Some remarks on the two-dimensional contact of dissimilar elastic solids under non-slipping boundary conditions

Abstract

Spence's self-similarity approach is often preferred to an incremental method for solving plane, non-slipping normal contacts of dissimilar elastic solids under progressive loading. The number of plane contact problems solved in this way so far is nevertheless very limited, since explicit expressions especially for the pressure distribution and the tangential tractions within the contact area require the solution of complicated singular integral equations. In contrast, the application of the incremental method leads to much simpler integral equations, which are derived here and applied to solve some new non-slipping contact problems including the one characterized by an initial power-law gap profile function. The incremental method is also capable to determine the so-called interface mismatch eigenstrain. In Spence's method, however, the determination of its magnitude represents a mandatory step within the solution procedure. By means of a comprehensive comparison of both methods this work provides new insights into the solution of non-slipping plane normal contact problems including explicit analytical solutions for the interface mismatch eigenstrain.