Dynamics of viscous liquid within a closed elastic cylinder subject to external forces with application to soft robotics

• Published in: Journal of fluid mechanics Vol. 758; pp. 221 - 237
• Main Authors: Elbaz, S. B., Gat, A. D.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 10.11.2014
• Subjects: Applied sciences; Compressibility; Computer science; control theory; systems; Contact pressure; Contact stresses; Control theory. Systems; Cylinders; Cylindrical shells; Deformation; Deformation effects; Diffusion; Dye dispersion; Dynamics; Elastic cylinders; Elastic deformation; Exact sciences and technology; Fields; Forces (mechanics); Fundamental areas of phenomenology (including applications); Inertia; Liquid-solid interfaces; Mathematical models; Physics; Residual stress; Robotics; Shear stress; Soft robotics; Solid mechanics; Solutions; Structural and continuum mechanics; Structures; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Viscous flow; low-Reynolds-number flows; lubrication theory; Low Reynolds number; Viscous fluid; Shear stress; Internal fluid; Fluid structure interaction; Cylindrical shell; Elastic deformation; Modeling; Thin wall; Robotics
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2014.527

Viscous flows in contact with elastic structures apply both pressure and shear stress at the solid–liquid interface and thus create internal stress and deformation fields within the solid structure. We study the interaction between the deformation of elastic structures, subject to external forces, and an internal viscous liquid. We neglect inertia in the liquid and solid and focus on viscous flow through a thin-walled slender elastic cylindrical shell as a basic model of a soft robot. Our analysis yields an inhomogeneous linear diffusion equation governing the coupled viscous–elastic system. Solutions for the flow and deformation fields are obtained in closed analytical form. The functionality of the viscous–elastic diffusion process is explored within the context of soft-robotic applications, through analysis of selected solutions to the governing equation. Shell material compressibility is shown to have a unique effect in inducing different flow and deformation regimes. This research may prove valuable to applications such as micro-swimmers, micro-autonomous systems and soft robotics by allowing for the design and control of complex time-varying deformation fields.