Study of the Dual Phase Lag Model of Thermoelasticity for a Half-Space Problem with Rigidly Fixed Surface in the Presence of a Thermal Shock

A two-dimensional problem for a half-space whose surface is rigidly fixed and subjected to a thermal shock is studied. The problem is solved in the context of the theory of generalized thermoelasticity with dual phase lag model (DPL). Laplace and Fourier transform techniques are used to obtain the exact forms of the temperature, displacements and stresses in the transformed domain. The numerical inversion of Laplace and Fourier transforms are evaluated using Durbin and Romberg techniques. The effects of the heat flux and temperature gradient phase-lags on the field variables are investigated. The Lord and Shulman and Green and Naghdi theories as well as the classical thermoelasticity theory are obtained as special cases. Numerical results are represented graphically and discussed.