【作者】 李潇；

【导师】 钟轶峰； 陈谱；

【作者基本信息】 重庆大学 ， 工程硕士（建筑与土木工程领域）（专业学位）， 2017， 硕士

【摘要】 磁致伸缩复合材料具有损失耗能小、磁场作用下响应速度快、产生应变明显、适用于各种工作环境等优点,采用Terfenol-D制作的稀土磁致伸缩换能器在桥梁结构健康监测中可有效的进行发射和声波采集,具有出色的应用效果。传统磁致伸缩材料存在受拉易脆断、诱导应变需大磁场和产生较强的涡流效应、频率范围等固有缺陷,限制了其性能发挥,引入聚合物或金属粘合剂制备的磁致伸缩复合材料可显著改善材料的脆性和提高工作频率。对复合材料实际使用过程中的力学性能（如变形失效和损伤机理等）进行研究分析和优化设计的过程,必须依靠其有效属性。然而复合材料存在着各向异性、微观非均匀性、组分性质不同等特点,同时实验的高成本和局限性特征、结果的离散性和复杂性现象等因素给准确预测有效属性带来诸多干扰。因此,为更好地设计和制备磁致伸缩复合材料,需对其有效属性进行精确有效的预测。传统分析手段依赖于太多预先假设（如RVE几何形状、材料性质、夹杂大小和形状等）且后期均匀化处理会对分析结果造成难以避免的误差,且未考虑局部场分布。使用传统有限元法建立完整结构的微观模型往往还会带来巨大繁琐的工作量。因此需要一套新的通用分析理论同时对材料宏观有效属性和局部场变量进行预测。本文得到国家自然科学基金面上项目:变分渐近精细模型及在功能梯度压电层合板壳多场耦合分析中的应用（资助编号:11272363）的资助。采用一种新颖的建模方法-变分渐近均匀化理论建立磁致伸缩复合材料的细观力学模型进行磁致伸缩复合材料的宏观有效属性预测和单胞局部场分析。利用单胞细-宏观尺度比考虑为小参数。由控制泛函的渐近分析中推导相关的多尺度渐近级数和周期性边界条件。通过求解含Lagrange乘子扩展后的系列近似能量泛函驻值,可得出预设场变量波动函数的解析解,后将求解波动函数与宏观响应进行局部场重构可得到局部场分布。数值模拟中,采用该理论编程的Swift Comp软件模拟结果与现有有限元软件计算结果进行比较,得出以下结论:（1）理论具有简化计算步骤、普适性的特点:变分渐近理论通过对能量泛函的渐近分析构建含有完整信息的细观力学模型,仅使用细观力学中有关于非均匀材料的两个初始假设（平均假设和材料固有属性假设）。直接通过均匀化后推导两组周期性边界条件,不用预先假设;相比传统有限元分析,变分渐近均匀化法可以建立一维（二元复合材料）、二维（纤维增强材料）、三维（颗粒增强材料）单胞模型处理任意数目、形状的广义各向异性复合材料,一维建模同样可包含三维材料属性。（2）可预测材料有效属性与局部场,精度较高:变分渐近理论唯一确定波动函数并将其作为基本变量,单胞的位移表示为位移均值与构建的波动位移函数之和,变分渐近法具有固有变分性质易实现。求解波动函数后可同时获得材料宏观有效属性与重构后局部场信息（即单胞内应力-应变等变量）。有效属性与局部场的精确度与波动函数有关,不用求出平均应力应变,一次分析即可得出完整的材料信息,无需后处理计算与额外微观结构分析。对比结果表明,变分渐近均匀化理论通过较少的分析步骤实现了较高的预测精度。（3）分析不同体积分数的CoFe₂O₄/epoxy纤维增强复合材料和Terfenol-D颗粒增强复合材料并与已有方法和文献对比,得出如下结论:（1）磁致伸缩复合材料的弹性模量随磁性颗粒含量的增大而增大;有效饱和磁致伸缩率随Terfenol-D体积分数的增加而增加;（2）磁性颗粒含量对局部应力集中有较大影响,体积分数较低时,应力集中发生在颗粒中;而颗粒体积分数较高时,应力集中发生在基体中;（3）基体材料和磁性颗粒的弹性模量对有效伸缩量有截然不同的影响:有效伸缩量随基体材料弹性模量的增加而减少,但随着磁性颗粒弹性模量的增加而增加。结合变分法与有限元法预测磁致伸缩材料的有效弹性属性和微观局部场分布,可促进固体力学、材料学、数学等学科在非均匀介质方面的综合发展。有效而准确预测磁弹性材料有效性能,重构局部场可得到材料微观结构的具体信息。在实际工程运用中可更好优化设计材料构件,制备符合性能需求的磁致伸缩复合材料。在材料制备和设计过程中提高效率减少耗时,具有重要的研究价值和广泛工程应用前景。更多还原

