Effects of three-phase-lag on two-temperature generalized thermoelasticity for infinite medium with spherical cavity

The thermoelastic interaction for the three-phase-lag （TPL） heat equation in an isotropic infinite elastic body with a spherical cavity is studied by two-temperature generalized thermoelasticity theory （2TT）. The heat conduction equation in the theory of TPL is a hyperbolic partial differential equation with a fourth-order derivative with respect to time. The medium is assumed to be initially quiescent. By the Laplace trans- formation, the fundamental equations are expressed in the form of a vector-matrix differ- ential equation, which is solved by a state-space approach. The general solution obtained is applied to a specific problem, when the boundary of the cavity is subjected to the ther- mal loading （the thermal shock and the ramp-type heating） and the mechanical loading. The inversion of the Laplace transform is carried out by the Fourier series expansion tech- niques. The numerical values of the physical quantity are computed for the copper like ma- terial. Significant dissimilarities between two models （the two-temperature Green-Naghdi theory with energy dissipation （2TGN-III） and two-temperature TPL model （2T3phase）） are shown graphically. The effects of two-temperature and ramping parameters are also studied.