interference of thermal and mechanical waves in a functionally graded hyperelastic model exhibits both temperature and coordinate dependencies

This work presents advanced models to investigate the interaction between thermal and mechanical waves in near-incompressible functionally graded materials simultaneously subjected to mechanical and thermal loads. both the position within the material and the temperature at each point affect the substance's qualities. the governing equations for a functionally graded thermo-hyperelastic model are derived using a nonlinear version of the helmholtz free energy, and solutions are found using a nonlinear finite element approach. in contrast to earlier models that solely examined wave behavior under mechanical or thermal loads, this study examines wave interaction within a hyperelastic framework. the results show that different wave propagation properties are caused by the interference between mechanical and thermal waves in these graded materials. complex wave behaviors are produced by the interaction of mechanical and thermal shocks as well as variations in material properties. the findings demonstrate how important temperature-dependent material characteristics are in influencing how waves propagate.