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

International Journal of Engineering Science 104 (2016) 20–33 Contents lists available at ScienceDirect International Journal of Engineering Science journal homepage: /locate/ijengsci A simple method for solving adhesive and non-adhesive axisymmetric contact problems of elastically graded materials Markus He?? Institute of Mechanics, Technical University of Berlin, Berlin, 10623, Germany article info Article history: Received 14 March 2016 Revised 6 April 2016 Accepted 13 April 2016 Available online 22 April 2016 Keywords: Functionally graded materials Power-law graded half-space Normal contact with adhesion Winkler foundation Method of dimensionality reduction JKR-theory abstract An e?cient 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 pro?les 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 de?ned 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 pro?le, which is proved. All the necessary mapping rules are derived and their ease of use explained by a recent example. ? 2016 Elsevier Ltd. All rights reserved. 1. Introduction 1.1. Fundamentals of functionally graded materials The technological progress and the demand for increasing the capabilities require the development of high-performance materials. This class includes the functionally graded materials (FGMs), whose application ?eld ranges from biomechanics, tribology and optoe