Influence of Operator Expansion Order on the Magneto-Thermoelastic Response of an Initially Stressed Half-Space Under Green–Lindsay Models

In this article, the magneto-thermoelastic response of an isotropic homogeneous half-space within several Green–Lindsay (GL) models is examined in relation to initial stress and operator expansion factors. Through a unifying operator-expansion framework, various stages of thermal relaxation are described by simple, refined, and exponential GL theories as well as classical thermoelasticity theory. The effects of the magnetic field and initial stress are taken into account in the governing coupled equations, and the normal mode approach is used to explain the resulting boundary-value problem. To investigate the impact of the initial stress factor and operator expansion order, numerical outcomes are provided for the temperature, displacement, and stress distributions. The projected thermoelastic responses of the classical, simple, refined, and exponential GL models varied significantly.