An Application of the Mossakovskii-Jäger Procedure for Solving Plane Strain Adhesive Contact Problems of Power-Law Graded Elastic Solids

Due to the growing demands on performance in mechanical engineering, an increased number of components are being manufactured from functionally graded materials. The prediction of their contact mechanical behavior usually requires complex numerical investigations, involving the finite element method or semi-analytical methods in combination with Fast Fourier Transformation. In the present work, we develop integral equations for solving plane strain contact problems between power-law graded elastic solids based on an incremental procedure introduced by Mossakovskii and revitalized by Jäger. The deduced formulae are very easy to handle and avoid the complicated solution of common singular integral equations. In this way, closed-form analytical solutions are obtained, which can serve as a qualitative estimation of the contact mechanical behavior of real functionally graded materials. Furthermore, we extend the formulae for solving contact problems with adhesion under both normal and tangential loading. The application of the novel method is exemplified by means of the plane strain adhesive contact between a rigid cylinder and a power-law graded half-space. The corresponding closed-form analytical solutions coincide with the results previously obtained only numerically by other authors.