A Comuputerized DRBEM model for generalized magneto-thermo-visco-elastic stress waves in functionally graded anisotropic thin film/substrate structures

Abstract

A numerical computer model, based on the dual reciprocity boundary element method (DRBEM) for studying the generalized magneto-thermo-visco-elastic stress waves in a rotating functionally graded anisotropic thin film/substrate structure under pulsed laser irradiation is established. An implicit-implicit staggered algorithm was proposed and implemented for use with the DRBEM to get the solution for the temperature, displacement components and thermal stress components through the structure thickness. A comparison of the results for different theories is presented in the presence and absence of rotation. Some numerical results that demonstrate the validity of the proposed method are also presented. Key wordsMagneto-Thermoviscoelasticity; Rotation; Functionally graded materials; Anisotropic; Dual Reciprocity Boundary Element Method; Distribution.A Comuputerized DRBEM model for generalized magneto-thermo-visco-elastic stress waves in functionally graded anisotropic thin film/substrate structures 1 INTRODUCTION Biot (1956) introduced the theory of coupled thermoelasticity to overcome the first shortcoming in the theory of uncoupled thermoelasticity introduced by Duhamel (1837) and Neuman (1885) where it predicts two phenomena not compatible with physical observations. First, the equation of heat conduction of this theory does not contain any elastic terms. Second, the heat equation is of a parabolic type, predicting infinite speeds of propagation for heat waves. Later on, generalized theories of thermoelasticity were introduced in order to eliminate the shortcomings of the uncoupled thermoelasticity. Lord and Shulman (1967) developed the theory of coupled thermoelasticity with one relaxation time by constructing a new law of heat conduction to replace the classical Fourier's law. This law contains the heat flux vector as well as its time derivative. It contains also new constant that acts as relaxation time. Since the heat equation of this theory is of the wave-type, it automatically ensures finite speeds of propagation for heat and elastic waves. Green and Lindsay (1972) cluded a temperature rate among the constitutive variables to develop a temperature-ratedependent thermoelasticity that does not violate the classical Fourier's law of heat conduction when the body under consideration has a center of symmetry; this theory also predicts a finite speed of heat propagation. This theory is known as the theory of thermoelasticity with two relaxation times. According to these theories, heat propagation should be viewed as a wave phenomenon rather than diffusion one Relevant theoretical developments on the subject were made by Naghdi (1992, 1993) they developed three models for generalized thermoelasticity of homogeneous isotropic materials which are labeled as model I, II and III. These theories of thermoelasticity LS, GL and GN theories are known as the generalized theories of thermoelasticity with finite thermal wave speed. In general, it is not easy to obtain analytical solutions to a dynamical magneto-...

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