Effect of Surface Roughness on Adhesive Instabilities for the Elastic Layer

If an incompressible elastic layer bonded to a rigid plane is placed close to a second rigid plane, adhesive interactions between the surfaces can cause elastic instabilities. These lead to spatially non-uniform traction and gap distributions which exhibit a regular pattern with a characteristic wavenumber. However, real surfaces are never completely plane. In this paper, we consider the influence of surface roughness on the instability, with particular reference to the force-displacement relation. With random roughness profiles, the traction distributions are always spatially irregular, so the onset of instability is more difficult to define. One approach is to monitor the amplitude of the power spectrum of the distribution near the characteristic wavenumber. Since surface roughness generally reduces the mean adhesive traction, we might expect it to exert a stabilizing effect. Numerical results confirm this for moderate to large RMS amplitudes, but show that low RMS roughness can actually trigger the instability in ranges where the uniform layer would be stable. The resulting traction-displacement relation is then found to be approximately linear with a slope close to that at the point where the uniform solution loses stability.