Effective Stress Analysis in a Magneto-Thermoelastic Medium Due to the Presence of Uniaxial Static Stresses

The formulation of effective (true) static stress acting on a deformed surface is based on well-established principles of continuum mechanics. In this study, the solid is expected to be exposed to a uniform static uniaxial stress field. By accounting for second-order stress-strain interactions, a modified set of elastic motion equations is obtained, which incorporates the influence of static surface forces and body forces on elastic wave propagation in isotropic media. The thermal response is modelled using the generalized heat conduction equation within the modified Lord–Shulman magneto-thermoelastic framework, augmented by a higher-order time derivative of order N. The resulting coupled system of governing partial differential equations is explained by assuming harmonic wave forms and employing the method of separation of variables. This formulation enables a systematic examination of magnetothermoelastic wave propagation and the corresponding stress behaviour of the solid, with particular emphasis on the role of the operator order. A comprehensive numerical analysis is carried out to examine the spatial and temporal variations of temperature, displacements, dilatation, and stress components. The results demonstrate that operator order N has a pronounced influence on the thermoelastic response: larger values of N significantly reduce thermal oscillations and enhance the decay of thermal disturbances, while the limiting case N → ∞ produces the smoothest and most stable temperature distribution.