1D applications on fractional generalized thermoelasticity associated with two relaxation times

• Published in: Mechanics of advanced materials and structures 2016-06, Vol.23 (6), p.689-703
• Main Authors: Hamza, F., Abd El-Latief, A. M., Abdou, M.
• Format: Article
• Language: English
• Subjects: Boundaries; coupled thermoelasticity; Derivatives; direct technique; fractional calculus; Green Lindsay model (G.L.); Holes; Laplace transforms; Mathematical models; numerical results; state space technique; Stress concentration; Thermal stresses; Traction; two relaxation times
• ISSN: 1537-6494; 1537-6532
• DOI: 10.1080/15376494.2015.1029158

Here, this work is concerned with some different one-dimensional (1D) problems of distribution of the thermal stresses and temperature in fractional generalized thermoelastic material, as follows: (i) 1D problem for a half-space of elastic material in the presence of heat sources has been solved by using Laplace transform and state space techniques; and (ii) 1D problem of distribution of thermal stresses and temperature in infinite medium with a spherical cavity subjected to a sudden change in the temperature of its internal boundary, which is assumed to be traction free, has been solved by Laplace transform and direct approach techniques. In the preceding problems, the numerical results for dimensionless variable fields are given and illustrated graphically. According to the numerical results, some comparisons have been shown in figures to estimate the effect of the fractional derivative parameter α about the new theory on all variable fields and discussion has been established for a copper-like material.