A problem of infinite elastic medium with cylindrical cavity under two-temperature thermoelasticity with thermal relaxation parameters

Abstract

The theory of two-temperature thermoelasticity is one of the non-classical theories of thermoelasticity in which the heat conduction depends on two different temperatures conductive temperature and thermodynamic temperature. The present work is concerned with seeking the solution of a problem of an infinite isotropic homogeneous medium with a cylindrical cavity whose surface is stress free and is subjected to a thermal shock in the context of the two-temperature generalized theory of thermoelasticity with two relaxation parameters, recently proposed by Youssef. 2006. With the aim of comparing the results of the present problem with the corresponding results of two-temperature thermoelasticity with one relaxation parameter, the problem is formulated on the basis of two different theories of twotemperature generalized thermoelasticity in a unified way. Laplace transform procedure and decoupling of coupled differential equations are employed to derive the solution in transform domain, which is then followed by the inversion of Laplace transform by a numerical method to obtain the solutions for displacement, conductive temperature, dynamic temperature and stresses in the physical domain. Numerical values of physical quantities are computed for copper material and results are illustrated graphically. A comparison between two models as well as with the classical one- temperature generalized thermoelastic models existing in the literature is presented.