Study of Thermal Stress Generated in an Elastic Half-Space in the Context of Generalized Thermoelasticity Theory

Abstract

Generalized thermoelasticity theories have been developed to eliminate the paradox of infinite velocity of thermal wave propagation and to correct the classical coupled thermoelasticity theory on the assumption that thermal wave propagates with a finite speed. Lord and Shulman, as well as Green and Lindsay, formulated independently generalized thermoelasticity theories by introducing one or two relaxation times in the process with a view to eliminate the paradox of infinite speed. In the last decade, relevant theoretical developments on this subject are due to Green and Naghdi, which provide sufficient basic modifications in the constitutive equations that permit treatment of a much wider class of heat flow problems. The present paper deals with a boundary value problem of an isotropic elastic half-space using generalized thermoelasticity of type II developed by Green and Naghdi. The plane boundary of the material medium is either (a) held rigidly fixed or considered as (b) traction-free and subjected to ramp-type heating. Introducing potential function in the process and applying Laplace transform technique, the closed-form solutions for the displacement, temperature and stress fields are obtained. Numerical estimates are also obtained for a particular example and are represented graphically.