A unified model for the dynamical flexoelectric effect in isotropic dielectric materials

Awad, Emad; Dhaba, A. R. El; Fayik, Mohsen A.

doi:10.1016/j.euromechsol.2022.104618

Cited by 13 publications

(22 citation statements)

References 68 publications

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“…The case (a, c), in which the micro-inertia is disregarded, has substantially a magnitude greater than the case (b, d) as h / l has a certain value, and the longitudinal propagation of the electric waves inside the dielectric medium occurs on a wider range at h / l = 0 , compared with the case h / l = 0 . 5 . This result has been emphasized in many works; in particular, we refer to the recent one-dimensional case [50] which based on utilizing the Laplace transform technique. Here, we generalize this result to the two-dimensional case.…”

Section: Numerical Results and Discussionmentioning

confidence: 95%

“…The governing equations for the dynamical flexoelectric model of an isotropic homogeneous dielectric crystal occupying the arbitrary domain ( x i , t ) ∈ V × ( 0 , ∞ ) associated with the boundary conditions on the surface x s ∈ S surrounding the volume V , consist of, see Awad et al, [50]…”

Section: Dynamical Flexoelectric Modelmentioning

confidence: 99%

“…Wang and Li [49] investigated the static/dynamic flexoelectric and surface effects on the natural frequencies for free vibration of circular and annular nano plates. Recently, Awad et al [50] presented a unified model for the description of the dynamical flexoelectric phenomenon in dielectrics, taking into consideration inertial and micro-inertial effects, dynamical polarization, and dynamical flexocoupling between displacement and polarization. They generalized Qi’s [47] derivation by including the external agents within the boundary conditions and providing a system of equations including the Mindlin’s Form II of strain gradient theory.…”

Section: Introductionmentioning

confidence: 99%

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On the plane strain problem of dynamical flexoelectric effect in dielectrics subject to Sinc-shaped surface loading

Fayik

Dhaba

Awad

2023

Mathematics and Mechanics of Solids

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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 function, that is, sincπ(x), with a temporal exponentially decay, is applied to the upper surface of a semi-infinite dielectric crystal. Two cases for the electric potential are considered: (1) Open circuit, in which there is zero charge on the terminals; and (2) Short-circuit, where there is a given value for the potential of the terminals. This type of surface loading is often used in applications such as seismic analysis and electrical engineering, especially signal processing and digital signal processing. Also, it can be used to model other types of dynamic loads, such as wind or wave loads. Furthermore, this setting generates a two-dimensional formulation, known as the plane strain problem. Laplace and Fourier transform techniques are employed for solving the field equations. Suitable numerical techniques are implemented to present the solution to the physical domain. We choose the Strontium Titanate material (SrTiO3) for the two-dimensional simulation. Discussion for the behavior of the dynamical polarization, electric field, electric potential, and stresses is provided in the two-dimensional setting. Effects of the model parameters on electricity generation and behavior are studied.

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Section: Numerical Results and Discussionmentioning

confidence: 95%

Section: Dynamical Flexoelectric Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the plane strain problem of dynamical flexoelectric effect in dielectrics subject to Sinc-shaped surface loading

Fayik

Dhaba

Awad

2023

Mathematics and Mechanics of Solids

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“…In this section, we use two numerical techniques to bring the solution ( 29)- (30) to the real domain. At first, we invert Laplace transform by employing the Durbin series [10,28,47,48] θ (x, y, t)…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

A comparative numerical study of a semi-infinite heat conductor subject to double strip heating under non-Fourier models

2022

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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, and Fourier transforms, we provide a solution of the problem (Green’s function) in Laplace domain. The thermal double-strip problem, allowing the wave interference within the heat conductor, is considered. A numerical technique, based on the Durbin series for inverting Laplace transform and the trapezoidal rule for calculating an integral form of the solution in the double-strip case, is adopted to recover the solution in the physical domain. Finally, discussions for different non-Fourier heat transfer situations are presented. We compare among the speeds of hyperbolic heat transfer models and shed light on the concepts of flux-precedence and temperature-gradient-precedence, hallmarks of the lagging response idea. Otherwise, we emphasize the existence of a relationship between the waves speed and the time instant of interference onset, underlying the five employed heat transfer models.

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“…In this section we bring the solutions of concentration and volumetric strain to the real domain by inverting numerically the Laplace transform in equations ( 34)-( 35), [16,[48][49][50]. The diffusion of lithium ions in silicon anode is chosen for this simulation.…”

Section: Resultsmentioning

confidence: 99%

Diffusion-induced stresses due to an impulsive mass source under non-Fickian mass transfer models

Fayik

Dhaba

Awad

2022

Preprint

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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 considered. The uncoupled theory of elastic diffusion, in which the diffusion process is described by non-Fickian laws, such as Cattaneo, Jeffreys-type and Burgers-type constitutive laws, is employed in this modeling. Diffusion of lithium ions inside the silicon anode is one of the physical situations in which diffusion-induced stresses may be significant. An impulsive initial value problem, consisting of an initial lithium ions amount starts impulsively to diffuse over the entire space of a silicon material, is considered. Direct approach together with Laplace and exponential Fourier transforms techniques are employed to obtain the solution in the Laplace transformed domain. Inverse Laplace transform is computed numerically to obtain the solution in the physical domain. Comparisons among the material responses to different diffusion regimes are presented.

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A unified model for the dynamical flexoelectric effect in isotropic dielectric materials

Cited by 13 publications

References 68 publications

On the plane strain problem of dynamical flexoelectric effect in dielectrics subject to Sinc-shaped surface loading

On the plane strain problem of dynamical flexoelectric effect in dielectrics subject to Sinc-shaped surface loading

A comparative numerical study of a semi-infinite heat conductor subject to double strip heating under non-Fourier models

Diffusion-induced stresses due to an impulsive mass source under non-Fickian mass transfer models

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