Determination of wrinkling criteria for an incompressible polymer membrane by non-linear elastic finite element method

Abstract

A wrinkling criterion for non-linear elastic membrane materials such as thin polymer, fabric or rubber structures has been determined by employing finite element analysis as an alternative to the difficult experimental counterpart. The hyperelastic constitutive equation proposed by Ogden was implemented into the commercial finite element program ABAQUS with user material subroutine VUMAT. The relation between strain energy and the principal values of the stretch tensor was obtained in order to trace the wrinkle/non-wrinkle boundaries. It was shown that the wrinkling of an elastic membrane can be regarded as being initiated at the instance of abrupt slope change of the strain energy-stretch curve, which was verified by comparing the criterion obtained by finite element analysis with the existing analytical solution.