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

摘要

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