A simple method for solving adhesive and non-adhesive axisymmetric contact problems of elastically graded materials

An efficient method is presented for solving axisymmetric, frictionless contact problems between a rigid punch and an elastically non-homogeneous, power-law graded half-space. Provided that the contact area is simply-connected profiles of arbitrary shape can be considered. Moreover, adhesion in the framework of the generalized JKR-theory can be taken into account. All results agree exactly with those given by three-dimensional contact theories. The method uses the fact that three-dimensional contact problems can be mapped to one-dimensional ones with a properly defined Winkler foundation; hence, the method is to be understood as an extension of the method of dimensionality reduction (MDR). A prerequisite of its applicability forms the generality of contact stiffness regardless of the geometry of the axisymmetric profile, which is proved. All the necessary mapping rules are derived and their ease of use explained by a recent example.