Research Projects

The project aims to develop a theoretical framework to model contact interactions between elastic rods, a slender body with a larger dimension and large displacements under small strain regimes. Current theories, such as Kirchhoff's rod theory, do not account for interactions between an elastic rod and itself, making it impossible for the rod to pass through itself. The project proposes two types of contact: global contact, where distant points on an elastic rod come close enough to establish contact, and local contact, which arises due to the finite thickness of the rod. The approach to modelling these contacts involves derived exact governing equations, interface conditions, analytical solutions for special cases under special limits, elaborate numerical schemes, and parametric studies to classify equilibrium configurations and compare them with existing theories. If successful, the theory could provide a conceptual leap in understanding and modeling contact in elastic rods, as most current efforts focus on computationally expensive tools like the Finite Element Method. The rod theory-based approach will lead to efficient computation of contact problems and aid in developing theoretical understanding of the phenomenon. Applications of a successful rod theory include mechanics of mooring lines, deployment of space tethers, and soft robotics. The theory may also impact recent efforts to model the mechanics of macromolecules, such as DNA, using the theory of elastic rods.