A. R. El-Dhaba

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• Professor
• Departement of Mathematics and computer science at Damanhour University

The description of the mass transfer mechanisms in various physical and engineering fields, e.g., Li-ion battery, is of a significant importance for optimizing their performance. The present work introduces a comparative study describing the different responses of a perfectly elastic material when different non-Fickian diffusion situations are cons...

In this article, we present a detailed variational formulation to study and analyze the geometrically nonlinear behavior of elastic materials at small scales, where the classical theory of elasticity becomes inadequate. The presented technique is based on the variation of the internal energy of the elastic material and the virtual work of the exter...

In this paper, we provide detailed variational formulations for the reduced micromorphic model in rectangular and cylindrical coordinates. In these formulations, the material is modeled as consisting of deformable particles that exhibit microstrain and macroscopic strain fields. This microstrain field is independent of the macroscopic strain field...

A nonlinear phenomenological model of flexoelectricity in thermoelastic solids is presented within the frame of continuum mechanics and extended thermodynamics, incorporating the quasi-electrostatic approximation where the time derivative of the electric displacement vector can be neglected in Maxwell–Ampère’s law. An expression for the energy flux...

We study the flexoelectric effect induced in an infinite strip of a dielectric material, due to an applied shear deformation at the upper surface, while the lower surface is fixed. The model incorporates dynamic spontaneous polarization, flexocoupling deformation, and microinertia effects to evaluate these effects combined. The variation of the Ham...

This work investigates the Flamant-Boussinesq problem for a half-space made of a homogeneous and isotropic dielectric material. The dynamical flexoelectric effect and the dynamical flexocoupling between displacement and polarization, due to mechanical and electrical states, are taken in consideration. The mechanical loading is taken as a wave of a...

Flexoelectricity is a nanoscale phenomenon in dielectric crystals, where the mechanical loads resulting from the first strain gradient shares producing electricity. In this work, we present a numerical investigation for the plane strain problem of the dynamical flexoelectric effect in isotropic dielectrics. A surface loading based on the Sinc funct...

The present work considers a two-dimensional (2D) heat conduction problem in the semi-infinite domain based on the classical Fourier model and other non-Fourier models, e.g., the Maxwell-Cattaneo-Vernotte (MCV) equation, parabolic, hyperbolic, and modified hyperbolic dual-phase-lag (DPL) equations. Using the integral transform technique, Laplace, a...

A simple expansion method is used to solve certain regular, uncoupled plane problems of thermoelastostatics for long rods in a rectangle. These solutions are exact when the involved boundary conditions are in polynomial form. A particular case involving heat source in the bulk and surface distributions of temperature and pressures is considered for...

A 2D first order linear system of partial differential equations of plane strain thermoelasticity within the frame of extended thermodynamics is presented and analyzed. The system is composed of the equations of classical thermoelasticity in which displacements are replaced with velocities, complemented with Cattaneo evolution equation for heat flu...

The description of the mass transfer mechanisms in various physical and engineering fields, e.g., Li-ion battery, is of a significant importance for optimizing their performance. The present work introduces a comparative study describing the different responses of a perfectly elastic material when different non-Fickian diffusion situations are cons...

A one-dimensional problem of wave propagation in phononic materials is solved under the reduced micromorphic model introduced recently. An efficient technique is used for the solution, based on one-sided Fourier transform. This allows obtaining an exact solution in closed form, which can be utilized to check approximate solutions obtained by other...

The present work proposes a unified model for studying the dynamical flexoelectricity by including effects of the micro-inertia, the dynamical polarization, and the dynamical flexocoupling between displacement and polarization upon the mechanical and electrical state of the dielectric material. The mathematical description is presented in the frame...

This paper aims to demonstrate how the flexoelectric effect can be incorporated into the reduced micromorphic model, where materials can be designed and fabricated with complex structures that possess electric properties. These kinds of materials are known as composite metamaterials with properties that do not exist in nature such as the flexoelect...

