Well conditioned mathematical modeling for homogenization of thermo-electro-mechanical behaviors of piezoelectric composites

Nada Tassi; Abderrahmane Bakkali; Nadia Fakri; Lahcen Azrar; Abdulmalik Aljinaidi

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Well conditioned mathematical modeling for homogenization of thermo-electro-mechanical behaviors of piezoelectric composites

机译：压电复合材料热电机行为均匀化的良好条件数学建模

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In the present paper, a mathematical modeling of effective properties of fully coupled thermo-electro-mechanical heterogeneous materials is elaborated. Constitutive equations combined with equilibrium equations lead to a coupled partial differential system. A methodological procedure is elaborated based on thermo-electro-elastic Green's functions, integral equations, and a micro-macro approach. Localization tensors are derived using the Mori-Tanaka mean-field assumptions and the fully coupled effective behavior is obtained through averaging techniques. Due to the large dispersion between elastic, dielectric, and piezoelectric coefficients ill-conditioned localization tensors are resulted. Block matrix decomposition is elaborated to overcome this drawback and the so-regularized localization tensor's inverses are used to get a well conditioned problem. Numerical computations are done in the general case of ellipsoidal inclusions and anisotropic behavior. Effective thermal conductivity and heat capacity coefficients are obtained with and without the heat strain effect for various volume fractions and types of inclusions. The global properties of thermo-electro-elastic reinforced composites are presented with respect to shape and volume fractions of inclusions.

机译：在本文中，阐述了完全耦合热电机异质材料的有效性能的数学建模。与平衡方程组合的本构方程导致耦合局部差分系统。基于热弹性绿色功能，整体方程和微宏方法来阐述方法学程序。使用Mori-Tanaka平均场假设来源的定位张量，通过平均技术获得完全耦合的有效行为。由于弹性，电介质和压电系数之间的较大分散，导致条件不良定位张量。阐明块矩阵分解以克服该缺点，并且使用所正常的定位张量的反转来获得良好的条件问题。在椭圆形夹杂物的一般情况下进行数值计算和各向异性行为。在各种体积分数和类型的夹杂物中获得有效的导热系数和热容量系数。相对于夹杂物的形状和体积分数给出了热电弹性增强复合材料的全局性质。

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来源
《Applied Mathematical Modelling》 |2021年第11期|276-293|共18页
作者
Nada Tassi; Abderrahmane Bakkali; Nadia Fakri; Lahcen Azrar; Abdulmalik Aljinaidi;
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作者单位

Research Center STIS M2CS Department of Applied Mathematics and Informatics ENSAM Mohammed V University in Rabat Morocco;

Department of Physics Faculty of Sciences of Tetouan Abdelmalek Essaadi University Tetouan Morocco MMC Faculty of Sciences and Techniques of Tangier Abdelmalek Essaadi University Tangier Morocco;

MMC Faculty of Sciences and Techniques of Tangier Abdelmalek Essaadi University Tangier Morocco;

Research Center STIS M2CS Department of Applied Mathematics and Informatics ENSAM Mohammed V University in Rabat Morocco Department of Mechanical Engineering Faculty of Engineering King Abdulaziz University Jeddah Saudi Arabia;

Department of Mechanical Engineering Faculty of Engineering King Abdulaziz University Jeddah Saudi Arabia;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Elliptic integral; Thermo-electro-elastic Green's functions; Block matrix decomposition; Effective thermo-electro-mechanical moduli; Mori-Tanaka approach; Thermal conductivity;

机译：椭圆形积分;热弹性绿色功能;块矩阵分解;有效的热电机械模量;森林田纳卡的方法;导热系数;

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1. An analytical model for predicting thermo-electro-mechanical response of 1-3 piezoelectric composites [J] . Sakthivel M., Arockiarajan A. Computational Materials Science . 2010,第4期

机译：1-3个压电复合材料的热机电响应预测模型
2. Effective piezoelectric coefficients of cement-based 2-2 type piezoelectric composites based on a multiscale homogenization model [J] . Fu Chuanqing, Wang Zhi, Jin Xianyu, Composite Structures . 2018,第JUNa期

机译：基于多尺度均质化模型的水泥基2-2型压电复合材料的有效压电系数
3. The micromechanics modeling piezoelectric composite materials by method of homogenization Mori Tanaka: study of piezo-composite SiO2/BaTiO3 [J] . Antonio Zecca Advanced Studies in Theoretical Physics . 2013,第15期

机译：田中森均化方法对压电复合材料的微观力学建模：压电复合SiO2 / BaTiO3的研究
4. Asymptotic derivation of a curved piezoelectric interface model and homogenization of piezoelectric composites [C] . S. T. GU, Q. C. HE, V. PENSEE, International Conference on Multifunctional Materials and Structures . 2008

机译：弯曲压电界面模型的渐近推导与压电复合材料的均匀化
5. Modeling elasto-plastic composite material behavior by meso-scale homogenization. [D] . Acton, Katherine A. 2009

机译：通过介观均质化对弹塑性复合材料的行为进行建模。
6. Modeling and Efficiency Analysis of a Piezoelectric Energy Harvester Based on the Flow Induced Vibration of a Piezoelectric Composite Pipe [O] . Maoying Zhou, Mohannad Saleh Hammadi Al-Furjan, Ban Wang 2018

机译：基于压电复合管流致振动的压电能量采集器建模与效率分析
7. Electromechanical response of (3–0,3–1) particulate, fibrous, and porous piezoelectric composites with anisotropic constituents: A model based on the homogenization method [O] . Iyer Sumantu, Venkatesh T.A. 2014

机译：具有各向异性成分的（3–0,3–1）颗粒，纤维和多孔压电复合材料的机电响应：基于均质化方法的模型

Well conditioned mathematical modeling for homogenization of thermo-electro-mechanical behaviors of piezoelectric composites

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