Modelling nonlinear viscous flow restriction via auxetic metamaterial lattices for inflatable soft robots

Inflatable soft robots, whose actuation comes from the intake of fluids into a soft body, are often tethered to valves and control equipment, limiting their ability to navigate their environment. Recent work has shown that autonomous sequencing through the use of thin tubes to restrict fluid flow through robots reduces system complexity without reducing performance. In this work, we encase an inflatable membrane with an auxetic lattice that similarly restricts the working fluid, imposing sequential motion on the device without additional external valves and fluid lines. Fluid models show that nonlinear interactions between incoming air and the auxetic lattice enable sequential inflation and embed intelligent behavior in the device. We present a design-oriented model to characterize this behavior of the device based on its auxetic geometry. We find the internal force of the lattice using nonlinear mechanics and modeling each auxetic element as a series of thin curved beams. Experiments validate and correct this model by replicating its fluid properties and geometry. We finally discuss applications of fluid sequencing through auxetic shells, focusing on areas where autonomous robotic responses to pressure changes are needed.