The Wrinkling of Thin, Flat, Rectangular Webs

A web is termed wrinkled when one of the in-plane principal stresses is tensile and the other is sufficiently compressive. A criterion is derived that predicts wrinkling of isotropic, compressible rectangular webs under uniform in-plane principal stresses. The compressive stress at impending wrinkling depends on the flexural stiffness, and it equals zero in the case of a membrane. A criterion of wrinkling is also derived using isotropic, incompressible membrane theory. This criterion predicts an infinite number of wrinkle waves in a wrinkled region. With small flexural stiffness, the number of wrinkle waves becomes finite at wrinkling and it is predictable along with the shape and the size of the wrinkled region. The number of the wrinkle waves increases as the aspect ratio of the rectangular web increases, as the in-plane principal tension increases, and as the flexural stiffness decreases. Analyses of wrinkling of a rectangular web under simple shear and under uniform longitudinal stretching illustrate the above predictions.