Discretization error and modelling error in the context of the rapid inflation of hyperelastic membranes

Abstract

The computational modelling of the rapid large inflation of hyperelastic circular sheets modelled as axisymmetric membranes is treated, with the aim of estimating engineering quantities of interest and their errors. Fine (involving inertia terms) and coarse (quasi-static) models of the inflation are considered and, using goal oriented techniques, both modelling and discretization error are estimated. Numerical results involving only discretization errors for the quasi-static problem, and both modelling and discretization errors for the dynamic problem are presented.