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Dynamics of a Viscous Liquid within an Elastic Shell with Application to Soft Robotics Shai B. Elbaz and Amir D. Gat Technion - Israel Institute of Technology Faculty of Mechanical Engineering 1 12/01/2013

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Background (1/2) – Soft Robotics Emerging field of experimental soft robotics. (Stokes et al.,2013, Shepherd et al. 2013, others ) – Embeded fluidic networks – Constant spatial pressure - inflation/deflation Essentially: creating a solid deformations field by a fluidic stress field. 2

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Background (2/2) - Biological Flows Interaction between fluid and solid dynamics involving viscous flow through elastic cylinders extensively studied. Heil & Pedley 1996,1997 studied the stability of cylindrical shells conveying viscous flow and stokes flow in collapsible tubes. Paidoussis (1998) extensively studied fluid-structure Interactions for the case of axial flow in slender structures. Canic & Mikelic 2003 studied viscous incomp. flow through a long elastic tube in the context of arterial blood flow. Many others. 3

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Our Goal Apply models and methods used in biological flows to study time varying deformation patterns in soft-robotics. Add a new level of control to soft-robotics Introduce visco-elastic motion to traditional mechanical eng. applications. (Math. Overview) 4

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Problem Definition Fluid-structure interaction between: – Viscous, Newtonian, incompressible flow. – Slender, linearly elastic cylindrical shell closed at one end. Assume negligible inertia in liquid and solid. External stress and pressure 5

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Elastic Medium (1/2) – Governing Eq. 6

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Elastic Medium (2/2) – Final Formulation 7

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Fluidic medium (1/2) – Governing Eq. 8

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Fluidic Medium (2/2) – Final Formulation 9

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Coupled Fluidic-Elastic System 10

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Results Overview 11

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Results (1/2) 12 Constant pressure inflation of a slender elastic cylinder with internal viscous flow

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Results (2/2) 13 Quasi-steady diffusion of a slender elastic cylinder with internal viscous flow

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Oscillatory Time Response 14

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Oscillatory Frequency Response 15

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Response to External Obstacle (1/2) 16

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Response to External Obstacle (2/2) 17

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Concluding Remarks Closed analytic solution for pressure, velocity and deformation fields. Characteristic time scale of the visco-elatic interaction. Analysis of governed inlet pressure and external domain on the deformation field of the shell. – Elastic material compressibility. – Inducing the flow off the base frequency. – Phase reversal. – Boundary pressure feedback – movement detection. 18

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Future Research The current study lays the foundation for treatment of an external fluidic domain. Control based on plant-model and boundary feedback to navigate/propel the vehicle. Multi-channel networks – complex deformations. A new breed of visco-elastic robots? 19

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