Graded materials or functionally graded materials (FGMs) are multiphase composites with continuously varying volume fractions and, consequently, thermo- mechanical properties. The concept of grading the thermo-mechanical properties of materials provides an important tool to design new materials for certain specific functions. To take full advantage of this new tool research is needed not only for developing efficient processing methods and material characterization techniques but also for carrying out basic mechanics studies to the safety and durability of the FGM components. The analytical procedure is based on obtaining the Green's functions of the half space problem in order to derive the integral equations of the contact problem. This book provides the solution of these integral equations to obtain a series of analytical benchmark solutions of the contact mechanics problems including critical contact stresses at the surface of the graded coating that may have a bearing on the fatigue and fracture of the components with FGM coatings.

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