The objective of this study is to investigate actuations based on the continuum deformation of flexible curved magnetically impregnated pipes conveying fluid. This flexible actuation due to flow-induced and magnetic forces offers a novel perspective in direct-ink-writing (DIW). The motion of the pipe’s tip-ends can be seen as a pen freely writing on paper. A kind of soft material, namely hard-magnetic soft (HMS) material, is selected to comprise the magnetic segment of flexible curved pipes. The HMS locally and totally distributed on the curved pipe are considered. The theoretical model is constructed based on the geometrically exact model to predict large deformations of HMS pipes conveying subcritical fluid flows under a magnetic field. The theoretical models for the flexible pipe with locally and totally distributed HMS are validated by experiments. Subsequently, the stability and critical fluid velocity are obtained to determine the DIW workspace of the flexible pipes. Accordingly, the deformations of flexible curved pipe guided DIW can be performed within the designated safe workspace. Horizontal and vertical DIWs are theoretically realized, with consideration of initial curved configurations. The results show that the writing route of the target in each DIW is strongly dependent on the magnetic field and fluid velocity. Furthermore, a curved pipe with a greater curvature can provide a larger writing workspace. For the same writing target, the DIW driven by the totally-distributed HMS pipe requires lower values of magnetic field and fluid velocity, compared to the locally-distributed HMS pipe.

中文翻译：

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基于柔性弯曲管道输送流体连续变形的直接墨水书写驱动

本研究的目的是研究基于柔性弯曲磁浸管输送流体连续变形的驱动。这种由流激力和磁力引起的灵活驱动为直接墨水书写 （DIW） 提供了新的视角。烟斗尖端的运动可以看作是一支笔在纸上自由书写。选用一种软材料，即硬磁软 （HMS） 材料，构成柔性弯管的磁段。考虑了 HMS 局部和完全分布在弯曲管上。该理论模型基于几何精确模型构建，用于预测在磁场下输送亚临界流体流的 HMS 管道的大变形。通过实验验证了具有局部和完全分布 HMS 的柔性管的理论模型。随后，获得稳定性和临界流体速度，以确定柔性管道的 DIW 工作空间。因此，柔性弯管导向的 DIW 的变形可以在指定的安全工作区内进行。理论上可以实现水平和垂直 DIW，并考虑初始弯曲配置。结果表明，每个 DIW 中目标的写入路径在很大程度上取决于磁场和流体速度。此外，曲率较大的弯曲管可以提供更大的书写工作空间。对于相同的写入目标，与局部分布的 HMS 管道相比，由完全分布的 HMS 管道驱动的 DIW 需要较低的磁场和流体速度值。