In this article, we introduce a complete set of constitutive relations and field equations for the linear reduced micromorphic model. We further investigate the internal variables and their relationship in the case of two-dimensional (2D) wave propagation. The dynamic response is investigated for composite materials, which is due to an external wav...

A plane within reduced micromorphic model subjected to external static load is studied using the finite element method. The reduced micromorphic model is a generalized continuum theory which can be used to capture the interaction of the microstructure. In this approach, the microstructure is homogenized and replaced by a reduced micromorphic materi...

We investigate linear, thermoelastic wave propagation in a layered piezoelectric material composed of a slab bonded to a half-space substrate of a dissimilar material, within dual-phase-lag model and under thermomechanical loads. One of the aims of the present work is to formulate a set of boundary conditions that is compatible with the field equat...

The static bending and the flexoelectric effect induced in an anisotropic dielectric nano-plate are studied in the frame of the simplified strain gradient elasticity theory (SSGT). The Kirchhoff plate theory is considered for a simply supported nano-plate loaded by a uniformly distributed constant forces at its upper surface. The displacement and t...

The simplified strain gradient elasticity theory (SSGT) is used to study the induced flexoelectric effect in an anisotropic dielectric beam due to bending. The beam cross-sections are uniform with internal cubic structure symmetry. Three different cases are studied in the context of the Timoshenko beam theory. In the first two cases, the simply sup...

The reduced micromorphic model (RMM) is used to study the effect of the applied force on a hemisphere made of phononic crystals that belongs to the metamaterials group. The strain tensor, the micro-strain tensor and the coupling between them are the kinematic relations used to measure the deformation and micro-deformation of the representative volu...

In this article, we study the flexoelectricity induced in a prismatic anisotropic bar due to torsion. The simplified strain gradient elasticity theory is considered in this study. The bar is uniform, that is, any cross-section of the bar has a rectangular shape with cubic internal structure symmetry. The traction and higher traction forces effect o...

In this study, the responsive-behavior of auxetic and non-auxetic polymer gels to mechanical loads is modeled. The elastic deformation patterns of gels with different structural and mechanical properties are depicted. The first strain gradient theory is employed to model the random structure of crosslinked polymer gels. The applicability of the fir...

In this study, the responsive-behavior of an anisotropic, elastic, flexoelectric material with cubic internal structure to mechanical loads is formulated and examined. The elastic deformation and spontaneous polarization patterns of these materials, as well as the mechanical properties are described. The first strain gradient theory is employed to...

The equations of generalized piezo-thermoelasticity within the frame of dual-phase-lag model are used to study the effect of gravitational force on the behavior of a half-space. Analytic expressions for the displacement components, temperature, stress and strain tensors components are obtained using normal mode analysis. Numerical results for the f...

This article is concerned with a strain gradient theory for thermoelastic diffusion materials. The work is motivated by the recent interest in the study of gradient theories and increasing use of materials which possess thermal and mass diffusion variations. First, we establish the basic equations of the nonlinear strain gradient theory for thermoe...

We investigate a nonlinear, one-dimensional problem of thermoelectroelasticity with thermal relaxation and in quasi-electrostatics. The system of basic equations is a restriction to one spatial dimension of that proposed earlier in Abou-Dina et al (2017). This model is based on the introduction of the heat flow vector as an additional state variabl...

Considering a simple form of the strain energy functional for anisotropic elastic materials as proposed with Lazar and Kirchner (Int J Solids Struct 44(7–8):2477–2486, 2007), Lazar and Po (Eur J Mech A Solids 50:152–162, 2015a), (Phys Lett A 379:1538–1543, 2015b), depending on the strain tensor and its derivatives. The field equations, boundary con...

A model of nonlinear thermo-electroelasticity is presented within the frame of extended thermodynamics and in the quasi-electrostatic regime. The model is based on a Cattaneo-type evolution equation and includes several couplings between the mechanical, thermal and electric fields, and may therefore be used to describe a broad range of interactions...

Semi-inverse method is used to find analytical solutions of squared two-dimensional second gradient linear homogeneous and isotropic materials. Such semi-inverse method is similar to that used by Saint-Venant to solve the omonimus problem for cylindrical three-dimensional first gradient linear homogeneous and isotropic materials. Two examples are a...

