Qualitative analysis for solutions of a class of nonlinear ordinary differential equations
The boundary value problem (BVP) for a class of nonlinear ordinary differential equations is examined. It can be used to describe the eversion problem for a spherical shell composed of a class of transversely isotropic incompressible Mooney-Rivlin materials. The solutions of the nonlinear equation describing the relation among deformed thickness, initial thickness and material parameters of the spherical shell are obtained. The effects of structure parameter and material parameters on the thickness of the everted spherical shell are discussed by numerical examples.
On the eversion of incompressible elastic spherical shells
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.

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(λ1,λ2,λ3) =φ(λ1)+φ(λ2)+φ (λ3), 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.