Normal configurations and the nonlinear elastostatic problems of bending, torsion, expansion, and eversion for compressible bodies

Abstract

First, we decompose a (deformed) equilibrium configuration into a disjoint union of a one-parameter family of surfaces, called lamina surfaces. We require that all of these lamina surfaces be two-dimensional universal solutions for homogeneous isotropic elastic membranes. Then the two tangential equations of equilibrium are satisfied without any body force, universally for all isotropic elastic (membrane) materials