Research Article Transient Analysis of a Functionally Graded Ceramic/Metal Layer considering Lord-Shulman Theory Antonios M. Nikolarakis and Efstathios E. Theotokoglou Department of Mechanics, Laboratory of Testing and Materials, School of Applied Mathematical and Physical Science, National Technical University of Athens, Zografou Campus, 15773 Athens, Greece Correspondence should be addressed to Efstathios E. Teotokoglou; stathis@central.ntua.gr Received 27 October 2017; Revised 25 February 2018; Accepted 26 March 2018; Published 28 May 2018 Academic Editor: Michael Vynnycky Copyright © 2018 Antonios M. Nikolarakis and Efstathios E. Teotokoglou. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Te transient displacement, temperature, and stress felds in a functionally graded ceramic/metal layer under uniform thermal shock conditions at the upper surface are numerically studied based on the Lord-Shulman model, employing a direct fnite element method. Te Newmark method is employed for the time integration of the problem. A Matlab fnite element code is developed for the numerical analysis of the one-dimensional problem under consideration. Te Voigt model (rule of mixture) is used for the estimation of the efective properties inside the functionally graded layer and the variation of the volume fraction of the materials follows the sigmoid function in terms of the introduced parameter . Furthermore, a parametric study with respect to the parameter  follows, where three diferent combinations of ceramic/metal materials are considered. It is concluded that the value =1, which corresponds to a linear variation of the properties, minimizes the maximum (tensile) stress applied at the middle of the functionally graded layer. 1. Introduction Ceramic materials are used as thermal barrier coatings for the thermal protection of metals in high-temperature envi- ronments. A common failure mechanism of those composite confgurations is the spallation of the ceramic coating close to the interface with the metal substrate, mainly due to their thermal expansion mismatch [1]. A possible solution for this problem is the use of functionally graded materials (FGMs), which are advanced materials with gradually varying proper- ties [2]. In FG thermal barrier coatings, an intermediate FGM layer connects the ceramic coating and the metal substrate. Te thermomechanical properties of the FGM layer vary from the properties of the ceramic material to the properties of the metal material in a continuous way, thus eliminating the material discontinuities. On the other hand, the classical theory of thermoelasticity predicts that the thermal disturbances propagate through a solid medium with infnite speed. During the last 50 years, generalized theories of thermoelasticity have been formu- lated that predict fnite-speed thermal waves and overcome this physical paradox. Te wave type heat propagation is fre- quently described as second sound. Although the efects of second sound are short-lived, they become important in thermal shock applications [3]. Ceramic/metal FG thermal barrier coatings are used as parts in machines that operate in high-temperature environ- ments. Combustion chambers, exhaust pipes, power genera- tors, aircraf engines, and space shuttles are typical examples of such machines. In these applications, the study of the ther- momechanical response of a ceramic/metal FGM layer under thermal shock conditions using generalized thermoelasticity theories is of great importance. Te frst generalized thermoelasticity theory was formu- lated by Lord and Shulman [4]. Te Lord-Shulman theory modifes the classical Fourier’s law of heat conduction by introducing a relaxation time, which can be interpreted as the time required to establish steady-state heat conduction in a volume element when a temperature gradient is suddenly imposed on that element [3, 4]. Another important general- ized theory is the Green-Lindsay theory [5], which introduces two relaxation times to modify the stress-strain relations and Hindawi Mathematical Problems in Engineering Volume 2018, Article ID 7371016, 11 pages https://doi.org/10.1155/2018/7371016