Buckling instabilities of layered materials are an important phenomenon that has been analyzed both analytically and numerically, but generally only in the absence of surface pressure. In this study, we present a linear stability analysis of the wrinkling of an inhomogeneous bilayer made up of dissimilar neo-Hookean elastic materials, under uniaxial compression with pressure applied to the top surface. Using a variational method, we investigate the effects of stiffness ratio and pressure boundary condition on buckling instabilities. In all cases, the addition of surface pressure decreases the stability of the system to some extent. For softer films, the pressure is the dominant influence on the instability of the system. In stiffer films, however, pressure loading and stiffness ratio interact to affect the unstable state of the bilayer system. Our results indicate that for a sufficiently high value of stiffness ratio ${\mu }_{\mathrm{f}}∕{\mu }_{\mathrm{s}}\gtrsim 10$, the instability of the system does not depend on pressure.

层状材料的屈曲不稳定性是一种重要现象，已通过分析和数值分析，但通常仅在没有表面压力的情况下进行。在这项研究中，我们对由不同的新霍克弹性材料制成的不均匀双层的起皱进行线性稳定性分析，在施加顶表面的压力下进行单轴压缩。使用变分方法，我们研究了刚度比和压力边界条件对屈曲不稳定性的影响。在所有情况下，表面压力的增加都会在一定程度上降低系统的稳定性。对于较软的薄膜，压力是影响系统稳定性的主要因素。但是，在较硬的薄膜中，压力负载和刚度比会相互作用，从而影响双层系统的不稳定状态。${\mu }_{\mathrm{F}}∕{\mu }_{\mathrm{s}}\gtrsim 10$，系统的不稳定性不取决于压力。