On Adhesive Theories in Multilayered Interfaces, With Particular Regard to "Surface Force Apparatus" Geometry

Abstract

Adhesion is a key factor in many tribological processes, especially wear. We generalize a recent formulation for the indentation of a multilayered material using an efficient integral transform method, to the case of adhesion, using a simple energetic transformation in the JKR regime. Then, we specialize the study for the geometry of the Surface Force Apparatus, which consists of two thin layers on a substrate, where the intermediate layer is softer than the other two. We find the pull-off force under "force control" (i.e. for "soft" loading systems), as well as under "displacement control" (i.e. for "rigid" systems), as a function of the geometrical thicknesses and material properties ratios, and the method is fully implemented in a fast Mathematica code, available to the public (see Appendix).

Accurate and Efficient Explicit Approximations of the Colebrook Flow Friction Equation Based on the Wright ω-Function: Reply to the Discussion by Majid Niazkar

“…For Equation (3) of [1], the maximal relative error was reduced by 50%, and for Equation ( 5) of [1] by 42%, while for Equation ( 6) of [1] is improved only by 3% as the original model was close to the optimum. We used the local "fminsearch" nonlinear solver, and then the global optimization procedure "globalsearch", both built-in Matlab optimization tools [15]. We reduced also the number of required digits for optimized constants by numerical experiments, in order to provide simple, but still accurate flow friction approximations.…”