Effective analytical approach to investigate wave propagation in nonlinear thermoelastic media under the influence of initial stress

This study identifies a significant gap in existing research regarding the impact of initial stress on the thermoelastic behavior of materials with temperature-dependent properties. Previous studies have primarily relied on simplified models that assume constant material parameters, often leading to inaccurate predictions of material responses under varying thermal conditions. The intricate relationship between initial stress and the evolving properties of thermoelastic materials remains largely unexplored. To address this issue, the research introduces the Improved Modified Extended Tanh Function (IMETF) technique, an advanced analytical method specifically designed to tackle nonlinear complexities. By integrating temperature-dependent material properties within the coupled thermoelastic framework, this study surpasses conventional models, enabling more accurate and realistic predictions of material behavior under thermal stress. The IMETF method serves as a robust tool for deriving exact analytical solutions to Nonlinear Partial Differential Equations (NLPDEs) governing thermoelasticity. The study successfully obtains a range of exact solutions, including hyperbolic solutions, dark, bright, and singular soliton solutions, rational solutions, Jacobi elliptic solutions, and exponential solutions, providing deeper insight into the dynamic behavior of thermoelastic materials subjected to internal heating. These findings are further reinforced by comprehensive graphical representations of displacement fields, temperature distributions, and thermal stress components, offering a clear visualization of the complex interactions between thermal and mechanical responses in temperature-sensitive media.