Membrane wrinkling revisited from a multi-scale point of view

Abstract

Abstract Background Membrane modeling in the presence of wrinkling is revisited from a multi-scale point of view. In the engineering literature, wrinkling is generally accounted at a macroscopic level by nonlinear constitutive laws without compressive stiffness, but these models ignore the properties of wrinkles, such as their wavelength, their size and spatial distribution. Methods A new multi-scale approach is discussed that belongs to the family of Ginzburg- Landau bifurcation equations. By using the method of Fourier series with variable coefficients, several nonlinear macroscopic models are derived that couple the membrane response with equations governing the evolution of the wrinkles. Results Contrary to previous approaches, these macroscopic models are completely deduced from the “microscopic” shell model without any phenomenological assumptions. Some analytical and numerical solutions are discussed that prove the relevance of the presented modeling. Conclusions A new class of models has been established. It permits to predict the characteristics of the wrinkles and their influence on membrane behavior.