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Open AccessArticle

Virtual Work Principle for Piezoelectric Semiconductors and Its Application on Extension and Bending of ZnO Nanowires

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Crystals 2023, 13(9), 1368; https://doi.org/10.3390/cryst13091368 - 12 Sep 2023

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Abstract

This paper presents the principle of virtual work (PVW) for piezoelectric semiconductors (PSs), which extends the piezoelectric dielectrics to involve the semiconducting effect. As an application of the PVW, a one-dimensional (1D) approximation theory for the extension and bending of PS nanowires is [...] Read more.

This paper presents the principle of virtual work (PVW) for piezoelectric semiconductors (PSs), which extends the piezoelectric dielectrics to involve the semiconducting effect. As an application of the PVW, a one-dimensional (1D) approximation theory for the extension and bending of PS nanowires is established by directly applying the PVW and Bernoulli–Euler beam theory with the aid of the second-order approximation of electrostatic potential. To illustrate the new model, the mechanical displacement, electrostatic potential, and concentration of electrons for extension and bending deformation of n-type ZnO nanowires are analytically determined. Additionally, numerical results show that, for n-type Zinc Oxide nanowires, the distribution of electrostatic potential is anti-symmetric along the thickness direction for extension deformation. In contrast, the bending deformation causes a symmetric distribution of electrostatic potential characterized by the zeroth-order and the second-order electrostatic potential. Furthermore, these two different deformations result in the redistribution of electrons. The electrostatic potential can be tuned by adjusting the amplitude of the applied mechanical load. Moreover, we find that the increase in doping level will reduce the magnitude of electrostatic potential due to the screening effect. The presented PVW provides a general approach to establishing structural theories and an effective way of implementing numerical methods. Full article

(This article belongs to the Special Issue Advances in Thin Structures and Materials Modelling)

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Open AccessArticle

Effect of Cu₂Te Back Surface Interfacial Layer on Cadmium Telluride Thin Film Solar Cell Performance from Numerical Analysis

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Crystals 2023, 13(5), 848; https://doi.org/10.3390/cryst13050848 - 20 May 2023

Cited by 1 | Viewed by 961

Abstract

Even though substantial advances made in the device configuration of the frontal layers of the superstrate cadmium telluride (CdTe) solar cell device have contributed to conversion efficiency, unresolved challenges remain in regard to controlling the self-compensation and minority carrier recombination at the back [...] Read more.

Even though substantial advances made in the device configuration of the frontal layers of the superstrate cadmium telluride (CdTe) solar cell device have contributed to conversion efficiency, unresolved challenges remain in regard to controlling the self-compensation and minority carrier recombination at the back contact that limits the efficiency. In this study, a SCAPS-1D simulator was used to analyze the loss mechanism and performance limitations due to the band-bending effect upon copper chloride treatment and subsequent Cu₂Te layer formation as the back contact buffer layer. The optimal energy bandgap range for the proposed back surface layer of Cu₂Te is derived to be in the range of 1.1 eV to 1.3 eV for the maximum conversion efficiency, i.e., around 21.3%. Moreover, the impacts of absorber layer’s carrier concentration with respect to CdTe film thickness, bandgap, and operational temperature are analyzed. The optimized design reveals that the acceptor concentration contributes significantly to the performance of the CdTe devices, including spectral response. Consequently, the optimized thickness of the CdTe absorber layer with a Cu-based back contact is found to be 2.5 µm. Moreover, the effect of temperature ranging from 30 °C to 100 °C as the operating condition of the CdTe thin-film solar cells is addressed, which demonstrates an increasing recombination tread once the device temperature exceeds 60 °C, thus affecting the stability of the solar cells. Full article

(This article belongs to the Special Issue Advances in Thin Structures and Materials Modelling)

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Open AccessArticle

Size-Dependent Buckling Analysis of Microbeams by an Analytical Solution and Isogeometric Analysis

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Crystals 2022, 12(9), 1282; https://doi.org/10.3390/cryst12091282 - 09 Sep 2022

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Abstract

This paper proposes an analytical solution and isogeometric analysis numerical approach for buckling analysis of size-dependent beams based on a reformulated strain gradient elasticity theory (RSGET). The superiority of this method is that it has only one material parameter for couple stress and [...] Read more.

