Arun Kumar

Project title: Thin ribbons: mathematical and numerical models, experimental validation and application to magnetic actuation

Host Institution: Ecole Polytechnique, Paris (l’X)

Host Supervisor: Prof. Basile Audoly

Co-host Institution: École Polytechnique Fédérale de Lausanne (EPFL)

Co-host Supervisor: Prof. Pedro M Reis

Summary project: Ribbons are thin, flexible structures with three different dimensions- length >> width >> thickness. The dimensional arrangement keeps the ribbons half-way between rods and plates. While theories for rods and plates have extensively been developed with a plethora of dedicated models, they have not been for ribbons. An accurate, rigorously derived, well-tested, and comprehensive ribbon model is still not present in the literature.

The first objective of this project is to develop a one-dimensional model that can capture the complex nonlinear behavior of thin ribbons; it will extend the existing models by considering both the extensibility of the ribbon and the higher-order effect associated with gradients of twist. To this end, a dimension reduction method proposed recently at Ecole Polytechnique will be used. A finite- element implementation of the 1D model will be obtained. Precision experiments will be set up with input from EPFL, with the aim to validate the model.

Once the elastic ribbon model is simulated and well-tested, it will be augmented to model ribbons made up of magnetic-rheological elastomers. Ribbons can exhibit multiple states and undergo sudden transitions without losing their structural integrity. A magnetic field will be set up to trigger transitions between competing equilibrium states of a ribbon. The structural sensitivity near a buckling bifurcation will be used to enhance the effect of magnetic actuation, and its applications to bending and coalescing ribbon robots and switching circuits in electric switches will be investigated.