Dongze Yan¹, Jianxiang Wang², Lihua Shao^1,*

The International Conference on Computational & Experimental Engineering and Sciences, Vol.27, No.1, pp. 1-2, 2023, DOI:10.32604/icces.2023.09357

Abstract Non-uniform strains produce a localized break in the microscopic inverse symmetry of materials, which leads to the electromechanical coupling phenomenon known as flexoelectricity in all dielectric materials. However, the size-dependent flexoelectric effect typically only manifests at small scales. Creating a considerable flexoelectric output at the macroscopic scale remains a bottleneck. Micro- and nano-porous materials own a significant number of randomly distributed microscopic pores and ligamentous structures, which can deform non-uniformly under arbitrary forms of macroscopic loading. Moreover, since the small size effect of flexoelectricity, the entire flexoelectricity of the micro- and nano-porous materials will be much more significant than that… More >

Qiufeng Yang¹, Xudong Li², Zhaowei Liu³, Feng Jin^1,*, Yilin Qu^1,*

The International Conference on Computational & Experimental Engineering and Sciences, Vol.26, No.3, pp. 1-2, 2023, DOI:10.32604/icces.2023.09073

Abstract Compared to piezoelectric effects restricted to noncentrosymmetric crystalline structures, flexoelectric effects exist universally in all crystalline structures [1,2]. Meanwhile, some crystals, say silicon, are also semiconductive, which raises interest in studying the interactions between mechanical fields and mobile charges in semiconductors with consideration of piezoelectricity or flexoelectricity [3,4]. In order to explain these coupling effects, macroscopic theories on elastic semiconductors considering piezoelectricity or flexoelectricity were proposed by Yang and co-authors [5,6]. For piezoelectric semiconductors, the formulation of finite elements is relatively straightforward since the governing partial derivative equation (PDE) is twice-order. As for elastic semiconductors with consideration of flexoelectricity, it… More >

Hongxing Shang^1,*, Xu Liang¹, Shengping Shen¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.25, No.1, pp. 1-1, 2023, DOI:10.32604/icces.2023.09816

Abstract Flexoelectricity is the coupling effect of polarization and strain gradients, which tends to be more pronounced in thin films owing to size dependency. When subjected to in-plane compression, a filmsubstrate system will form complex wrinkle morphologies along with large-area and tunable strain gradients. The wrinkle-induced strain gradients can locally break the inversion symmetry of dielectrics and thus introduce flexoelectric polarization. Here, an electromechanical coupling model is developed to theoretically deal with flexoelectric polar patterns in wrinkled thin films. By analyzing the energy competition of elastic potential and electrostatic energy, the amplitude, wavelength, and critical strain of the wrinkles with flexoelectricity… More >

Miroslav Repka^1,*, Jan Sladek¹, Vladimir Sladek¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.23, No.1, pp. 10-10, 2021, DOI:10.32604/icces.2021.08308

Abstract The flexoelectric effect is investigated in quantum dot (QD) nano-sized structures. The lattice mismatch between QD and matrix results in non-uniform strains and presence of the strain gradients in the structure. The strain gradients induces the change of the polarization in QD structure as a consequence of the flexoelectric effect. When the dimensions of the QDs are of the same order of magnitude as the material length scale, gradient elasticity theory should be used to account for the size dependent of such nano-sized QDs. In this work the flexoelectric theory is applied for 3D analysis of QDs with the functionally… More >

Hamid Ghasemi¹, Harold S. Park², Xiaoying Zhuang^{3, 4, *}, Timon Rabczuk^{5, 6}

CMC-Computers, Materials & Continua, Vol.65, No.2, pp. 1157-1179, 2020, DOI:10.32604/cmc.2020.08358

Abstract Flexoelectricity is a general electromechanical phenomenon where the electric polarization exhibits a linear dependency to the gradient of mechanical strain and vice versa. The truncated pyramid compression test is among the most common setups to estimate the flexoelectric effect. We present a three-dimensional isogeometric formulation of flexoelectricity with its MATLAB implementation for a truncated pyramid setup. Besides educational purposes, this paper presents a precise computational model to illustrate how the localization of strain gradients around pyramidal boundary shapes contributes in generation of electrical energy. The MATLAB code is supposed to help learners in the Isogeometric Analysis and Finite Elements Methods… More >

Khader M. Hamdia², Hamid Ghasemi³, Xiaoying Zhuang^4,5, Naif Alajlan¹, Timon Rabczuk^1,2,*

CMC-Computers, Materials & Continua, Vol.59, No.1, pp. 79-87, 2019, DOI:10.32604/cmc.2019.05882

Abstract In this study, machine learning representation is introduced to evaluate the flexoelectricity effect in truncated pyramid nanostructure under compression. A Non-Uniform Rational B-spline (NURBS) based IGA formulation is employed to model the flexoelectricity. We investigate 2D system with an isotropic linear elastic material under plane strain conditions discretized by 45×30 grid of B-spline elements. Six input parameters are selected to construct a deep neural network (DNN) model. They are the Young's modulus, two dielectric permittivity constants, the longitudinal and transversal flexoelectric coefficients and the order of the shape function. The outputs of interest are the strain in the stress direction… More >

Ying Xu¹, Shuling Hu¹, Shengping Shen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.91, No.5, pp. 397-408, 2013, DOI:10.3970/cmes.2013.091.397

Abstract Flexoelectricity presents a strong size effect, and should not be ignored for nanodevices. In this paper, the flexoelectric effect is taken into account to investigate the electrostatic potential distribution in a bent flexoelectric semiconductive nanowire, and the numerical solution is obtained by using the finite difference method. The effect of donor concentration on the electrostatic potential are also investigated. The results show that, the flexoelectricity increases the value of the voltage on the cross section. The flexoelectric effect is varied with the size, i.e. when the radius of the nanowire is small the flexoelectric effect is significant. It is also… More >

Jianfeng Lu¹, Xu Liang^1,2, Shuling Hu^1,2

CMC-Computers, Materials & Continua, Vol.45, No.3, pp. 145-162, 2015, DOI:10.3970/cmc.2015.045.145

Abstract Flexoelectricity phenomenologically describes the universal electromechanical coupling effect between electric polarization and strain gradient, and electric field gradient and elastic strain. In contrast to piezoelectricity which is invalid in materials with inversion symmetry, flexoelectricity exists, commonly, in all solid dielectrics. In this paper, a summary of the research on flexoelectricity is presented to illustrate the development of this topic. Flexoelectricity still have many open questions and unresolved issues in the developing field, although it has attracted a surge of attention recently. Here we review the theoretical investigations and experimental studies on flexoelectricity, and the aim of the current paper is… More >