Study of the physical behavior of nonlinear thermoelastic waves in the Green-Lindsay model using advanced analytical technique

Purpose The study aims to address the limitation of conventional thermoelastic models that assume constant material properties by investigating the effects of temperature-dependent material parameters. It seeks to enhance the accuracy of thermoelastic modeling and better represent the interaction between internal heat generation and evolving material behavior under thermal variations. Design/methodology/approach The research introduces the modified extended mapping method (MEMM) as an analytical technique for solving nonlinear partial differential equations within the Green–Lindsay (G-L) thermoelastic framework. The method incorporates temperature-dependent material characteristics and generates exact analytical solutions (exponential, Jacobi elliptic, rational and hyperbolic) to model complex thermoelastic responses. Findings The results reveal that incorporating temperature-dependent properties significantly improves the realism and accuracy of thermoelastic simulations. Exponential solutions effectively capture rapid, diffusiondominated thermal responses, while hyperbolic solutions are well-suited for localized, steady thermoelastic wave behavior under nonlinear effects. Graphical analyses highlight the intricate coupling between displacement, temperature fields, and thermal stresses. Practical implications The generated solution structures and enhanced modeling accuracy provide engineers and researchers with more reliable tools for predicting material performance under thermal loads. This can improve design and assessment processes involving heat-sensitive materials in applications such as aerospace mechanical systems, and high-temperature structural components. Originality/value The study advances thermoelastic analysis by integrating temperature-dependent material properties into the G-L theory using the innovative MEMM. It represents a significant methodological contribution by delivering exact analytical solutions to nonlinear thermoelastic systems and improving the depth and precision of thermal-mechanical modeling.