  Bilayers (soft substrates coated with stiff films) are commonly found in
nature with examples including skin tissue, vesicles, or organ membranes. They
exhibit various types of instabilities when subjected to compression, depending
on the contrast in material properties between the two components. We present
wrinkling instabilities for 3D hyperelastic bilayer systems, including auxetics
(materials with negative Poisson's ratio), under uni-axial tension. In tension,
a soft bilayer can experience large lateral contraction, and we find that with
an adequate contrast in the Poisson ratios, compressive stresses may develop
and generate wrinkles aligned with the tensile direction. We rely on an
analytic modelling of the phenomenon, and validate it with a user-defined
Python script with periodic boundary conditions and constitutive relation
implementation in advanced Finite Element simulations. Our findings reveal that
wrinkles are observed 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 of instability shoots up rapidly, and the wrinkling
disappears. We also confirm these results by asymptotic analysis. This
wrinkling analysis has significant potential in controlling surface patterns of
auxetic skin grafts and hydrogel organ patches under mechanical loads.
Moreover, the asymptotic expressions in this work can be used under finite
strain for buckling-based metrology applications.
