Mathematical Model on Gravitational Electro-Magneto-Thermoelasticity with Two Temperature and Initial Stress in the Context of Three Theories

The main aim of this paper is to study two temperature thermoelasticity in a generalization form to solve the half-space problem of two dimensions under gravity, perturbed magnetic field, and initial stress. The fundamental equations are solved considering a new mathematical technique under Lord-Şhulman (LS), Green-Naghdi (GN type III) and three-phase-lag (3PHL) theories to investigate displacement, stress components, and temperature distribution. The results obtained by the three theories, i.e., (LS), (GN type III), and (3PHL), considering the absence and the presence of gravity, initial stress, and magnetic field have been compared. The results were numerically calculated and graphically displayed to exhibit the physical meaning of the phenomenon and the external parameters’ effect. A comparison has been presented between the results obtained in the absence and the presence of the external considered parameters and with the previously obtained results by other researchers.