An analytical model for granular jamming beams with applications in morphing aerostructures

Modern aircraft wings use discrete, flapped control surfaces that are simple and effective, but which create a significant drag and noise penalty when used. This research is working towards the replacement of these flaps with a continuous morphing device that can increase the aerodynamic performance and reduce noise emissions. However, the need to create smoothly morphing aerostructures presents a fundamental challenge in that the structures need to be stiff enough to resist aerodynamic and inertial loads while being flexible enough to change shape with minimal energy required. One way to address this competing set of constraints would be to use a material that is able to actively vary its stiffness. Such a device could be softened while morphing and then stiffened to hold its morphed shape. In this work, granular jamming is proposed as a mechanism for creating a material which can change stiffness from a liquid-like state to a solid-like state through the application of an applied pressure field which jams together the grains to stiffen an otherwise soft material. The basic concept of switchable stiffness for morphing aircraft has been shown in previous work. This paper introduces an analytical model to describe the bending dominated behaviour of granular jamming based morphing structures. Four-point bending experiments are performed to validate the model, and detailed strain fields from digital image correlation measurements are used to further elucidate the micro mechanics. The experimental data was compared against predictions from the proposed model, where it was seen that while the model is able to capture the presence of different regimes of response, the overall stiffness and strength are overpredicted. Possible sources of discrepancy are highlighted and motivate future work.