Efficient Modification Scheme of Stress-Strain Tensor for Wrinkled Membranes

Abstract

A new modification scheme of the stress-strain tensor for wrinkled membranes is presented on the basis of the tension field theory. The scheme is applicable to finite element analysis of partly wrinkled membranes with arbitrary shapes. Derivation of the modification scheme rests on an introduction of the so-called wrinkle strain and a simplification of the virtual work equation of wrinkled membranes. Because all of the modifications required to account for wrinkling are totally confined within the stress-strain relations of membranes, the scheme can be easily implemented with existing finite element codes. Furthermore, the modified stress-strain tensor automatically leads to the consistent tangent stiffness matrix, where changes in both the wrinkling direction and the amount of wrinkliness are taken into account. Three numerical examples are treated to show the accuracy and effectiveness of the proposed modification scheme.