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Non-axisymmetric deformations of a soft spherical shell with inward and outward concentrated load at its apex

From:

Cheng Zhang, Yu-Kun Hao, Bo Li, Xi-Qiao Feng and Huajian Gao, “Wrinkling patterns in soft shells”, Soft Matter, Vol. 14, 1681, 2018, DOI: 10.1039/c7sm02261a

ABSTRACT: Curvature plays an important role in the morphological evolution of soft shells under stretch. Here, through a combination of experiment, theory and simulation, we investigate the behavior of a hemispherical soft shell subject to an increasing outward point force at its pole. In contrast to an inward point force inducing a polygonal pattern of buckling in the shell, we observe a four-stage morphological transition and symmetry breaking under an increasing outward point force. The shell undergoes axisymmetric deformation around its pole and then buckles into a non-axisymmetric shape with a number of shallow wrinkles emanating from the pole, followed by the emergence of crater-like deep crumples and ultimately a transformation into a wrinkled pseudocone. Our theoretical analysis and numerical simulations yield the critical conditions for the morphological transitions at each stage of deformation and reveal the underlying interplays between elastic bending and stretching energies and the curvature of the shell.

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