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Unified fractional derivative models of magneto-thermo-viscoelasticity theory

100%

Ezzat M. A. , El-Bary A. A.

Archives of Mechanics

2016

tom Vol. 68, nr 4

285--308

A unified mathematical model of fractional magneto-thermo-viscoelasticty for isotropic perfectly conducting media involving fractional relaxation operator is given. Some essential theorems on the linear coupled and generalized theories of thermoviscoelasticity can be easily obtained. The new fractional model is applied to a halfspace subjected to two different forms of time-dependent thermal shock in, the presence of a transverse magnetic field. The Laplace transform techniques are used. Numerical computation is performed by using a numerical inversion technique and the resulting quantities are shown graphically. The effects of the fractional orders on viscoelastic material are discussed.

A general model of generalized thermoelasticity with temperature-dependent modulus of elasticity

80%

Ezzat M. A. , Zakaria M. , El-Karamani A. S.

Journal of Technical Physics

2005

tom Vol. 46, no 2

67-82

A new formula of generalized thermoelasticity equations for isotropic media is established. The present model does apply to generalizations, the Lord-Shulman theory with one relaxation time and the Green-Lindsay theory with two relaxation times, as well as to the coupled theory. The normal mode analysis is used to obtain the exact expressions for the temperature distribution, thermal stresses, and the displacement components. The resulting formulation is applied to three different concrete problems. The first one deals with a thick plate subject to heating on parts of the upper and lower surfaces of the plate; the second one concerns the case of a heated punch moving across the surface of a semi-infinite thermoelastic half-space subject to appropriate boundary conditions; and the third problem deals with a plate with thermo-insulated surfaces subjected to time-dependent compression. Numerical results are given and illustrated graphically for the problem considered. A comparison was made with the results obtained in the case of temperature-independent modulus of elasticity in each theory.