Discontinuities in generalized thermo-viscoelasticity under four theories

A model of the equations of generalized thermoviscoelasticity for isotropic media is given. The formulation is applied to the generalized thermoelasticity theories-Lord-Shulman, Green-Lindsay, and Chandrasekharaiah and Tzou-as well as to the dynamic coupled theory. The state-space approach is adopted for the solution of the one-dimensional problem of plane distribution of heat sources. The Laplace transform technique is used The expansions of the stress component, the temperature increment, and the displacement, in Laplace transform domain, in power series, and the exact inversions for arbitrary time, are given. The jump discontinuities are calculated for the four theories and the kinematic conditions of compatibility are verified Numerical results are given and illustrated graphically by employing the numerical method for the inversion of the Laplace transforms. Comparisons are made with the results predicted by the four theories.