Inhomogeneous deformations of a cone of a neo-Hookean solid

摘要

We study the inhomogeneous deformations of a cone due to squeezing or expanding the cone. Reminiscent of solutions to Jefferey-Hamel flows between intersecting planes and the deformation of elastic wedges, we find that depending on the cone angle we can have solutions that correspond to radial filaments being purely stretched or contracted, or solutions in which the displacement does not have the same sense, certain subparts being stretched, while others are contracted.