Elastic contact problems of layered solids

The objective of this study is to develop a methodology for the frictional contact problems of layered solid based on displacement formulation. Displacement formulation is a simple and straight approach for displacement or mixed boundary value problems, such as solids under contact. First, the problem is formulated with a semi-infinite homogenous solid and solved using Fourier integral method. Solutions for complete and incomplete contacts and indentation by a wedge are provided. The method developed is then applied to the solids coated with layers. Stresses and displacements in a layered solid with boundary tractions are solved. Calculated results are obtained for the cases of boundary line-load and strip-load in normal and tangential directions. The effects of the thickness of films, the elastic modulus ratios between film and substrate and the ratio of contact width to film thickness are investigated. The plane strain problem is also extended to the analysis of multi-layered composites. Stresses at the film and substrate interface have been examined for boundary traction problems. Boundary traction contact on an axi-symmetric layered solid is another extension for the application of displacement formulation. Problems are solved using Hankel transform method. Stresses in film and substrate are calculated for normal and shear boundary tractions.; Based on the displacement formulation, indentation problem involving mixed boundary conditions is formulated. Solutions of contact normal pressure for frictionless contact are first obtained. Solutions of Fourier series and Chebychev polynomial are evaluated. Cases involving indentations by a cylinder and flat-ended stamp are examined. In a frictional contact, both stick and slip zones exist between two contacting bodies. It leads to changes in frictional stresses at the contact interface. A theoretical solution for the frictional contact on a layered solid involving stick-slip zones is obtained using Chebychev polynomial. Contact forces and stresses in the film-substrate field are calculated.