Stress anisotropy regulated wrinkling pattern evolution on a core-shell soft cylinder

Diverse wrinkling patterns can occur on curved bilayer systems under differential growth or expansion. In such systems, stress anisotropy is frequently encountered, and the coupling effect of curvature and stress anisotropy on the pattern evolution remains largely unexplored. In this study, we investigate the evolution of wrinkling patterns on a cylinder core-shell system with stress anisotropy leveraging both theoretical analysis and finite element simulations. Critical buckling analysis has identified three distinct critical buckling modes regulated by the stress anisotropy, i.e., axial sinusoidal mode, checkerboard mode, and circumferential sinusoidal mode. Our finite element simulations, along with post-buckling analysis, reveal seven distinct evolutionary paths stemming from the three critical buckling modes. We present phase diagrams for both the critical buckling modes and their evolutionary paths, which are determined by dimensionless curvature and stress anisotropy. Our results not only expand the theoretical research on surface wrinkling of a core-shell soft cylinder but also introduce stress anisotropy as a significant parameter for regulating the wrinkling patterns and their evolutionary paths in curved bilayer systems. The revelation of a multitude of wrinkling patterns and their evolutionary pathways holds great potential for advancing applications that leverage tunable wrinkle surfaces.