Varga Spherical Shell Flip Deformation Wkb Analysis

It is well-known that a spherical shell may not stay spherical after eversion and it may prefer to adopt a wrinkled configuration. In the paper, WKB method is introduced through a model problem whose algebraic equation about the leading order has repeated-roots. With the use of elastic mechanics, the incremental equations of an everted Varga spherical shell are deduced. Then, we apply WKB method to the analysis of the buckling of an everted Varga spherical shell of incompressible, isotropic hyperelastic material. Firstly, we obtained a simple asymptotic expression for the critical ratio of the inner radius to the outer radius, with the mode number used a large parameter. Excellent agreement between the asymptotic and numerical results is found over almost the whole mode-number regime. Secondly, we also show, for A-B = 0(m-1/2), no non-zero solution can be obtained.