具有不同泊松比的沙滩球的数值收缩：从球形到碗形
Numerical deflation of beach balls with various Poisson's ratios: from sphere to bowl's shape
摘要：
我们提出了一个数值研究的形状由一个球形弹性表面时，它包围的体积减少。对于2D参数的范围内，这样的表面可以模拟一个薄壳的各向同性弹性材料，变形模式，开发一个单一的凹陷进行了详细研究。它首先通过从球体向轴对称凹坑的屈曲发生，然后通过沿子午线部分折叠而在凹陷失去其轴对称性的地方发生第二次屈曲。我们可以展示出第一次和第二次屈曲发生时相对体积变化的统一主曲线，并阐明泊松比的作用。在第二次屈曲后，研究了折叠次数和内部压力，从而可以仅从观察和/或外部约束的知识来推断壳体特征。
英文摘要：
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.
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