This paper proposes an analytical solution and isogeometric analysis numerical approach for buckling analysis of size-dependent beams based on a reformulated strain gradient elasticity theory (RSGET). The superiority of this method is that it has only one material parameter for couple stress and another material parameter for strain gradient effects. Using the RSGET and the principle of minimum potential energy, both non-classical Euler–Bernoulli and Timoshenko beam buckling models are developed. Moreover, the obtained governing equations are solved by an exact solution and isogeometric analysis approach, which conforms to the requirements of higher continuity in gradient elasticity theory. Numerical results are compared with exact solutions to reveal the accuracy of the current isogeometric analysis approach. The influences of length–scale parameter, length-to-thickness ratio, beam thickness and boundary conditions are investigated. Moreover, the difference between the buckling responses obtained by the Timoshenko and Euler–Bernoulli theories shows that the Euler–Bernoulli theory is suitable for slender beams. Full article

(This article belongs to the Special Issue Advances in Thin Structures and Materials Modelling)

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Open AccessArticle

An Isogeometric Bézier Finite Element Method for Vibration Optimization of Functionally Graded Plate with Local Refinement

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Xing Wei

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Dongdong Liu

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Shuohui Yin

Crystals 2022, 12(6), 830; https://doi.org/10.3390/cryst12060830 - 11 Jun 2022

Cited by 1 | Viewed by 1319

Abstract

An effective free vibration optimization procedure in combination with the isogeometric approach (IGA), particle swarm optimization (PSO) and an integrated global and local parameterization is presented. The natural frequency of functionally graded (FG) plates is calculated by the IGA based on the Bézier [...] Read more.

An effective free vibration optimization procedure in combination with the isogeometric approach (IGA), particle swarm optimization (PSO) and an integrated global and local parameterization is presented. The natural frequency of functionally graded (FG) plates is calculated by the IGA based on the Bézier extraction of non-uniform rational B-splines (NURBS) with the cubic NURBS basis function. The material composition is assumed to vary only in the thickness direction, and the volumetric fraction is described by the NURBS basis function in light of the superior properties of NURBS curves. The volume fractions of the control points are then optimized by the PSO. In most of the previous work, the control points for the volume fraction are usually equally spaced, which is incapable of identifying the optimal location of the graded zones in most cases. To overcome this bottleneck, a novel local refinement strategy is proposed. The reliability and effectiveness of the proposed approach are demonstrated through several numerical examples. It is interesting to observe that the optimal results are sandwich or laminate plates, and few parameters are involved in the integrated global and local parameterization. Full article

(This article belongs to the Special Issue Advances in Thin Structures and Materials Modelling)

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Open AccessArticle

Variational Formulations and Isogeometric Analysis of Timoshenko–Ehrenfest Microbeam Using a Reformulated Strain Gradient Elasticity Theory

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Crystals 2022, 12(6), 752; https://doi.org/10.3390/cryst12060752 - 24 May 2022

Cited by 1 | Viewed by 1222

Abstract

This paper presents a novel non-classical Timoshenko–Ehrenfest beam model based on a reformulated strain gradient elasticity theory. The strain gradient effect, couple stress effect, and velocity gradient effect for vibration are included in the new model by only one material length scale parameter [...] Read more.

