Simulating Thin Sheets: Buckling, Wrinkling, Folding and Growth

7th Brazilian Meeting on Simulational Physics

Vetter, Roman^1 ; Stoop, Norbert^1,2 ; Wittel, Falk K.^1 ; Herrmann, Hans J.^1

Computational Physics for Engineering Materials, IfB, ETH Zurich, Schafmattstrasse 6, CH-8093 Zurich, Switzerland^1

IAS Institute of Applied Simulations, ZHAW Zurich University of Applied Sciences, CH-8820 Wädenswil, Switzerland^2

关键词: Anisotropic growth;    Driving forces;    Kirchhoff Love;    Model use;    Non-linear response;    Rayleigh-ritz;    Subdivision surfaces;    Thin sheet;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/487/1/012012/pdf
DOI  :  10.1088/1742-6596/487/1/012012

来源: IOP

【 摘 要 】

Numerical simulations of thin sheets undergoing large deformations are computationally challenging. Depending on the scenario, they may spontaneously buckle, wrinkle, fold, or crumple. Nature's thin tissues often experience significant anisotropic growth, which can act as the driving force for such instabilities. We use a recently developed finite element model to simulate the rich variety of nonlinear responses of Kirchhoff-Love sheets. The model uses subdivision surface shape functions in order to guarantee convergence of the method, and to allow a finite element description of anisotropically growing sheets in the classical Rayleigh-Ritz formalism. We illustrate the great potential in this approach by simulating the inflation of airbags, the buckling of a stretched cylinder, as well as the formation and scaling of wrinkles at free boundaries of growing sheets. Finally, we compare the folding of spatially confined sheets subject to growth and shrinking confinement to find that the two processes are equivalent.