Wrinkling of stretched thin sheets: Is restrained Poisson’s effect the sole cause?

It is widely accepted that wrinkling of thin sheets under tension is due to the compressive stresses that emerge in central zone, orthogonally to the direction of applied tension, being caused by the variation of Poisson’s effect from the fixed supports to central zone of the sheet. By means of an analytical approach consisting of displacement fields (designated as “modes”) that kinematically enrich the solution of pre-wrinkling stress field, this paper shows that Poisson’s effect is not the sole cause of wrinkling. Starting from an extensional mode, other modes with physical meaning (associated to Poisson’s effect and warping shear) are consecutively added to the final displacement field. This modal approach unveils that transversal compressive stresses, which trigger the sheet wrinkling, are due not only to restrained Poisson’s effect (known factor) but also due to warping shear deformation. This identification is the main and original contribution of the present work. The reduction of warping shear in stretched sheets (e.g., via the addition of transversal fibers) could possibly avoid wrinkling phenomena of elastic thin sheets and membranes used in aerospace applications, such as inflatable antennas and solar sails. Additionally, the paper presents approximate analytical solutions of pre-wrinkling fields (displacements, strains, stresses) that are deemed useful to derive future fully analytical formulae for the prediction of critical wrinkling loads.