基于直接多层有限元模拟的二维压电材料的力电性能研究

PDF(2949 KB)

振动与冲击 ›› 2024, Vol. 43 ›› Issue (21) : 46-54.

论文

基于直接多层有限元模拟的二维压电材料的力电性能研究

陈磊磊1,2，王佳晨2，李帅3，陈攀1

作者信息 +

Electro-mechanical performance of 2D piezoelectric material based on direct multi-layer finite element simulation

CHEN Leilei1,2, WANG Jiachen2, LI Shuai3, CHEN Pan1

Author information +

文章历史 +

摘要

本文采用直接多层有限元模拟（Direct FE2）方法，模拟非均质材料的力-电耦合问题。该方法突破了传统并发多尺度分析方法必须依赖控制脚本进行宏—微观跨尺度信息传递的固有框架。首先，通过有限元的控制方程和并发多尺度分析所需的Hill-Mandel均质化条件，推导出可直接实现宏观与微观信息实时传递的多节点约束（MPCs）方程。其次，将并发多尺度分析所需的宏观结构模型和代表体积单元（RVE）模型合并为一个有限元模型，避免了在两个尺度之间的重复数据传输。最后，通过算例验证本文算法的正确性和有效性。

Abstract

This paper adopts the Direct FE2 method for simulating the electromechanical coupling problem of heterogeneous materials. This method breaks through the inherent framework of traditional concurrent multiscale analysis methods that rely on control scripts for macro-to-micro across scale information transfer.It derives the multi-point constraint (MPCs) equations that enable the direct real-time transfer of macroscopic and microscopic information by utilizing the finite element control equations and the Hill-Mandel homogenization conditions required for concurrent multiscale analysis. This method combines the macroscopic structural model and the Representative Volume Element (RVE) model required for concurrent multiscale analysis into a single finite element model, eliminating the need for repetitive data transfer between the two scales. Finally, the correctness and effectiveness of the proposed algorithm are verified through several numerical examples.

导出引用

陈磊磊1, 2, 王佳晨2, 李帅3, 陈攀1. 基于直接多层有限元模拟的二维压电材料的力电性能研究[J]. 振动与冲击, 2024, 43(21): 46-54

CHEN Leilei1, 2, WANG Jiachen2, LI Shuai3, CHEN Pan1. Electro-mechanical performance of 2D piezoelectric material based on direct multi-layer finite element simulation[J]. Journal of Vibration and Shock, 2024, 43(21): 46-54

