Soft-magnetorheological elastomers (s-MREs) are particulate composites made of a non-magnetic elastomeric matrix dispersed with micron-sized particles of a “soft-magnetic” material. The phenomenon of magnetostriction in specimens made from s-MREs is the change in their shape when they are subjected to an external magnetic field. Experiments in the literature show that for circular cylindrical specimens subjected to an axially applied magnetic field the magnetostriction is strongly dependent on their aspect-ratio, with specimens with a low ratio of the length to the diameter exhibiting a larger tensile magnetostrictive strain than specimens with a large aspect-ratio — the “shape-effect.” This response is also hysteretic because of the underlying viscoelasticity of the matrix material. In this paper we report on a large deformation magneto-viscoelasticity theory for s-MREs and its finite element implementation. Using our theory we show that we can model this non-intuitive geometry-dependent magnetostrictive response of cylindrical s-MRE specimens. We show that the effect of the magnetization m of the cylinder is to decrease the magnetic field h within the cylinder relative to the applied magnetic field happ outside the cylinder, the well-known demagnetization effect, and that this demagnetization is diminished in more slender cylinders due to magnetic fringing at the boundaries of the cylinder. This is the physical reason behind the macroscopically-observed “shape-effect.”

中文翻译：

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软磁流变弹性体的磁致伸缩


软磁流变弹性体 （s-MRE） 是由非磁性弹性体基体与微米级“软磁”材料颗粒分散而成的颗粒复合材料。由 s-MRE 制成的样品中的磁致伸缩现象是它们在受到外部磁场时形状的变化。文献中的实验表明，对于受到轴向磁场影响的圆柱形试样，磁致伸缩在很大程度上取决于它们的纵横比，长度与直径之比较低的试样比大纵横比的试样表现出更大的拉伸磁致伸缩应变——“形状效应”。由于基体材料的潜在粘弹性，这种响应也是滞后的。在本文中，我们报告了 s-MRE 的大变形磁粘弹性理论及其有限元实现。利用我们的理论，我们表明我们可以模拟圆柱形 s-MRE 样品的这种非直观的几何依赖性磁致伸缩响应。我们表明，圆柱体的磁化强度 m 的作用是减小圆柱体内的磁场 h 相对于圆柱体外施加的磁场 h，这是众所周知的退磁效应，并且由于圆柱体边界处的磁边，这种退磁在更细长的圆柱体中会减弱。这就是宏观观察的“形状-效应”背后的物理原因。