Fractional order model of micropolar thermoelasticity and 2D half-space problem

Abstract

In this manuscript, the generalized micropolar theory of thermoelasticity is modified using fractional calculus. The revised equations are used to solve a problem for a half-space whose boundary is rigidly fixed and subjected to an axisymmetric thermal shock. Laplace and Hankel transform techniques are used. The analytical solution in the transform domain is obtained by using a new direct approach without the customary use of potential functions. By using a numerical method based on the Fourier expansion technique, the inverse of the double transform can be obtained. The numerical results for displacement, microrotation, stress, micro-stress, and temperature are obtained and represented graphically. Comparisons are made with the results of the older theory.