  This work focuses on planar growth-induced instabilities in three-dimensional
bilayer structures, i.e., thick stiff film on a compliant substrate.
Growth-induced instabilities are examined for a different range of fiber
stiffness with a five-field Hu-Washizu type mixed variational formulation. The
quasi-incompressible and quasiinextensible limits of transversely isotropic
materials were considered. A numerical example was solved by implementing the
T2P0F0 element on an automated differential equation solver platform, FEniCS.
It was shown that both the wavelength and critical growth parameter g decrease
by increasing the fiber stiffness for the first instability, which is obtained
along the stiff fiber direction. The effect of the fiber stiffness is minor on
the secondary buckling, which was observed perpendicular to the fiber
direction. For a range of fiber stiffnesses, bifurcation points of
instabilities were also determined by monitoring displacements and energies.
The energy contributions of layerswith different ranges of fiber stiffnesses
were examined. It is concluded that the energy release mechanism at the
initiation of the primary buckling is mainly due to isotropic and anisotropic
contributions of the stiff filmlayer. For high fiber stiffnesses, the effect of
the anisotropic energy on the first buckling becomes more dominant over other
types. However, in the secondary instability, the isotropic energy of the film
layer becomes the dominant one. Numerical outcomes of this study will help to
understand the fiber stiffness effect on the buckling and post-buckling
behavior of bilayer systems.
