Actuations in direct-ink-writing based on continuum deformations of a flexible curved pipe conveying fluid

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.