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Recent work demonstrates that finite-deformation nonlinear elasticity isessential in the accurate modeling of wrinkling in highly stretched thin films.Geometrically exact models predict an isola-center bifurcation, indicating thatfor a bounded interval of aspect ratios only, stable wrinkles appear and thendisappear as the macroscopic strain is increased. This phenomenon has beenverified in experiments. In addition, recent experiments revealed the followingstriking phenomenon: For certain aspect ratios for which no wrinkling occurredupon the first loading, wrinkles appeared during the first unloading and againduring all subsequent cyclic loading. Our goal here is to present a simplepseudo-elastic model, capturing the stress softening and residual strainobserved in the experiments, that accurately predicts wrinkling behavior on thefirst loading that differs from that under subsequent cyclic loading. Inparticular for specific aspect ratios, the model correctly predicts thescenario of no wrinkling during first loading with wrinkling occurring duringunloading and for all subsequent cyclic loading.

The Mullins effect in the wrinkling behavior of highly stretched thin films