited, and thus, diverse Ruga-phases can coexist, under cyclic loading. Our irreversibility map will be useful in controlling reversibility as well as uniformity of Ruga configurations in many practical applications.