参考文献

[1] Shen D, Wen J, Ma J, et al. A novel linear inertial piezoelectric actuator based on asymmetric clamping materials[J]. Sensors and Actuators A: Physical, 2020, 303: 111746.
[2] Yao D, Cui H, Hensleigh R, et al. Achieving the upper bound of piezoelectric response in tunable, wearable 3D printed nanocomposites[J]. Advanced Functional Materials, 2019, 29(42): 1903866.
[3] Chen P, Liu J, Zhang H, et al. Increase of capacitance of thick dielectrics by fringe effect[J]. IEEE Transactions on Dielectrics and Electrical Insulation, 2019, 26: 1716-1719.
[4] Chen P, Zhou W, Zhang H, et al. Large Thermal–Electrical Response and Rectifying Conduction Behavior in Asymmetrically Reduced Ferroelectric Ceramics[J]. ACS Applied Electronic Materials, 2019, 1.
[5] 梅杰,宋钢,李立杰,等.压电材料平面Ⅰ型裂纹模拟仿真分析[J].起重运输机械,2023,(17):58-65.
MEI J, SONG G, LI L J, et al. Piezoelectric Material Plane I-Type Crack Modeling and Simulation Analysis[J]. Lifting the transport machinery, 2023, (17): 58-65.
[6] 张璇,刘海涛.负泊松比圆弧蜂窝压电超材料的力电性能研究[J].燕山大学学报,2021,45(05):424-429.
ZHANG X, LIU H T. Study on electromechanical properties of arc honeycomb piezoelectric metamaterials with negative Poisson's ratio[J]. Journal of Yanshan University, 2021, 45(05): 424-429.
[7] 周标,柯宏威,陈旭等.基于压电分支阻尼技术的航空发动机叶片振动抑制方法研究[J].振动与冲击,2020,39(01): 209-215.
ZHOU B, KE H W, CHEN X, et al. Aero-engine blade vibration suppression method based on piezoelectric shunt damping technique[J]. Journal of Vibration and Shock, 2020, 39(01): 209-215.
[8] 张浩,李俊杰,康飞.基于压电智能骨料的混凝土梁裂缝损伤监测研究[J].振动与冲击,2021,40(21):215-222.
ZHANG H, LI J, KANG F. Crack damage monitoring of concrete beam based on piezoelectrie intelligent aggregate[J]. Journal of Vibration and Shock, 2021, 40(21): 215-222.
[9] 胡统号,沈纪苹,姚林泉.弹性边界径向功能梯度压电环板面内振动[J].振动与冲击,2018,37(08):225-237.
HU Tonghao,SHEN Jiping,YAO Linquan.In-plane vibration of radial functional graded piezoelectric annular plates with elastic boundary[J]. Journal of Vibration and Shock,,2018,37(8):225-237.
[10] 何晋丞,陈国平,谭星,等.压电陶瓷支承对梁的横向振动与支反力抑制作用[J].振动与冲击,2022,41(23):257-264+299.
HE J C， CHEN G P, TAN X, et al. GuopingSuppressing action of piezoelectric ceramic support ontransverse vibration and support reaction of beam[J]. Journal of Vibration and Shock, 2022, 41(23): 257-264+299.
[11] 郭攀,卫洪涛,武文华,等.层合压电材料冲击问题的时域间断Galerkin有限元方法求解[J].振动与冲击,2018,37(24): 195-200.
GUO P, WEI H T, WU W H, et al. A time discontinuous Galerkin finite element method for the solution of impact problemof laminated piezoelectric material[J]. Journal of Vibration and Shock, 2018, 37(24): 195-200.
[12] Haertling G H. Ferroelectric Ceramics: History and Technology[J]. Journal of the American Ceramic Society, 1999, 82(4): 797-818.
[13] Mackrell A. Multiscale composite analysis in Abaqus: Theory and motivations[J]. Reinforced Plastics, 2017, 61(3): 153-156.
[14] Bishay P L, Dong L, Atluri S N. Multi-physics computational grains (MPCGs) for direct numerical simulation (DNS) of piezoelectric composite/porous materials and structures[J]. Computational Mechanics, 2014, 54(5): 1129-1139.
[15] Lenglet E, HL, Adky Hennion A C, Debus J C. Numerical homogenization techniques applied to piezoelectric composites[J]. The Journal of the Acoustical Society of America, 2003, 113(2): 826-833.
[16] Otero J, Castillero J, Ramos R. Homogenization of heterogeneous piezoelectric medium[J]. Mechanics Research Communications, 1997, 24(1): 75-84.
[17] Ammosov D, Vasilyeva M, Nasedkin A, et al. Generalized Multiscale Finite Element Method for piezoelectric problem in heterogeneous media[J]. Engineering Analysis with Boundary Elements, 2022, 135: 12-25.
[18] Fish J, Wagner G, Keten S. Mesoscopic and multiscale modelling in materials[J]. Nature Materials, 2021, 20: 774-786..
[19] HernÁndez J, Oliver J, Oliver A E, et al. High-performance model reduction techniques in computational multiscale homogenization[J]. Computer Methods in Applied Mechanics and Engineering, 2014, 276: 149-189.
[20] Smit R J, Brekelmans W M, Meijer H E. Prediction of the mechanical behavior of nonlinear heterogeneous systems by multi-level finite element modeling[J]. Computer methods in applied mechanics and engineering, 1998, 155(1-2): 181-192.
[21] Feyel F, Chaboche J L. FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials[J]. Computer methods in applied mechanics and engineering, 2000, 183(3-4): 309-330.
[22] Feyel F. A multilevel finite element method FE2 to describe the response of highly non-linear structures using generalized continua[J]. Computer Methods in Applied Mechanics and Engineering, 2003, 192(28): 3233-3244.
[23] Tikarrouchine E, Benaarbia A, Chatzigeorgiou G, et al. Non-linear FE2 multiscale simulation of damage, micro and macroscopic strains in polyamide 66-woven composite structures: Analysis and experimental validation[J]. Composite Structures, 2021, 255: 112926.
[24] Tikarrouchine E, Chatzigeorgiou G, Chatzigeorgiou F, et al. Three-dimensional FE2 method for the simulation of non-linear, rate-dependent response of composite structures[J]. Composite Structures, 2018, 193: 165-179
[25] Tan V B C, Raju K, Lee H P. Direct FE2 for concurrent multilevel modelling of heterogeneous structures[J]. Computer Methods in Applied Mechanics and Engineering, 2020, 360: 112694.