磁流变体有限变形数值模拟及本构建模研究

发布时间：2018-05-09 06:53

本文选题：磁流变弹性体 + 力学行为　；参考：《西北工业大学》2015年博士论文

【摘要】：磁流变弹性体是一种新型的智能材料，它是将微米尺度的铁磁性颗粒掺入到高分子聚合物中，在磁场环境下固化，从而基体内的颗粒具有链或柱状结构，形成各向异性的磁流变弹性体。如果在无磁场环境下固化，则为各向同性的磁流变弹性体。这种材料的宏观模量尤其是各向异性磁流变弹性体，可随外加磁场强度的变化而变化，因此可以在变刚度器件等方面得到广泛的应用。与普通磁流变液相比，磁流变弹性体不但具有可控性、可逆性、响应迅速等高技术特征，还具有稳定性好等独特的优点。本文借助于理论分析、有限元仿真和实验研究等方法，对磁流变弹性体的基础力学性能进行研究，并提出了新的应变能密度函数类型。主要研究内容和成果如下： 1）运用基于周期性边界条件的代表性体积单元法，用理论分析和有限元两种方法对比研究了无磁场条件下各向同性和各向异性磁流变弹性体的宏观杨氏模量和剪切模量。正交各向同性磁流变弹性体数值模拟的结果和基于Eshelby夹杂理论的Mori-Tanaka和Double-Inclusion模型预测的结果完全一致。用这两种方法得到的宏观模量比简单的Voigt模型（均匀应变假设）和Reuss（均匀应力假设）模型要精确很多。颗粒填充材料对橡胶的力学性能有影响，初始杨氏模量和初始剪切模量都有增强的作用。 2）通过引入Maxwell应力张量，研究了各向异性磁流变弹性体在不同磁感应强度下对磁场诱导产生的杨氏模量和剪切模量的影响。用代表性体积单元的方法证明了：磁流变弹性体由于磁场诱导产生的杨氏模量是负数，但总的杨氏模量是正数，且其大小随磁感应强度的增大而增大。而其初始剪切模量则始终为正数，其大小随着磁场强度的增大而增大，这与偶极子理论推导得到的结论一致。 3）运用先进的三维数字散斑动态应变测量分析系统（XJTUDIC）对磁流变弹性体的基质材料（橡胶）进行了拉伸力学测试，研究了橡胶基质在有限变形下适合的超弹性材料的几种应变能密度函数类型。使用了商业有限元分析软件ABAQUS并分别选用材料类型Yeoh模型、Neo-Hookean和Mooney-Rivlin模型对实验结果进行拟合，发现对于中等程度的变形，Mooney-Rivlin超弹性材料模型的模拟结果与实验结果吻合。 4）由于各向异性磁流变弹性体和纤维增强复合材料细观结构的近似性，对于无磁场条件工作下的各向异性磁流变弹性体，参考纤维增强复合材料的有限变形，基于Spencer的连续介质力学不变量理论，提出了一种考虑纤维弯曲刚度的非线性超弹性本构模型。理论和实验分析均表明：传统的基于连续介质力学的纤维增强复合材料有限变形理论不适用于弯曲变形，必须考虑弯曲刚度的影响。数值仿真结果也验证了在应变能函数中增加弯曲刚度项是必要的。 5）对于工作在磁场条件下的各向异性磁流变弹性体，参考两族纤维增强的复合材料，基于Spencer的不变量理论，对颗粒形成的链和磁场方向分别定义两个方向的不变量，，从而建立了一个新的磁流变弹性体的应变能密度函数类型。并研究了在这个新的本构模型下拉伸和简单剪切工况下的力学性能，进而分析了磁场方向和颗粒链方向对于宏观力学性能的影响。
[Abstract]:The magneto - rheological elastomer is a new kind of intelligent material , it is a kind of new kind of intelligent material , it is to incorporate micron - scale ferromagnetic particles into the polymer polymer , it is solidified under the magnetic field environment , so that the particles in the base body have chain or columnar structure to form anisotropic magneto - rheological elastomer .

1 ) The macroscopic Young ' s modulus and shear modulus of isotropic and anisotropic magneto - rheological elastomers under the condition of non - magnetic field are studied by means of theoretical analysis and finite element method . The results of the numerical simulation of the orthogonal isotropic magnetorheological elastomers and the results of the prediction of the Mori - tanaka and Double - Inclusion models based on the Eshelby inclusion theory are quite consistent . The macroscopic modulus obtained by these two methods is much more accurate than the simple Voigt model ( uniform strain hypothesis ) and the Reuss ( uniform stress hypothesis ) model .

2 ) By introducing Maxwell stress tensor , the influence of anisotropic magneto - rheological elastomer on the Young ' s modulus and shear modulus induced by magnetic field under different magnetic induction intensity is studied . The method of representative volume unit proves that the Young ' s modulus produced by magnetic field induction is negative , but the total Young ' s modulus increases with the increase of magnetic induction intensity . The initial shear modulus is always positive , and its size increases with the increase of magnetic field strength , which is consistent with the conclusion obtained by dipole theory .

3 ) Using the advanced 3D digital speckle dynamic strain measurement and analysis system ( XJTUDIC ) to test the matrix material ( rubber ) of the magneto - rheological elastomer , the types of strain energy density functions of the super - elastic materials suitable for the finite deformation of the rubber matrix were studied .

4 ) Due to the approximation of the meso - structure of the anisotropic magneto - rheological elastomer and the fiber - reinforced composite material , the nonlinear hyperelastic constitutive model considering the bending stiffness of the fiber is presented for the anisotropic magneto - rheological elastomer under the condition of no magnetic field , and the nonlinear hyperelastic constitutive model considering the bending stiffness of the fiber is presented .

5 ) For the anisotropic magneto - rheological elastomer working under the condition of magnetic field , referring to the two - family fiber - reinforced composite material , based on Spencer ' s invariant theory , two independent variables are defined in the direction of the chain and the magnetic field formed by the particles , so as to establish a new strain energy density function type of the magneto - rheological elastomer , and the influence of the magnetic field direction and the particle chain direction on the macroscopic mechanical properties is analyzed .

【学位授予单位】：西北工业大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TB381

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