Wrinkling dynamics of thin crystalline sheets and its dependency on topological defects

Abstract

We investigate the wrinkling dynamics of thin crystalline sheets under uniaxial compression using a Surface Phase-Field-Crystal-Helfrich (SPFCH) model, which captures the coupling between crystalline order, out-of-plane deformations, and topological defects. In particular, the model allows us to track and characterize two distinct classes of defects, namely those forming in the underlying hexagonal crystal lattice, such as dislocations and grain boundaries, and defects in the wrinkling patterns, known as wrinklons. By resolving the evolution and interactions of these defects, we investigate how the interplay between in-plane and out-of-plane relaxation mechanisms influences wrinkling onset and the coarsening regime. Our results indicate that crystalline defects do not affect coarsening scaling, but they quantitatively affect the onset of wrinkling and the emerging wrinkling wavelength, promote more irregular wrinkle patterns with a higher density of wrinklons, and modify long-timescale morphological evolution.