Abstract The deformation of a circular sector into a full self-contacting circle can be sustained in all homogeneous, isotropic, incompressible materials by surface tractions alone. In this class of nonlinear elastic materials, this works investigates the controllability of such a peculiar mapping having uniform constant strains and a creasing singularity. By performing a perturbative analysis based on small–on–large incremental methods, we determine the critical conditions for the normal traction load to trigger a morphological transition from the circular ground state to an elliptic shape. Such predictions are given for neo-Hookean, Gent and polynomial material models to illustrate how both geometrical and physical nonlinearities concur to this elastic instability.

中文翻译：

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关于非线性弹性圆扇形中压痕奇异点的可控性

摘要 在所有均质、各向同性、不可压缩材料中，仅通过表面牵引力就可以使扇形变形为完整的自接触圆。在这类非线性弹性材料中，这项工作研究了这种具有均匀恒定应变和压痕奇异性的特殊映射的可控性。通过基于小对大增量方法进行微扰分析，我们确定了正常牵引载荷的临界条件，以触发从圆形基态到椭圆形的形态转变。对新胡克、根特和多项式材料模型给出了这样的预测，以说明几何和物理非线性如何与这种弹性不稳定性相一致。