A Simple Semi-Analytical Method for Solving Axisymmetric Contact Problems Involving Bonded and Unbonded Layers of Arbitrary Thickness

Abstract

In the present work, a recently extended version of the method of dimensionality reduction (MDR) for layered elastic media is applied for the first time using a semi-analytical approach. It is based on a priori knowledge of the cylindrical flat punch solution which is determined numerically using the boundary element method (BEM). We consider arbitrary indenters of revolution producing a circular area of contact with bonded and unbonded layers of arbitrary thickness. The proposed method reduces the contact solution to the numerically efficient evaluation of simple one-dimensional integrals. We further show that the solution of JKR-adhesive contacts with layers and contacts with linear-viscoelastic layers is straightforward using the well-known MDR formalisms. A specific focus has been devoted to study the thickness effect in different application examples. Comparisons with the literature and finite element simulations show very good agreement with the proposed method.