4. Analytical Treatment of Hyperbolic Equations for Stress Analysis

Laser ultra-short pulse heating of metallic surfaces causes the hyperbolic behavior of energy transport in the heated region. The consideration of the parabolic nature of the non-equilibrium heating situation fails to formulate the correct heating process. Although heating duration is ultra-short, material response to the heating pulse is not limited to only heat transfer and the mechanical response of the heated surface also becomes important. Consequently, mechanical response of the surface under ultra-short thermal loading becomes critical in terms of the generation of the high stress levels. In this chapter, hyperbolic behavior of heat transfer is introduced in the laser heated region. The closed for solutions for the temperature and stress fields are obtained for various heating situations. Two-dimensional effect of heating on temperature rise is also considered for nano-scale applications.