The primary bilayer ruga-phase diagram I: Localizations in ruga evolution

It has been observed that coexistence of multiple ruga (wrinkle, crease, fold or ridge) phases hinders advancement of nano and soft materials technology to control and manufacture uniform ruga phases in bilayer material systems. In this paper, we construct the primary bilayer (PB) ruga-phase diagram which can guide manipulation of various ruga configurations in bilayer systems. The PB ruga-phase diagram is a generic phase diagram of a bilayer system composed of a thin film on a half-space substrate, both of which are represented as incompressible neo-Hookean solids. On the PB ruga-phase diagram, various phase boundaries represent bifurcation sites of ruga structures caused by lateral compression of the bilayer. We have identified eleven different ruga phases and five triple points of ruga phases on the PB ruga-phase diagram. All the ruga phases eventually evolve to a limit phase of either global crease or global fold localization, depending on the stiffness ratio of the bilayer, when compressed up to the Biot critical strain of 0.456. Another global localization-ridge localization which is principally caused by large substrate pre-stretch (or mismatch strain)-is treated in a sequel paper.