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Simulating Thin Sheets: Buckling, Wrinkling, Folding and Growth

机译:模拟薄板:屈曲,皱纹,折叠和生长

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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.
机译:经历大变形的薄板的数值模拟是计算的。在场景上,它们可能自发地扣,皱纹,折叠或皱纹。脾脏的薄膜经常会遇到显着的极大的极性生长,这可以充当这种稳定性的驱动力。我们使用最近开发的有限元模型来模拟Kirchhoff-Love床单的丰富各种非线性响应。该模型使用细分表面形状功能以保证该方法的收敛,并且允许在经典的Rayleigh-Ritz形式主义中允许各向异性生长片的有限元描述。我们通过模拟安全气囊的充气来说明这种方法的巨大潜力,拉伸圆筒的屈曲,以及在生长片材的自由边界处形成和缩放。最后,我们将空间限制片材的折叠进行比较,该薄片受到生长并缩小限制,以发现两个过程是等同的。

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