Finite Element Analysis of Wrinkling Membranes

A new iterative scheme is proposed for finite element analysis of wrinkling or tension structures. The scheme is based upon the observation that there exists an invariant relationship, due to the uniaxial tensile stress state of wrinkling, between some of the strain components referred to the local frame aligned with wrinkling in a region where wrinkling occurs. This enables us to update the stress state and the internal forces correctly taking into account the existence of wrinkling. The finite element implementation of the scheme is straightforward and simple, and only minor modifications of the existing total Lagrangian finite element codes for membranes are needed. The validity of the scheme is demonstrated via numerical examples for the torsion of a membrane and the quasi-static inflation of an automotive airbag, both made of isotropic or anisotropic elastic membranes. The examples suggest that the present iterative scheme has a good convergence characteristic even for a large loading step.