Variational Asymptotic Property Characterization Of Magnetostrictive Composites For Bridge Health Monitoring Sensors

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.