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首页> 美国卫生研究院文献>Proceedings of the National Academy of Sciences of the United States of America >A refined theory of magnetoelastic buckling matches experiments with ferromagnetic and superparamagnetic rods
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A refined theory of magnetoelastic buckling matches experiments with ferromagnetic and superparamagnetic rods

机译：完善的磁弹性屈曲理论与铁磁和超顺磁棒的匹配实验

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摘要

In its simplest form the magnetoelastic buckling instability refers to the sudden bending transition of an elastic rod experiencing a uniform induction field applied at a normal angle with respect to its long axis. This fundamental physics phenomenon was initially documented in 1968, and, surprisingly, despite many refinements, a gap has always remained between the observations and the theoretical expectations. Here, we first renew the theory with a simple model based on the assumption that the magnetization follows the rod axis as soon as it bends. We demonstrate that the magnetoelastic buckling corresponds to a classical Landau second-order transition. Our model yields a solution for the critical field as well as the shape of the deformed rods which we compare with experiments on flexible ferromagnetic nickel rods at the centimeter scale. We also report this instability at the micrometer scale with specially designed rods made of nanoparticles. We characterized our samples by determining all of the relevant parameters (radius, length, Young modulus, magnetic susceptibility) and, using these values, we found that the theory fits extremely well the experimental results for both systems without any adjustable parameter. The superparamagnetic feature of the microrods also highlights the fact that ferromagnetic systems break the symmetry before the buckling. We propose a magnetic “stick–slip” model to explain this peculiar feature, which was visible in past reports but never detailed.
机译：磁弹性屈曲不稳定性最简单的形式是指弹性杆的突然弯曲过渡，经历相对于其长轴成法线角施加的均匀感应场。这种基本的物理现象最初记录于1968年，令人惊讶的是，尽管进行了许多改进，但观测值与理论预期值之间始终存在差距。在这里，我们首先基于一个简单的模型来更新理论，该模型基于以下假设：磁化强度一旦弯曲就会跟随杆的轴线。我们证明了磁弹性屈曲对应于经典的Landau二阶过渡。我们的模型为临界场以及变形棒的形状提供了解决方案，我们将其与以厘米为单位的柔性铁磁镍棒上的实验进行了比较。我们还报告了由纳米粒子制成的特殊设计的棒在微米级的不稳定性。我们通过确定所有相关参数（半径，长度，杨氏模量，磁化率）来表征样品，并使用这些值发现，该理论非常适合没有任何可调参数的两个系统的实验结果。微棒的超顺磁性特征还凸显了铁磁性系统在屈曲之前破坏对称性这一事实。我们提出了一个磁性的“粘滑”模型来解释这一特殊功能，该功能在过去的报告中可见，但从未详细介绍。

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