A visco-elastic layer overlaid by a thick layer on top of an elastic half space in the generalized theory of thermoelasticity

Abstract

In this work, we presented a model which consists of three layers with different materials; the second layer was taken to be viscous-elastic material, while the first and third layers are made of elastic material. This model is solved in the context of the generalized thermoelasticity theory with one relaxation time. The first layer's upper surface is taken to be traction-free and is subjected to a constant thermal shock. Nobody forces or heat sources affecting the layer. Laplace transform techniques are used. The solution in the transformed domain is obtained by using a direct approach. The inverse Laplace transforms are obtained using a numerical method based on the Fourier expansion technique. The effect of thermal shock is discussed and studied of the three layers on the behavior of the solutions, in the presence of viscoelastic effects and its absence. Numerical results are computed and represented graphically for the temperature, displacement, and stress distributions.

KEYWORDS:

• Different layers
• half-space
• generalized thermoelasticity
• Laplace transform
• generalized thermo-viscoelasticity

Disclosure statement

No potential conflict of interest was reported by the author(s).