The post-critical analysis of axisymmetric hyper-elastic membranes by the finite element method Original Research Article

An axisymmetric finite element that can model rubber-like hyper-elastic material has been employed to study post-critical response in the inflation of axisymmetric membranes. An extensive parametric study has been performed to investigate the non-linear response of a tube under internal pressure. The issue of combined proportional and non-proportional loading in the context of incremental-iterative solution is discussed. Further, a robust bracketing procedure, useful to compute clustered bifurcation points, is proposed. Finally, the eigen-mode injection method is used to branch into the post-critical paths. Contrary to previous findings, the Newton-Raphson method worked satisfactorily in all the cases tested.