Paper detail

Deformation of an Elastic Beam due to Viscous Flow in an Embedded Parallel Channel Network

Elastic deformation due to embedded fluidic networks is currently studied in the context of soft-actuators and soft-robotic applications. In this work, we analyze interaction between the elastic deflection of a slender beam and viscous flow within a long serpentine channel, embedded in the elastic beam. The channel is positioned asymmetrically with regard to the midplane of the beam, and thus pressure within the channel creates a local moment deforming the beam. We focus on creeping flows and small deflections of the elastic beam and obtain, in leading order, a fourth-order partial integro-differential equation governing the time-dependent deflection field. This relation enables the design of complex time-dependent deformation patterns of beams with embedded channel networks, including inertia-like standing and moving wave solutions in configurations with negligible inertia.