Asymptotic Analysis of the Eversion of Nonlinearly Elastic Shells

In this paper we study the eversion of axisymmetric, strictly convex, nonlinearly elastic shells within a general, geometrically exact theory in which the shell can suffer flexure, extension, and shear. Each such theory is endowed with a thickness parameter ε². For such shells with free or with fixed hinged edges, we give conditions on ε and the data ensuring that there is an everted state under zero applied load, we show how to approximate it effectively with an asymptotic series in ε whose error we can estimate, we determine the qualitative properties of the everted state, paying particular attention to the formation of a lip near the edge, and we give specific formulas for the shape, the strains, and the stress resultants. This revised version was published online in August 2006 with corrections to the Cover Date.