Wave Buckling of Thin Plates Under Non-uniform In-plane Loading

Abstract

Wave buckling of plates is ubiquitous in nature and our daily lives, such as leaves of plants having rippled edges, wetted paper, and wrinkles in human skin. Here, we combine a theory, finite element simulations, and experiments to analyze the relationship between the non-uniform stress distribution and the shape of wave buckling. First, we develop a theoretical model that predicts the formation of wave buckling based on the strain energy method of Ritz-Galerkin. Then, finite element analyses are conducted to validate theoretical results in good agreement for various in-plane loading conditions. Experiments examine how a thin elastomeric strip undergoes buckling instability when non-uniform stress is induced by swelling due to the diffusion of silicone oil. We measure time-dependent amplitude and wavelength of wave buckling and find good agreement with theoretical results. Finally, we conduct parametric exploration and find that the normalized amplitude and wavelength are governed by the aspect ratio of plates and the ratio of maximum compressive stress to the elastic modulus.