## 1 Introduction
In such cases, solutions for temperature and stress distributions should be derived using the coupled thermoelasticity equations. It should be noted that the classical theory presents an uncoupled view of thermoelasticity, which does not accurately reflect the physical behavior of the medium. In classical theory, the thermal equation takes a parabolic form, implying infinite speeds for heat wave propagation--a notion that is physically impossible, particularly in scenarios involving thermal shocks. Over the past decade, several non-classical theories have been developed to address these issues. These theories propose modifications to [PERSON]'s law of heat conduction, incorporating hyperbolic heat transfer equations that account for finite thermal pulse velocities. According to these models, thermal propagation can be regarded as a wave phenomenon rather than a diffusion process [15]. The recent years have highlighted that the investigation into the mechanical behavior of high-tech materials for structural uses is often insufficient. Consequently, research on the interplay between mechanical and thermal effects in solid materials has garnered significant attention. The hyperbolic form refers to the finite velocities of heat distributions, known as second sound, which was first introduced by [PERSON] [16]. This second sound phenomenon allows for finite speeds in thermoelastic wave propagation, particularly in situations involving thermal shocks, in contrast to the implications of [PERSON]'s law, which suggests that waves travel through a body without delay, which is not realistic. In 1967, [PERSON] and [PERSON] [17] proposed a wave-form thermal equation, suggesting a new approach to heat conduction that deviates from [PERSON]'s law. They introduced the concept of relaxation time, and their theory indicates a linear relationship between temperature and heat flux that incorporates both the rate of temperature change and the thermal rate [15]. [PERSON] and [PERSON] [18] expanded this concept in 1972, presenting a second generalized theory where the temperature rate is treated as a dependent variable influenced by two distinct relaxation times. They also established two separate lag times within the entropy expression and the correlation of stress [15]. [PERSON] and [PERSON] [19] introduced a new model that does not take energy wastage into account, utilizing the displacement-temperature-flux rate in [PERSON]'s law. Unlike the classical heat conduction model that adheres to [PERSON]'s law, a key feature of this new model is its exclusion of energy loss. In their theory, [PERSON] and [PERSON] put forward three distinct forms of constitutive response functions [15]. Recently, non-destructive analysis has emerged as a fundamental requirement for experimental applications, with the need to be based on simple analytical methods. Thus, non-destructive stress analysis, referred to as the thermoelastic effect, has emerged as an effective method for engineering and industrial stress analysis. In [13,14], a theoretical framework for the thermoelastic effect has been developed, offering a simple mathematical model to support the interpretation of non-destructive analysis experimental results only limited to SPATE (Stress Pattern Analysis by the measurement of Thermal Emission), i.e., an equipment for the radiometric monitoring of the temperature changes induced by cyclic loading in the elastic range. This paper aims to generalize the thermophysical approach, achieving a model for the measurement of thermophysical properties of materials under experimental techniques that are not necessarily periodic. To do so, we utilize the intrinsic formulation of linear thermoelasticity theory [20], linking temperature changes to stress variation, under some theoretical approximation; indeed, the outcome is influenced by the first and second invariants of stress, whereas the second invariant becomes negligible when there is only one principal stress component. In summary, we develop a theoretical model describing thermal effects on elastic behavior.