Wrinkling instability of 3D auxetic bilayers in tension

Bilayers, soft substrates coated with stiff films, are commonly found in nature, with examples including skin tissue, vesicles, and organ membranes. They exhibit different types of instabilities when subjected to compression, depending on the contrast in material properties between the two components. In this work, we unravel the mechanisms behind wrinkling instabilities in auxetic bilayer systems under uniaxial tension. We find that a soft bilayer in tension can experience significant lateral contraction, and with sufficient contrast in Poisson ratios, compressive stresses may induce wrinkles aligned with the tensile direction. We analytically model the onset of wrinkles and validate our predictions using Finite Element simulations in ABAQUS. Our findings reveal that wrinkles may occur when the Poisson ratio of the substrate is greater than that of the film. As the two Poisson ratios converge to a common value, the critical stretch for instability shoots up rapidly and the wrinkles disappear. We also confirm these results through asymptotic analysis. Using inverse analysis, we design film microstructures to achieve desired effective Poisson ratios and further validate the effective properties with the Finite Element code FEAP. We show that the critical stretch ratio for buckling in auxetic structures with microstructural patterns is in strong agreement with the homogenized model predictions. The proposed method has significant potential for controlling surface patterns in auxetic skin grafts and hydrogel organ patches under mechanical loads. Moreover, the asymptotic expressions for compressible bilayers developed in this work can also be applied under finite strain for buckling-based metrology.