磁致伸缩复合材料有效性能的变分渐近细观力学模型  

A variational asymptotic micromechanics model for effective properties of magnetostrictive composites

作　　者：钟轶峰[1,2] 李潇[1,2] 梅宝平 周小平[1,2] ZHONG Yifeng LI Xiao MEI Baoping ZHOU Xiaoping(School of Civil Engineering, Chongqing University, Chongqing 400045, China Key Laboratory of New Technology for Construction of Cities in Mountain Area （Chongqing University）, Ministry of Education, Chongqing 400045, China)

机构地区：[1]重庆大学土木工程学院,重庆400045 [2]山地城镇建设与新技术教育部重点实验室(重庆大学),重庆400045

出　　处：《复合材料学报》2017年第3期574-581,共8页Acta Materiae Compositae Sinica

基　　金：国家自然科学基金(11272363;51279218);中央高校基本科研业务费专项基金(106112014CDJZR200017)

摘　　要：基于一种新颖的建模方法——变分渐近均匀化理论,建立了磁致伸缩复合材料的细观力学模型,以准确预测材料的有效属性和局部应力、磁通密度分布。从建立磁致伸缩复合材料的总磁焓入手,将总磁焓中的场变量精确解表示为平均值和波动函数之和。根据最小势能原理,利用细宏观尺度比作为小参数对约束条件下总磁焓求驻值(最小化)建立细观力学模型。为分析实际工程中的微观结构,利用有限元离散技术实现构建模型的数值模拟。CoFe_2O_4/环氧树脂复合材料数值算例结果表明:构建的模型可准确预测磁致伸缩复合材料的有效属性和局部场分布,并可扩展到其他多相复合材料的有效属性和局部场分析中。Based on a novel micromechanics modeling method—variational asymptotic homogenization theory,a micromechanics model for magnetostrictive composites was established to accurately predict the effective material properties and local distribution of stress and magnetic flux density.Starting from the total magnetic enthalpy of the magnetostrictive composites,the exact solutions of field variables in the magnetic enthalpy were expressed as the sum of mean values and the fluctuation function.According to the principle of minimum potential energy,the micromechanics model was formulated as a constrained stationary problem by taking advantage of the small parameters of the ratio of microscopic scale to macroscopic scale.To handle the microstructures in realistic engineering applications,the new model using the finite element discretization technique was implemented.The numerical example of CoFe2O4/epoxy composites show that the model can accurately predict the effective properties and the local field distribution of magnetostrictive composites,and can be extended to the effective properties and local field analysis of other multiphase composites.

关 键 词：磁致伸缩复合材料 细观力学 有限元 变分渐近法 均匀化 

分 类 号：TB330.1[一般工业技术—材料科学与工程]