The Wrinkling of Thin Membranes: Part I—Theory

A method to describe the stress situation in a wrinkled membrane is presented. In this paper it will be shown that a special deformation tensor can be chosen which leads to the correct stress state of a membrane after wrinkling when it is substituted in the constitutive equation. The method can be used for anisotropic membranes in geometrically and physically nonlinear analysis. The case of simple shear and stretching of a membrane is considered to illustrate the potency of the method.