Magnetorheological elastomers are active materials which can be actuated by the applied magnetic field. Hard magnetic soft (HMS) materials, a type of magnetorheological elastomers, show great potential in the fields of biomedical engineering and soft robotics, due to their short response time, remote operation, and shape programmability. To exploit its potential, a series of theoretical frameworks of HMS rods have been developed, but they are mainly limited to the static rod models or classical curved rod models that fail to consider the effect of the “initial curvature” on the distribution of the stress. In this work, we develop a curved rod theory to predict the 3D dynamic motion of the rod-like HMS robotics under large deformation. Based on the geometrically exact rod theory, we include the heterogeneous initial length of the longitudinal fiber caused by “initial curvature” into our model and obtain the reduced balance equations of the HMS robotics. As a result, the “tension-bending” and “shear-torsion” coupling effects of curved rods emerge in the present model. A numerical implementation of our model based on the classical Newmark algorithm is presented. To validate our model, three numerical examples, including the dynamic snap-through behavior of a bistable arch, are performed and compared with the simulation or experiment results reported in literatures, which show a good agreement. Finally, we experimentally study the 2D and 3D static and dynamic motion of a quarter arc HMS robotic arm under an applied magnetic field of 10 mT, and our model gives a satisfactory prediction, especially for static deformation.

中文翻译：

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用于动态分析的几何精确 3D 任意弯曲杆理论：在预测硬磁软机器人手臂运动中的应用


磁流变弹性体是可以通过施加的磁场驱动的活性材料。硬磁软（HMS）材料是一种磁流变弹性体，由于其响应时间短、远程操作和形状可编程性，在生物医学工程和软机器人领域显示出巨大的潜力。为了挖掘其潜力，一系列的HMS杆的理论框架已经被开发出来，但它们主要局限于静态杆模型或经典的弯曲杆模型，没有考虑“初始曲率”对应力分布的影响。在这项工作中，我们开发了一种曲杆理论来预测棒状 HMS 机器人在大变形下的 3D 动态运动。基于几何精确杆理论，我们将“初始曲率”引起的纵向纤维初始长度的异质性纳入模型中，得到了HMS机器人的简化平衡方程。因此，本模型中出现了曲杆的“拉弯”和“剪扭”耦合效应。提出了基于经典纽马克算法的模型的数值实现。为了验证我们的模型，执行了三个数值示例，包括双稳态拱的动态突跳行为，并将其与文献中报道的模拟或实验结果进行了比较，结果显示出良好的一致性。最后，我们实验研究了四分之一弧HMS机械臂在10 mT外加磁场下的2D和3D静态和动态运动，我们的模型给出了令人满意的预测，特别是对于静态变形。