Existence of exact solutions for the eversion of elastic cylinders

The existence of eversion deformations of an elastic cylinder into another right circular cylinder is studied. It is found that such deformations are associated with strain-energy functions of separable form W(lambda(1), lambda(2), lambda(3)) = phi(lambda(1)) + phi(lambda(2)) + phi(lambda 3), and thus can serve as a test for materials of this kind. Under certain constitutive assumptions, there always exists a cylindrical eversion deformation that satisfies exact pointwise traction free boundary conditions over the entire surface of the cylinder. For such solutions the cavity must remain open upon eversion.