【Abstract】 Magnetostrictive composite material has the advantages of low energy loss,fast response,obvious strain,and is suitable for various working environments.The rare earth magneto-strictive transducer made by Terfenol-D used to transmit and acoustic acquisition effectively in bridge structural health monitoring,can achieve excellent application results.Most magnetostrictive materials exist inherent defects such as brittle fracture,requires large magnetic field to induce strain,and strong eddy effect.These shortcomings limit the frequency range and performance.In the actual use of the process,effective properties are necessary on the analysis and optimization design of the mechanical properties of composite materials such as deformation failure and damage mechanism.However,due to these characteristics such as anisotropic,microscopic heterogeneity,the different components and some uncertain factors such as the high cost of experiment,the dispersion of results and the complex phenomena,these factors make many problems to predict the effective properties of composite materials.Therefore,it is necessary to predict the properties of magnetostrictive composites in order to design and prepare them.However,the traditional analysis methods depend on too many previous assumptions（such as RVE geometry,material properties,inclusion size and shape）and the late homogenization treatment will cause to unavoidable errors on the results of the analysis,and without considering the local field distribution.Traditional finite element method analyzing the microstructure of the material often brings a huge amount of work.Therefore,a new set of general analysis theory is needed to predict the macroscopic effective properties and local field variables.This paper is supported by the National Natural Science Foundation of China: The Variational Asymptotic Fine Model and Its Application In Multi-field Coupling Analysis of Functionally Graded Piezoelectric Laminated Plates（Grant No.11272363）.In this paper,a new modeling method,the variational asymptotic homogenization theory,is used to establish the micromechanical model of magnetostrictive Composite materials to predict the macroscopic effective properties and analyze the local field of the cell.Using the cell fine macro scale ratio as the small parameter,the asymptotic series and periodic boundary conditions are derived from the asymptotic analysis of the control function.The analytical solutions of the preset field variable fluctuation function are obtained by solving series of approximate energy functional values containing Lagrange multipliers.The local field distribution can be obtained by the local field reconstruction of the wave functions and the macroscopic response.In the following numerical simulation,the simulation results of the Swift Comp software with the theory are compared with the existing finite element software.Then we can obtain these following conclusions:（1）The theory has the characteristics of simple calculation steps and universality: only two initial assumptions about the non homogeneous material in the micromechanics（the assumption of the average and the assumption of the inherent property of the material）is required to construct the micromechanical model with complete information by the asymptotic analysis of the energy functional with the variational asymptotic theory.The two sets of periodic boundary conditions are derived directly by homogenization without prior assumption;Compared with the traditional finite element analysis,variational asymptotic homogenization method can establish one-dimensional（two element composite）,2D（fiber reinforced material）,3D（particle reinforced material）generalized anisotropic composite cell model with arbitrary number and shape.One dimensional modeling can also include three dimensional material properties.（2）The effective properties and local field of the material can be predicted precisely: The variational asymptotic theory uniquely determines the wave functions and takes them as the basic variable.The displacement of the cell is expressed as the sum of the average displacement and the constructed wave displacement functions.The variational asymptotic method is easy to implement with the inherent variational properties.After solving the wave function,we can obtain the macroscopic effective properties of the material and the local information of the reconstruction meanwhile（i.e.,the stress strain of the cell）;Effective properties and accuracy of the local fields is related to the wave function.It is not necessary to obtain the average stress and strain,and the complete material information can be obtained by one analysis without post processing calculation and additional microstructural analysis.The comparison results show that the variational asymptotic homogenization theory can achieve higher prediction accuracy with fewer analysis steps.（3）Compared the analysis results of CoFe₂O₄/epoxy fiber reinforced composites and Terfenol-D particulate reinforced composites with different volume fractions to the existing methods and literatures,we can draw the following conclusions:1.The elastic modulus of the magnetostrictive composites increase with the increase of the content of the magnetic particles,and the effective saturation magnetostrictions increase with the increase of the volume fraction of Terfenol-D;2.The density of magnetic particles has a great influence on the local stress concentration.When the volume fraction is low,the stress concentration occurs in the particles;When the particle volume fraction is high,the stress concentration occurs in the particles;3.The elastic modulus of matrix material and magnetic particles have different effects on the effective expansion amount: effective expansion amount decreases with the increasing of the matrix modulus,but increased with the increase of the elastic modulus of magnetic particles.Combining the variational method and the finite element method to predict the effective elastic properties and the microscopic local field distribution of magnetostrictive materials can promote the comprehensive development of solid mechanics,materials science,mathematics and other disciplines.Effective and accurate prediction of the elastic material properties and the reconstruction of the local field can get the detailed information on material microstructure.We can optimize the design of the material components,and prepare the magnetostrictive composites for performance requirements.This theory can improve the efficiency of material preparation and design process.It deserve an important research value and wide engineering application prospect.更多还原