NONLINEAR CONSTITUTIVE RELATIONS FOR MAGNETOSTRICTIVE MATERIALS WITH APPLICATIONS TO 1-D PROBLEMS
NONLINEAR CONSTITUTIVE RELATIONS FOR MAGNETOSTRICTIVE MATERIALS WITH APPLICATIONS TO 1-D PROBLEMS
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DOI：
10.1177/1045389x9500600508
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发表时间：
1995-09-01
影响因子：
2.7
通讯作者：
MITROVIC, M
中科院分区：
文献类型：
--
作者：
CARMAN, GP;MITROVIC, M
本文提出了一种磁致伸缩材料的非线性本构关系，该关系考虑了温度/预紧力与磁场强度之间的非线性耦合效应。这些关系式是从热力学原理出发，利用吉布斯自由能在泰勒级数中展开，只包含现有文献中的实验证据所确定的相关常数。通过假定磁致伸缩材料在偏置磁场中工作，并以较小的值对其进行扰动，导出了现有文献中存在的非线性材料常数与线性系数之间的关系。通过将在磁场和应力偏置下工作的Terfenol-D棒的实验结果与理论值进行比较，评估了非线性本构关系的准确性。结果表明，该模型能较好地预测特定区域的非线性应变/场关系。将非线性本构关系整合到一维非线性有限元模型中，用于结构构件的研究。利用加权余量法和牛顿-拉夫森迭代技术推导了耦合磁弹性问题。分析模型的结果表明，线性方法不适合模拟这种材料在结构中的响应。
In this paper, we present a nonlinear constitutive relation for magnetostrictive materials that includes nonlinear coupling effects arising between temperature/preload and magnetic field strengths. The relations are derived from thermodynamic principles using Gibbs free energy expanded in a Taylor series with only the pertinent constants included as determined from experimental evidence present in existing literature. By assuming that the magnetostrictive material is operated in a biased magnetic field and perturbing this field with a small value, relations between the nonlinear material constants and linear coefficients present in existing literature are derived. The accuracy of the nonlinear constitutive relation is evaluated by comparing experimental results obtained on a Terfenol-D rod operating under both magnetic field and stress biases with theoretical values. Results indicate that the model adequately predicts the nonlinear strain/field relations in specific regimes. The nonlinear constitutive relations are also integrated into a 1-dimensional nonlinear finite element model for studying structural components. The coupled magneto elasticity problem is derived using a weighted residual method along with a Newton-Raphson iteration technique. Results of the analytical model indicate that linear approaches are inappropriate for modeling the response of this material in a structure.