On the surface effects on gravity-driven instability of elastic layers

A widely adopted formulation of the incompressible elastic incremental deformation and the Steigmann–Ogden model of surface elasticity are used to study the effects of surface elasticity and an applied surface pressure on the gravity-driven instability of incompressible elastic layers. An explicit gravity parameter–wavenumber relation is derived to determine the critical condition for the gravity-driven instability, which reduces to the known formula in the absence of the surface elasticity and the applied surface pressure. Detailed results are shown to illustrate the effects of an applied surface pressure and various surface elasticity parameters on the critical value for instability and the associated wavenumber of unstable mode. Our results show that the applied surface pressure has a crucial effect on the critical value for the instability, and the effects of surface elasticity on the critical value of instability heavily depend on the magnitudes of various surface elasticity parameters.