Study of Recent Advances in Thermoelasticity

Abstract This review provides an extensive examination of recent advancements in the domain of thermoelasticity, with a particular focus on generalized theories that account for the second sound effect. Contemporary investigations have increasingly centered on the refinement and extension of generalized thermoelastic models. In contrast to classical thermoelastic theory, which is based on parabolic heat conduction, these generalized approaches typically incorporate hyperbolic-type heat conduction equations, motivated by experimental observations that reveal wave-like thermal behavior. Various researchers across multiple disciplines have contributed to the development and application of these models, addressing a wide spectrum of physical problems and elucidating the unique characteristics inherent to each formulation. The review systematically explores the theoretical underpinnings, mathematical frameworks, limitations, and analytical or numerical methods employed to solve problems involving different geometrical configurations and boundary conditions. Although classical thermoelasticity remains a valuable tool for evaluating temperature distributions, thermal stresses, and mechanical responses, generalized theories offer enhanced accuracy in modeling non-Fourier heat conduction phenomena. Furthermore, a comparative analysis of solution strategies indicates that numerical approaches—such as the generalized differential quadrature method and finite element analysis—exhibit greater efficacy in addressing strongly nonlinear and geometrically complex problems. Conversely, analytical techniques, particularly those utilizing Laplace and Fourier transforms, are more suitably applied to problems involving memory effects or fractional-order derivatives. This review delineates the underlying theoretical constructs, mathematical models, inherent limitations, and solution methodologies employed for various geometrical domains and loading scenarios. It emphasizes that, although classical thermoelasticity provides a foundational framework, it lacks the capability to accurately capture non-Fourier heat conduction behavior observed in contemporary engineering applications. As a result, the adoption of generalized thermoelastic models becomes essential for achieving realistic and reliable thermal analyses.