A two-dimensional problem of a mode I crack in a type III thermoelastic medium

Abstract

The present work is concerned with resolving a dynamical problem of an infinite type III thermoelastic space weakened by a finite linear mode I crack. The material of the medium is considered to be homogeneous and isotropic. The boundary of the crack is subjected to a prescribed stress distribution and temperature. The thermoelasticity theory of type III developed by Green and Naghdi has been employed, and integral transforms have been used to obtain the solution to the problem. A system of four dual integral equations have been obtained, the solution of which is shown to be equivalent to the solution of a Fredholm’s integral equation of the first kind. These integral equations are solved numerically by the regularization method. The inversion of the Laplace transform is also carried out numerically, and numerical values of the displacement components, temperature and stresses in the physical domain are computed for copper material by considering particular cases. The results are presented graphically.