This paper deals with the two-dimensional, non-homogeneous boundary value problem for static, isotropic and thermoelastic material occupying an infinitely long cylinder with a rectangular cross-section. The cylinder is surrounded by a given temperature and subjected to variable pressures at its boundaries. We deal with static, uncoupled, linear ther...

We find the deformation and stresses in an infinite rod of an electric conducting material with square normal cross section, carrying uniform electric current and subjected to an external, initially uniform magnetic field. The complete solution of the uncoupled problem is obtained using a boundary integral method. The results are discussed in detai...

A boundary integral method is used to obtain the numerical solution of a problem of thermoelasticity for a long cylinder with square cross-section subject to an external pressure and a heat source inside the cylinder. An ambient temperature and a Robin radiation condition are considered. The corners are smoothened suitably. Quantities of practical...

In this paper, we introduce a simple method to solve a static, plane boundary value problem in elasticity for an isotropic rectangular region. The method depends on finite Fourier transform to transfer the biharmonic equation to a nonhomogeneous ordinary differential equation of the fourth order. Also, by transferring the boundary conditions, one ca...

We find the deformation and stresses occurring in an infinite rod of a magnetizable material with square normal cross-section, subjected to an external, transversal and initially uniform magnetic field of arbitrary direction. The numerical solution of the uncoupled problem is obtained using a boundary integral method. This yields the boundary value...

The static, plane uncoupled problem of thermo-magnetoelasticity for a long elastic cylinder of square cross-section carrying a steady, axial electric current is investigated numerically by a boundary integral method. The lateral surface of the cylinder may be subjected, additionally, to an external distribution of pressures. The deformation is indu...

The static, plane uncoupled problem of thermo-magnetoelasticity for a long elastic cylinder of square cross-section carrying a steady, axial electric current is investigated numerically by a boundary integral method. The lateral surface of the cylinder may be subjected, additionally, to an external distribution of pressures. The deformation is indu...

The static, uncoupled problem of thermomagnetoelasticity for long cylinders carrying a steady, axial current is investigated in stresses within a numerical approach by a boundary integral method in terms of real harmonic functions.This is the numerical realization of the field equations, boundary conditions and other relations presented in [1]. The...

A We use a boundary integral method to obtain the numerical so-lution of the first fundamental problem of elasticity for a long cylinder with Cassini curve cross-section under a uniformly distributed pressure on the bound-ary.

A boundary integral method earlier proposed by two of the authors is used to solve a problem of uncoupled magneto- thermoelasticity for an infinite, elliptical cylindrical conductor carrying a steady axial, uniform electric current. The cylin- der is placed in a variable ambient temperature and is allowed to exchange heat with the surrounding medium...

We solve the first fundamental problem of elasticity for an infinite ,elliptical cylinder of amagnetizable material, subjected to anexternal, initially uniform magnetic field and to a uniform bulk heating. The cylinder is placedin a variable ambient temperature.The complete solution ofthe uncoupled problem isobtainedusing a bound-ary integral metho...

A boundary integral method earlier proposed by two of the authors [M. S. Abou-Dina and A. F. Ghaleb, Int. J. Appl. Electromagnet. Mech. 11, 185–201 (2000)] is used to solve a problem of uncoupled magnetothermoelasticity for an infinite elliptical cylindrical conductor carrying a steady axial uniform electric current. The cylinder is placed in a var...

A boundary integral method earlier proposed by two of the authors is used to solve a problem of uncoupled magneto-thermoelasticity for an infinite, elliptical cylindrical conductor carrying a steady axial, uniform electric current. The cylinder is placed in a variable ambient temperature and is allowed to exchange heat with the surrounding medium. T...

A boundary integral method is used to solve the problem of plane, uncoupled linear thermoelasticity with heat sources for an infinite cylinder with elliptical cross section, subjected to a uniform pressure and to a thermal radiation condition on its boundary. The complete solution of the problem is obtained. The results reduce to those for the infi...