  The deformation problem for a transversely isotropic elastic layer bonded to
a rigid substrate and coated with a very thin elastic layer made of another
transversely isotropic material is considered. The leading-order asymptotic
models (for compressible and incompressible layers) are constructed based on
the simplifying assumptions that the generalized plane stress conditions apply
to the coating layer, and the flexural stiffness of the coating layer is
negligible compared to its tensile stiffness.
