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.

Keywords

• axial symmetry
• elastic layers
• method of dimensionality reduction
• cartilage layer
• viscoelastic layer
• adhesion