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.

We examine transient axial creeping flow in the annular gap between a rigid cylinder and a concentric elastic tube. The gap is initially filled with a thin fluid layer. The study focuses on viscous-elastic time-scales for which the rate of solid deformation is of the same order-of-magnitude as the velocity of the fluid. We employ an elastic shell model and the lubrication approximation to obtain a forced nonlinear diffusion equation governing the viscous-elastic interaction. In the case of an advancing liquid front into a configuration with a negligible film layer (compared with the radial deformation of the elastic tube), the governing equation degenerates into a forced porous medium equation, for which several closed-form solutions are presented. In the case where the initial film layer is nonnegligible, self-similarity is used to devise propagation laws for a pressure driven liquid front. When advancing external forces are applied on the tube, the formation of dipole structures is shown to dominate the initial stages of the induced flow and deformation regimes. These are variants of the dipole solution of the porous medium equation. Finally, since the rate of pressure propagation decreases with the height of the liquid film, we show that isolated moving deformation patterns can be created and superimposed to generate a moving wave-like deformation field. The presented interaction between viscosity and elasticity may be applied to fields such as soft-robotics and micro-scale or larger swimmers by allowing for the time-dependent control of an axisymmetric compliant boundary.

We study pressure-driven propagation of gas into a two-dimensional microchannel bounded by linearly elastic substrates. Relevant fields of application include lab-on-a-chip devices, soft robotics and respiratory flows. Applying the lubrication approximation, the flow field is governed by the interaction between elasticity and viscosity, as well as weak rarefaction and low-Mach-number compressibility effects, characteristic of gaseous microflows. A governing equation describing the evolution of channel height is derived for the problem. Several physical limits allow simplification of the governing equation and solution by self-similarity. These limits, representing different physical regimes and their corresponding time scales, include compressibility–elasticity–viscosity, compressibility–viscosity and elasticity–viscosity dominant balances. Transition of the flow field between these regimes and corresponding exact solutions is illustrated for the case of an impulsive mass insertion in which the order of magnitude of the deflection evolves in time. For an initial channel thickness which is similar to the elastic deformation generated by the background pressure, a symmetry between compressibility and elasticity allows us to obtain a self-similar solution which includes weak rarefaction effects. The presented results are validated by numerical solutions of the evolution equation.

This work analyzes the viscous flow and elastic deformation created by the forced axial motion of a rigid cylinder within an elastic liquid-filled tube. The examined configuration is relevant to various minimally invasive medical procedures in which slender devices are inserted into fluid-filled biological vessels, such as percutaneous revascularization, interventional radiology, endoscopies and catheterization. By applying the lubrication approximation, thin shell elastic model, as well as scaling analysis and regular and singular asymptotic schemes, the problem is examined for small and large deformation limits (relative to the gap between the cylinder and the tube). At the limit of large deformations, forced insertion of the cylinder is shown to involve three distinct regimes and time-scales: (i) initial shear dominant regime, (ii) intermediate regime of dominant fluidic pressure and a propagating viscous-peeling front, (iii) late-time quasi-steady flow regime of the fully peeled tube. A uniform solution for all regimes is presented for a suddenly applied constant force, showing initial deceleration and then acceleration of the inserted cylinder. For the case of forced extraction of the cylinder from the tube, the negative gauge pressure reduces the gap between the cylinder and the tube, increasing viscous resistance or creating friction due to contact of the tube and cylinder. Matched asymptotic schemes are used to calculate the dynamics of the near-contact and contact limits. We find that the cylinder exits the tube in a finite time for sufficiently small or large forces. However, for an intermediate range of forces the radial contact creates a steady locking of the cylinder inside the tube.

Growing soft materials which follow a three dimensional (3D) path in space are critical to applications such as search and rescue and minimally invasive surgery. Herein, a concept for a single‐input growing multi‐stable soft material, based on a constrained straw‐like structure is presented. This class of materials are capable of maneuvering and transforming their configuration by elongation while executing multiple turns. This is achieved by sequenced actuation of bi‐stable frusta with predefined constraints. Internal viscous flow and variations in the stability threshold of the individual cells enable sequencing and control of the robot's movement so as to follow a desired 3D path as the structure grows. A theoretical description of the shape and dynamics resulting from a particular set of constraints is derived. To validate the model and demonstrate the suggested concept, experiments of maneuvering in models of residential and biological environments are presented. In addition to performing complex 3D maneuvers, the tubular structure of these robots may also be used as a conduit to reach inaccessible regions, which is demonstrated experimentally.