Numerical deflation of beach balls with various Poisson's ratios: from sphere to bowl's shape

Catherine Quilliet (1)

1 LIPhy - Laboratoire Interdisciplinaire de Physique [Saint Martin d’Hères]

We present a numerical study of the shape taken by a spherical elastic surface when the volume it encloses is decreased. For the range of 2D parameters where such surface may modelize a thin shell of an isotropic elastic material, the mode of deformation that develops a single depression is investigated in detail. It first occurs via buckling from sphere toward an axisymmetric dimple, followed by a second buckling where the depression loses its axisymmetry, by folding along portions of meridians. We could exhibit unifying master curves for the relative volume variation at which first and second buckling occur, and clarify the role of the Poisson's ratio. After the second buckling, the number of folds and inner pressure are investigated, allowing to infer shell features from mere observation and/or knowledge of external constraints.

Mots clés: Buckling; thin shells; colloidal shells; capsules; spherical shells; elastic surfaces; folds; extreme deformations; axisymmetric buckling; polygonal indentation; auxetic materials; elasticity; curvature; in-plane compressibility; stretch modulus; bending modulus; thin plate; gaussian curvature

Domaines: Matière Molle [cond-mat.soft]

Catherine Quilliet. Numerical deflation of beach balls with various Poisson's ratios: from sphere to bowl's shape. 2011. ⟨hal-00641894v4⟩