The extension of the method of dimensionality reduction to layered elastic media

The method of dimensionality reduction (MDR) has been extended to the axisymmetric unilateral contact problem for a layered elastic medium so that the case of continuously inhomogeneous elastic foundation is covered as well. The corresponding MDR formalism has been developed for a circular contact area. Both the non‐adhesive contact and the JKR‐type adhesive contact are considered. The developed theory is verified by means of two special cases, and new results, in particular, have been derived for the case of a functionally graded solid with an exponential law of inhomogeneity. The method of dimensionality reduction (MDR) has been extended to the axisymmetric unilateral contact problem for a layered elastic medium so that the case of continuously inhomogeneous elastic foundation is covered as well. The corresponding MDR formalism has been developed for a circular contact area. Both the non‐adhesive contact and the JKR‐type adhesive contact are considered. The developed theory is verified by means of two special cases, and new results, in particular, have been derived for the case of a functionally graded solid with an exponential law of inhomogeneity.