Unraveling rugae in compressed fiber-reinforced bilayers - New scaling laws for wrinkling, symmetry breaking, and beyond

Wrinkling is a bifurcation phenomenon frequently observed in natural and engineered systems, where mismatches in physical properties of the components produce wavy patterns on the system's surface. This often occurs in bilayers, where a thin film adheres to a compliant substrate. Although wrinkling in isotropic bilayers is captured by established scaling laws at high substrate-to-film elastic mismatches, comparable formulations for anisotropic bilayers remain undeveloped. The thesis addresses this gap by analyzing wrinkling of plane-strain, hyperelastic, fiber-reinforced bilayers under lateral contraction. In this work, an appropriate analytical framework is developed, yielding asymptotic expansions for the onset of wrinkling, applicable across the full range of elastic mismatches. Here, we model the film as an elastic extensible plate with bending rigidity, and we account for the presence of two families of fibers in the substrate through available averaged hyperelastic laws for such composites. The latter accounts for concentration-mediated fiber stiffness, orientation, and dispersion. The analysis reveals two distinct wrinkling regimes, primarily governed by the elastic stiffness ratio between the film and the matrix, namely the mismatch between the two. Each regime is characterized by a distinct set of scaling laws for both the critical strain and the wavenumber at the wrinkling onset. When the film controls the bifurcation across a wide range of mismatches, from very high to moderately low, this is referred to as the "direct" regime. On the other hand, for lower mismatches, the influence of the substrate turns out to mediate this phenomenon. In the sequel, this is labeled as the “dual” regime. The threshold characterizing the transition between the behaviors described above is analytically determined and indicates which of the asymptotic expressions for the wrinkling features must be applied. Asymptotic expansions for isotropic bilayers are also recovered as special cases. Altogether, this study provides a comprehensive framework that captures corrugation in fiber-reinforced bilayers across all elastic mismatches, paving the way for understanding similar bifurcation phenomena in anisotropic media.