This paper presents a novel non-classical Timoshenko–Ehrenfest beam model based on a reformulated strain gradient elasticity theory. The strain gradient effect, couple stress effect, and velocity gradient effect for vibration are included in the new model by only one material length scale parameter for each. The variational formulation and Hamilton’s principle are applied to derive the governing equations and boundary conditions. Both an analytical solution and an isogeometric analysis approach are proposed for static bending and free vibration of the microbeam. A non-uniform rational B-splines (NURBS) isogeometric analysis with high-order continuity can effectively fulfill the higher derivatives of the displacement variables in the reformulated gradient beam model. Convergence studies and comparisons to the corresponding analytical solutions verify the model’s performance and accuracy. Finally, different boundary conditions, material length scale parameters, and beam thicknesses are investigated in order to certify the applicability of the proposed approach. Full article

(This article belongs to the Special Issue Advances in Thin Structures and Materials Modelling)

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Open AccessArticle

Bending and Wave Propagation Analysis of Magneto-Electro-Elastic Functionally Graded Porous Microbeams

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Crystals 2022, 12(5), 732; https://doi.org/10.3390/cryst12050732 - 19 May 2022

Cited by 4 | Viewed by 1236

Abstract

In this paper, a microstructure-dependent magneto-electro-elastic functionally graded porous (MEEFGP) beam model is proposed using a variational approach. To account for the microstructure effect, the extended modified couple stress theory is incorporated in the new model. In addition, the porosity variation of the [...] Read more.

In this paper, a microstructure-dependent magneto-electro-elastic functionally graded porous (MEEFGP) beam model is proposed using a variational approach. To account for the microstructure effect, the extended modified couple stress theory is incorporated in the new model. In addition, the porosity variation of the two-phase beam model through the thickness direction is also considered. The new developed model is verified in terms of its correctness with a FEM model. Based on the equations of motion and boundary conditions derived by Hamilton’s principle, the static bending and wave propagation behaviors of the new model are analytically determined. The results prove the existence of the microstructure effect and the magneto-electro-elastic multi-field coupling effect. There are significant differences between the new model and the classical model at the microscale. Moreover, the porosity also has an important influence on the mechanical properties of the new model. The results predicted by the new model can provide the theoretical basis for the design of microscale acoustic wave devices and micro-electro-mechanical systems. Full article

(This article belongs to the Special Issue Advances in Thin Structures and Materials Modelling)

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Open AccessArticle

A Multi-Objective Identification of DEM Microparameters for Brittle Materials

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Crystals 2022, 12(3), 387; https://doi.org/10.3390/cryst12030387 - 13 Mar 2022

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Abstract

The discrete element method (DEM) [...] Full article

(This article belongs to the Special Issue Advances in Thin Structures and Materials Modelling)

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Open AccessArticle

Receding Contact Problem of Multi-Layered Elastic Structures Involving Functionally Graded Materials

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Jie Yan

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Cong Wang

Crystals 2022, 12(3), 354; https://doi.org/10.3390/cryst12030354 - 06 Mar 2022

Cited by 1 | Viewed by 1557

Abstract

This paper studies a receding contact problem of a functionally graded layer laminate pressed against a functionally graded coated homogeneous half-plane substrate by a rigid flat indenter. The shear modulus of the functionally graded materials with a constant Poisson’s ratio is modeled by [...] Read more.

This paper studies a receding contact problem of a functionally graded layer laminate pressed against a functionally graded coated homogeneous half-plane substrate by a rigid flat indenter. The shear modulus of the functionally graded materials with a constant Poisson’s ratio is modeled by an exponential function which varies along the thickness direction. Both the governing equations and the boundary conditions of the receding contact problem are converted into a pair of singular integral equations using the Fourier integral transforms, which are numerically integrated by the Chebyshev–Gauss quadrature. The contact pressure and the contact size at both contact interfaces are eventually obtained iteratively, as developed from the steepest descent algorithm. Extensive parametric studies suggest that it is possible to regulate the contact pressure and contact size by constructing the top layer from a soft functionally graded material. Full article

(This article belongs to the Special Issue Advances in Thin Structures and Materials Modelling)

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