Semi-inverse method for a plane strain gradient orthotropic elastic rectangle in tension

Mathematics and Mechanics of Solids

Awad

2023

Self Cite

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.

Section: Dynamical Flexoelectric Modelmentioning

confidence: 99%

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

Fayik

Mathematics and Mechanics of Solids

Awad

2023

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“…According to 22 , 28 – 30 , the free energy in RMM is taken in the form where and are the elastic moduli of the microstructure, and are the elastic moduli of the matrix material between two particles, and are two elastic moduli accounting for the coupling between the micro-strain and the macro-strain, and and are length scale parameters. The free energy function in two dimensions can be written in a matrix form as 35 …”

Section: The Rmm In Cartesian Coordinatesmentioning

confidence: 99%

Analysis of planes within reduced micromorphic model

Mousavi

2021

Sci Rep

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 material model. Then, avoiding the complexity of the microstructure, the reduced micromorphic model is analyzed to reveal the interaction of the microstructure and the external loading. In this study, the three-dimensional formulation of the reduced micromorphic model is dimensionally reduced to address a plane under in-plane external load. The governing system of partial differential equations with corresponding consistent boundary conditions are discretized and solved using the finite element method. The classical and nonclassical deformation measures are then demonstrated and discussed for the first time for a material employing the reduced micromorphic model.

“…The wedge forces. Following Placidi et al [33], Andreaus et al [34], Placidi et al [35], Placidi and El Dhaba [36], and [37], we can represent the wedge forces as follows…”

Section: The Field Equations and Boundary Conditionsmentioning

confidence: 99%

“…El Dhaba [37] introduced generalization of the method used by Vardoulakis and Sulem [38] and Exadaktylos and Vardoulahis [39] to solve the plane problem in a strain gradient orthotropic elastic rectangle in tension.…”

Section: Solution For the Field Equationsmentioning

confidence: 99%

See 1 more Smart Citation

Flexoelectric effect induced in an anisotropic bar with cubic symmetry under torsion

Mathematics and Mechanics of Solids

Gabr

2019

Self Cite

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 on the deflection and spontaneous polarization of the bar with different boundary conditions are also discussed. The induced wedge forces are also considered during this study. The magnesium oxide (MgO) physical quantities values are chosen to present a numerical example as one of the practical applications of the problem. The results are discussed and introduced graphically. The most interesting finding in this study is the wedge force directions. When the displacements inside the cross-section of the bar are uniformly distributed, the resultant wedge forces have the same inclination with the cross-section boundary. Meanwhile, if the displacement is not uniformly distributed, the wedge force inclinations with the cross-section boundary are not equal.