Diagonalization Method to Hyperbolic Two-Temperature Generalized Thermoelastic Solid Sphere under Mechanical Damage Effect

Abstract

This study is the first to use the diagonalization method for the new modelling of a homogeneous, thermoelastic, and isotropic solid sphere that has been subjected to mechanical damage. The fundamental equations were derived using the hyperbolic two-temperature generalized thermoelasticity theory with mechanical damage taken into account. The outer surface of the sphere has been assumed to have been shocked thermally without cubical dilatation. The numerical results for the dynamical and conductive temperatures increment, strain, displacement, and average of the principal stresses components have been represented graphically with different values of the hyperbolic two-temperature parameter and mechanical damage parameters. The two-temperature model parameter and the mechanical damage parameter have significant effects. The propagations of the thermomechanical waves take place at finite speeds in the context of the hyperbolic two-temperature theory as well as in the usual context of the Lord–Shulman theory with one-temperature.

Analysis of axisymmetric deformation in generalized micropolar thermoelasticity within the framework of Moore-Gibson-Thompson heat equation incorporating non-local and hyperbolic two-temperature effect

“…As a result, they modified the two-temperature model to the hyperbolic twotemperature model, in which the difference between the second derivative concerning the time of the dynamical and conductive temperature is proportional to the heat supply, and found that this model introduces a thermal wave that propagates with a limited speed. Recently, [22][23][24] discussed different types of problems in the context of the HTT theory of thermoelasticity.…”

The Influences of the Hyperbolic Two-Temperatures Theory on Waves Propagation in a Semiconductor Material Containing Spherical Cavity

“…Saeed and Abbas [10] studied the hyperbolic two-temperature photothermal interaction in semiconducting mediums. Al-Lehaibi [11] studied the diagonalizations approach to hyperbolic two-temperature thermoelastic solid spheres under mechanical damage effects. Abbas et al [12] discussed the hyperbolic two-temperature photothermal interactions in semiconducting materials with cylindrical holes.…”