Abstract.
We consider the problem of everting spherical shells of incompressible, isotropic hyperelastic material. Firstly, we show that there exists a unique spherically symmetric everted solution for all shell thicknesses provided only that the material satisfies the Baker--Ericksen inequalities. We also give a sufficient condition, satisfied by many materials, which ensures that the shell contains a cavity on eversion. Secondly we look at the bifurcation problem. We find that thicker shells will undergo a bifurcation on eversion and so we would only expect to see spherically symmetric solutions for thinner shells.
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Received: April 28, 1998; revised: June 18, 1998
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Haughton, D., Chen, YC. On the eversion of incompressible elastic spherical shells. Z. angew. Math. Phys. 50, 312–326 (1999). https://doi.org/10.1007/s000330050153
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DOI: https://doi.org/10.1007/s000330050153