a b s t r a c tIn this work, a new theory of thermoelasticity is derived using the methodology of fractional calculus. The theories of coupled thermoelasticity and of generalized thermoelasticity with one relaxation time follow as limit cases. A uniqueness theorem for this model is proved. A variational principle and a reciprocity theorem are derived.

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In this work, we apply the fractional order theory of thermoelasticity to a 1D thermal shock problem for a half‐space. Laplace transform techniques are used. The predictions of the theory are discussed and compared with those for the coupled and generalized theories of thermoelasticity. Numerical results are computed and represented graphically for the temperature, displacement and stress distributions.

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In this work, we apply the fractional order theory of thermoelasticity to a 1D problem for a half-space overlaid by a thick layer of a different material. The upper surface of the layer is taken to be traction free and is subjected to a constant thermal shock. There are no body forces or heat sources affecting the medium. Laplace transform techniques are used to eliminate the time variable t. The solution in the transformed domain is obtained by using a direct approach. The inverse Laplace transforms are obtained by using a numerical method based on Fourier expansion techniques.The predictions of the fractional order theory are discussed and compared with those for the generalized theory of thermoelasticity. We also study the effect of the fractional derivative parameters of the two media on the behavior of the solution. Numerical results are computed and represented graphically for the temperature, displacement and stress distributions.

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We consider a homogeneous isotropic thermoelastic half-space in the context of the theory of thermoelasticity without energy dissipation. There are no body forces or heat source acting on the half-space. The surface of the half-space is affected by a time dependent thermal shock and is traction free. The Laplace transform with respect to time is used. The inverse transforms are obtained in an exact manner for the temperature, thermal stress, and displacement distributions. These solutions are represented graphically and discussed for several cases of the applied heating. Comparison is made between the predictions here and those of the theory of thermoelasticity with one relaxation time.