Journal ArticleDOI
Application of fractional order theory of thermoelasticity to a 1D problem for a half‐space
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In this paper, the fractional order theory of thermoelasticity was applied to a 1D thermal shock problem for a half-space, and the predictions of the theory were discussed and compared with those for the coupled and generalized theories of thermodynamic properties.Abstract:
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.read more
Citations
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Effect of variable thermal conductivity on a half-space under the fractional order theory of thermoelasticity
TL;DR: In this article, the authors considered the problem of a half-space formed of a material with variable thermal conductivity and applied the theory of fractional order theory of thermoelasticity to the problem.
Journal ArticleDOI
Memory-dependent derivatives theory of thermo-viscoelasticity involving two-temperature
M. A. Ezzat,A. A. El-Bary +1 more
TL;DR: In this paper, a new model of two-temperature generalized thermo-viscoelasticity theory based on memory-dependent derivative is constructed and the equations of the new model are applied to one-dimensional problem of a half-space.
Journal ArticleDOI
Electro-thermoelasticity theory with memory-dependent derivative heat transfer
TL;DR: In this paper, a mathematical model of electro-thermoelasticity has been constructed in the context of a new consideration of heat conduction with memory-dependent derivative, which can be chosen freely according to the necessity of applications.
Journal ArticleDOI
Thermo-viscoelastic materials with fractional relaxation operators
TL;DR: In this article, a new model of linear thermo-viscoelasticity for isotropic media taking into consideration the rheological properties of the volume with fractional relaxation operators is given.
Journal ArticleDOI
On dual-phase-lag thermoelasticity theory with memory-dependent derivative
TL;DR: In this paper, a new mathematical model of generalized thermoelasticity with memory-dependent derivatives for the dual-phase-lag heat conduction law is constructed and the governing equations of the new model are applied to a half-space subjected to ramp-type heating.
References
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Journal ArticleDOI
A generalized dynamical theory of thermoelasticity
TL;DR: In this article, a generalized dynamical theory of thermoelasticity is formulated using a form of the heat transport equation which includes the time needed for acceleration of heat flow.
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Thermoelasticity and Irreversible Thermodynamics
TL;DR: In this article, a unified treatment of thermoelasticity by application and further developments of the methods of irreversible thermodynamics is presented, along with a new definition of the dissipation function in terms of the time derivative of an entropy displacement.
Journal ArticleDOI
A method for the numerical inversion of Laplace transforms
TL;DR: A numerical inversion method for Laplace transforms, based on a Fourier series expansion developed by Durbin [5], is presented in this article, where the disadvantage of the inversion methods of that type, the encountered dependence of discretization and truncation error on the free parameters, is removed by the simultaneous application of a procedure for the reduction of the Discretization error, a method for accelerating the convergence of the Fourier Series and a procedure that computes approximately the "best" choice of the free parameter.
Journal ArticleDOI
A new dissipation model based on memory mechanism
TL;DR: The model of dissipation based on memory introduced by Caputo is generalized and checked with experimental dissipation curves of various materials.