For the structure of a neo-Hookean surface layer bonded to a neo-Hookean half-space which is subjected to a uniaxial compression, a linear stability analysis shows that the bonded structure is less stable than the half-space if r < 1 and more stable if r > 1, where r is the ratio of the shear modulus of the half-space to that of the layer. When the layer is stiffer than the half-space (r < 1), there exists a critical buckling mode number corresponding to a minimum (critical) compression. In this paper we derive the evolution equation for a single near-critical mode. The coefficient of the cubic nonlinear term in the evolution equation determines whether the bonded structure is sensitive to imperfections and its dependence on r is calculated. it is found that the bonded structure is sensitive to imperfections if 0.575 < r < 1. Some asymptotic results valid in the thin-layer limit are derived and comparisons are made with the classical model for plates on elastic foundations. Participation of sideband modes in the buckling process makes it possible to have localized buckling solutions, but we show that localized buckling solutions are unstable to localized perturbations in the present context.
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