There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

A novel generalized thermoelasticity model based on memory-dependent derivative

In this article, we consider the problem of a two-dimensional thermoelastic half-space in the context of generalized thermoelastic theory with one relaxation time. The surface of the half-space is taken to be traction free and thermally insulated. The solution of the considered physical quantity can be broken down in terms of normal modes. The nonhomogeneous basic equations have been written in the form of a vector-matrix differential equation, which is then solved by an eigenvalue approach. The exact analytical solution is adopted for the temperature, the components of displacement and stresses. The results obtained are presented graphically for the effect of laser pulse to display the phenomena physical meaning. The graphical results indicate that the thermal relaxation time has a great effect on the temperature, the components of displacement and the components of stress.

Analytical solution of thermoelastic interaction in a half-space by pulsed laser heating

This problem deals with the determination of thermo-elastic interaction due to step input of temperature on the boundaries of a functionally graded orthotropic hollow sphere in the context of linear theories of generalized thermo-elasticity. Using the Laplace transformation the fundamental equations have been expressed in the form of vector–matrix differential equation which is then solved by eigenvalue approach. The inverse of the transformed solution is carried out by applying a method of Bellman et al. Stresses, displacement and temperature distributions have been computed numerically and presented graphically in a number of figures. A comparison of the results for different theories (TEWOED(GN-II), TEWED(GN-III) and three-phase-lag model) is presented. When the material is homogeneous, isotropic and outer radius of the hollow sphere tends to infinity, the corresponding results agree with that of existing literature for GN-III model.

Generalized thermoelastic functionally graded orthotropic hollow sphere under thermal shock with three-phase-lag effect

This article presents a refined two-temperature multi-phase-lags thermoelasticity theory for the thermomechanical response of microbeams. The modified couple stress theory has been developed to capture the size effect in the small-size investigation. The microbeam is subjected to an inclined load of a linear combination of normal and tangential ones. Three partial differential equations of the modified couple stress microbeam are derived and solved exactly using the normal mode analysis. The influences of changing inclination angle, two-temperature parameter, and scale parameter on the field quantities like temperature, displacements, stresses, and couple stresses are investigated. Results of some earlier works are also deduced from the present investigation as special cases. Some comparisons are tabulated and presented graphically to estimate the effects of the scale parameter, the two-temperature parameter, the dual-phase-lags parameters, and the inclination angle. It is shown that the two-temperature parameter has a strong effect on the thermodynamic and conductive temperatures. However, the scale parameter and inclination angle have a very strong effect on all the field quantities of the microbeam.

Refined two-temperature multi-phase-lags theory for thermomechanical response of microbeams using the modified couple stress analysis

Generalized thermoelastic functionally graded solid with a periodically varying heat source

The present paper aims at studying the thermo-visco-elastic interaction in a homogeneous, infinite Kelvin-Voigt-type viscoelastic, thermally conducting medium due to the presence of periodically varying heat sources. Three-phase-lag thermoelastic model, GN model II (TEWOED) and GN model III (TEWED) are employed to study the thermomechanical coupling, thermal and mechanical relaxation effects. In the absence of mechanical relaxations (viscous effect), the results for various generalized theories of thermoelasticity may be obtained as particular cases. The governing equations are expressed in Laplace-Fourier double transform domain and are solved in that domain. The inversion of the Fourier transform is carried out by using residual calculus, where poles of the integrand are obtained numerically in complex domain by using Laguerre’s method and the inversion of Laplace transform is done numerically using a method based on Fourier series expansion technique. The numerical estimates of the displacement, temperature and stress are obtained for a hypothetical material. A comparison of the results for different theories (three-phase-lag model, GN model II, GN model III) is presented and the effect of viscosity is also shown. In absence of viscous effect the results corresponding to GN model II and GN model III agree with the results of the existing literature.

Generalized thermoviscoelastic interaction due to periodically varying heat source with three-phase-lag effect

This paper deals with a two dimensional problem for a transversely isotropic thick plate having heat source. The upper surface of the plate is stress free with prescribed surface temperature while the lower surface of the plate rests on a rigid foundation and is thermally insulated. The study is carried out in the context of generalized thermoelasticity proposed by Green and Naghdi. The governing equations for displacement and temperature fields are obtained in Laplace–Fourier transform domain by applying Laplace and Fourier transform techniques. The inversion of double transform has been done numerically. The numerical inversion of Laplace transform is done by using a method based on Fourier Series expansion technique. Numerical computations have been done for magnesium (Mg) and the results are presented graphically. The results for an isotropic material (Cu) have been deduced numerically and presented graphically to compare with those of transversely isotropic material (Mg).

A two dimensional problem for a transversely isotropic generalized thermoelastic thick plate with spatially varying heat source

This paper is concerned with an internal penny-shaped crack subjected to prescribed temperature and stress distribution in an infinite thermoelastic solid which obeys classical coupled thermoelasticity theory (CCTE), the Lord–Shulman (L-S) and Green–Naghdi (G-N) models of thermoelasticity. The generalized coupled thermoelasticity theories are combined into a unified formulation introducing the unified parameters. The Laplace and Hankel transforms are used to solve the problem. The boundary conditions of the problem give a set of four dual integral equations. The operators of fractional calculus are used to transform the dual integral equations into a Fredholm integral equation of second kind, which is then solved numerically. The infersions of double transforms have been done numerically and for numerical inversion of Laplace transform Bellman method is used. Numerical results for temperature, displacements, stress near the crack and stress intensity factor are shown graphically for classical coupled ther...

A Unified Generalized Thermoelasticity Formulation: Application to Penny-Shaped Crack Analysis

Abstract After almost twenty years of intense work on the celebrated LaAlO 3 /SrTiO 3 system, the recent discovery of a superconducting two-dimensional electron gas (2-DEG) in (111)-oriented KTaO 3 -based heterostructures injects new momentum to the field of oxides interface. However, while both interfaces share common properties, experiments also suggest important differences between the two systems. Here, we report gate tunable superconductivity in 2-DEGs generated at the surface of a (111)-oriented KTaO 3 crystal by the simple sputtering of a thin Al layer. We extract the superfluid stiffness of the 2-DEGs and show that its temperature dependence is consistent with a node-less superconducting order parameter having a gap value larger than expected within a simple BCS weak-coupling limit model. The superconducting transition follows the Berezinskii-Kosterlitz-Thouless scenario, which was not reported on SrTiO 3 -based interfaces. Our finding offers innovative perspectives for fundamental science but also for device applications in a variety of fields such as spin-orbitronics and topological electronics. 

https://www.nature.com/articles/s41467-022-32242-y.pdf

Sadek Hossain Mallik

Papers

Generalized thermoelastic functionally graded solid with a periodically varying heat source

Generalized thermoviscoelastic interaction due to periodically varying heat source with three-phase-lag effect

A two dimensional problem for a transversely isotropic generalized thermoelastic thick plate with spatially varying heat source

A Unified Generalized Thermoelasticity Formulation: Application to Penny-Shaped Crack Analysis

Superfluid stiffness of a KTaO3-based two-dimensional electron gas