Surface pressure reduces stability in bilayered systems under compression

摘要

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(f)/mu(s) greater than or similar to 10, the instability of the system does not depend on pressure.