Theory and finite element formulation of rubberlike membrane shells using principal stretches

A theory of rubberlike membrane shells undergoing large elastic deformations is derived. The stresses are deduced from Ogden's material law, which is formulated in terms of the principal values of the right stretch tensor. Incompressibility is fulfilled exactly using the plane stress constraint. Furthermore, a finite element formulation of the membrane theory is given. The use of the tangential stiffness matrix, derived analytically, provides a quadratically convergent solution process. Several numerical examples show the robustness of the developed finite element.