Dr Rehan Shah has been awarded funding from the Quarterly Journal of Mechanics and Applied Mathematics Fund (QJMAM) administered by the Institute of Mathematics and its Applications (IMA) to attend and present his latest research at the major international European Solid Mechanics Conference (ESMC) being held in July 2025 in Lyon, France by the European Mechanics Society (EUROMECH).

Dr Shah will present research findings through a mini-symposia talk from his work on 'Static friction models, buckling and lift-off for a rod deforming on a cylinder' based on his recently published papers, Shah and van der Heijden, 2023 and Shah and van der Heijden, 2024 in the Journal of Mechanics and Physics of Solids (JMPS) stemming from his collaboration with Prof Gert van der Heijden from University College London.

The work outlines the development of a comprehensive geometrically-exact theory for an end-loaded elastic rod constrained to deform on a cylindrical surface. By viewing the rod-cylinder system as a special case of an elastic braid, the theory allows determination of all forces and moments imparted by the deforming rod to the cylinder as well as all contact reactions. The framework also provides a complete treatment of static friction consistent with force and moment balance and also accounts for a cylinder with an arbitrary orientation to account for the effects of gravity.

Applications of the theory include buckling of the constrained rod under compressive and torsional loads, finding critical loads that depend on Coulomb-like friction parameters and investigating the the tendency of a rod to lift off the cylinder under further loading due to friction and/or gravity. The results are relevant for many engineering and medical applications in which a slender structure winds inside or outside a cylindrical boundary.

As part of the QJMAM grant dedicated to supporting UK research in the broad area of applied mathematics and theoretical mechanics, Dr Shah has also been encouraged to submit his future work in this field concerning the formulation of the theory for a rod deforming on a torus with applications to instabilities of toroidal DNA condensates as a research paper for the Quarterly Journal of Mechanics and Applied Mathematics.