Thermo-Mechanical Interactions in a Three-Dimensional Nonlocal Elastic Medium with Thermal Relaxation

A unique three-dimensional model of generalized thermoelasticity, incorporating a single relaxation time and relying on stress gradient nonlocal elasticity, is presented in this study. The fundamental coupled equations governing the model are applied to a semi-infinite spatial medium with a rigidly fixed bounding surface, which is exposed to a time-dependent thermal shock. The general solution for the field variables is obtained in a closed form through the utilization of normal mode analysis and the eigenvalue approach technique. Numerical results, specific to a substance resembling copper, are provided for the field variables. Parametric studies are conducted to assess the impact of elastic nonlocality on various physical quantities. The graphical representation reveals a noteworthy influence of the nonlocal parameter on the field variables. The study further discusses and compares predictions from the new model with the Lord and Shulman theory of generalized thermoelasticity. Ultimately, the article concludes with a summary of key remarks.