Analytical solutions of biothermoelastic interactions in viscoelastic skin tissues under the GNII model

Background Accurate prediction of thermo-mechanical responses in biological tissues is essential for thermal therapies such as hyperthermia. The Green–Naghdi (GN) theory provides a suitable framework for modeling non-Fourier heat conduction in biological media. Objective This study investigates the coupled thermo-mechanical behavior of viscoelastic biological media under transient thermal excitation using the Green–Naghdi type II (GN-II) theory. Methods A coupled thermo-viscoelastic model is formulated for a stress-free medium subjected to a time-dependent, exponentially attenuated thermal load. The governing equations are solved using the Laplace transform and an eigenvalue-based spectral approach. Temperature, displacement, and stress fields are evaluated numerically, followed by a parametric analysis. Results The results demonstrate significant coupling between thermal and mechanical fields. Thermal loading and material parameters strongly influence the distributions of temperature, displacement, and stress. Distinct responses are observed between dissipative and non-dissipative thermal models. Conclusion The proposed eigen-spectral approach effectively describes thermo-mechanical responses in viscoelastic biological media. The findings demonstrate the importance of non-Fourier heat conduction and viscoelastic effects in modeling thermal therapies and optimizing treatment conditions.