Analysis of the thermoelastic response of a semi-space to a short laser pulse

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Renz, Gary
Mechanical engineering
thesis / dissertation description
A study of the thermoelastic response of a semi-space medium to a short laser pulse generated heat is presented. This study uses the generalized thermoelasticity theory proposed by Green and Lindsay. This theory generalizes the classical theory of thermoelasticity by developing hyperbolic heat conduction equations and temperature-rate dependent constitutive equations. By so doing, an inherent paradox and physically unrealistic result in the classical theory of thermoelasticity that proposes infinite speed of thermal responses through a medium is corrected. Its validity is justified by the satisfaction of Fourier's law by which classical thermoelasticity is based. The Green-Lindsay theory adopts two thermal relaxation times and a thermoelastic coupling constant as specific material parameters to account for finite speed thermoelastic waves. The model presented in this study uses a semi-space medium that has imposed on its boundary a laser induced heat of the form of a product of an exponentially decreasing function of the semi-space depth and a skewed Gaussian temporal profile. A numerical analysis of the exact closed form solution is presented. This analysis reveals that for a fixed cross section of the semi-space depth, the stress-temperature response is represented by a pair of smooth transiental functions of time and display two distinct planar thermal wave fronts of finite speed.