Effect of Magnetic Field and a Mode-I Crack 3D-Problem in Micropolar Thermoelastic Cubic Medium Possessing Under Three Theories

Abstract

A model of the equations of two dimensional problems in a half space, whose surface in free of micropolar thermoelastic medium possesses cubic symmetry as a result of a Mode-I Crack is studied. There acts an initial magnetic field parallel to the plane boundary of the half- space. The crack is subjected to prescribed temperature and stress distribution. The formulation in the context of the Lord-Şhulman theory LS includes one relaxation time and Green-Lindsay theory GL with two relaxation times, as well as the classical dynamical coupled theory CD. The normal mode analysis is used to obtain the exact expressions for the displacement, microrotation, stresses and temperature distribution. The variations of the considered variables with the horizontal distance are illustrated graphically. Comparisons are made with the results in the presence of magnetic field. A comparison is also made between the three theories for different depths.