2-D mathematical model of hyperbolic two-temperature generalized thermoelastic solid cylinder under mechanical damage effect

This paper presents the construction of a two-dimensional mathematical model of a thermoelastic, homogeneous, and isotropic solid cylinder with its bounding surface subjected to a thermal shock. It has been discovered that the governing differential equations may be constructed in the framework of the hyperbolic two-temperature generalized thermoelasticity theory based on the study of the damage mechanics variable. It has been demonstrated visually that different values of the two-temperature parameter, damage mechanics variable and cylindrical length may produce numerically significant increases in dynamical and conductive temperatures, strain, and the average of the major stress components. The two-temperature parameter, as well as the diameter of the cylindrical axis, has substantial effects on all the functions under consideration. The damage mechanics variable has very little impact on the conductive and dynamical temperatures, but it has large implications on the strain and stress distributions, as seen in the graphs. The thermal wave can propagate at a limited pace using the hyperbolic two-temperature theory. The hyperbolic two-temperature theory offers a finite speed of propagation to the thermal wave.