三维修正高精度广义胞元法及其在复合材料宏细观弹塑性力学分析中的应用  

3D Modified High Fidelity Generalized Method of Cells and Its Application in Macro-Meso Scale Elastoplastic Mechanical Analysis of Composite Materials

作　　者：洪乔 王明路 胡延东[1,2] 冯淼林 HONG Qiao;WANG Minglu;HU Yandong;FENG Miaolin(Department of Engineering Mechanics,School of Naval Architecture,Shanghai Jiao Tong University,Shanghai 200240,China;State Key Laboratory of Ocean Engineering,Shanghai Jiao Tong University,Shanghai 200240,China)

机构地区：[1]上海交通大学船舶海洋与建筑工程学院工程力学系,上海200240 [2]上海交通大学海洋工程国家重点实验室,上海200240

出　　处：《力学季刊》2023年第2期269-280,共12页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(U2067220);中国核工业集团领创科研项目。

摘　　要：高精度广义胞元法(HFGMC)是模拟分析多尺度复合材料的有效技术方法.修正高精度广义胞元法(MHFGMC)的提出,在高精度广义胞元法位移插值函数基础上引入了二次耦合项,改善了剪切场计算精度不足的问题.本文提出了三维修正高精度广义胞元法理论,通过引入由局部坐标的高阶勒让德多项式表示的非弹性应变场和高阶的应力场,建立了三维复合材料弹塑性宏观应力应变关系式.通过对三维复合材料的宏观力学性能和细观应力场的预测,与有限元方法结果进行了对比验证.三维修正高精度广义胞元法结合局部坐标下塑性应变场,在不引入其他变量的情况下,不仅能够预测复合材料弹塑性应力应变响应,还能有效预测复合材料的细观剪切应力分布.The High Fidelity Generalized Method of Cells(HFGMC)is an effective technique to simulate and analyze multi-scale composites.The Modified High Fidelity Generalized Method of Cells(M-HFGMC)is proposed to increase the accuracy of shear field calculation,by introducing quadratic directional coupling terms based on the interpolation function of HFGMC.In this paper,the theory of three-dimensional M-HFGMC is proposed.By introducing the plastic strain field and high-order stress field represented by high-order Legendre polynomials in local coordinates,the elastoplastic macro stress-strain relationship of threedimensional composites is established.The predicted macro mechanical properties and micro stress field of 3D composites are compared with the results of the finite element method.The 3D M-HFGMC combined with the plastic strain field in local coordinates can not only predict the elastic-plastic stress-strain response of composite materials,but also effectively predict the micro shear stress distribution of composite materials without introducing other variables.

关 键 词：复合材料 三维修正高精度广义胞元法 插值函数 局部应力场 

分 类 号：O343.7[理学—固体力学]