Granular drag and lift force on a flexible fiber

In this work, we investigate the forces acting on a flexible fiber dragged through a granular bed. Using discrete element simulations, we observe that, after a sufficiently large displacement, the system reaches a steady state in which both the fiber's shape and the forces acting on it become, on average, constant. Under these conditions, we identify two characteristic lengths that describe the fiber's shape and propose unique scaling laws for the drag and lift forces, valid across a wide range of fiber flexibilities, from highly deformable to nearly rigid, based on these lengths. We highlight that the fiber--grains interaction is governed by a single dimensionless elastogranular parameter, defined as the ratio of the fiber's elastic properties to the granular pressure. Finally, we demonstrate that both the forces and the characteristic lengths can be expressed solely as functions of this dimensionless parameter. Our findings offer a fundamental insight into the behavior of a flexible fiber interacting with a granular medium.