Granular Resistive Force Theory Implementation for Three-Dimensional Trajectories

Modelling interaction forces as bodies intrude into granular media is a longstanding challenge in the design and control of machines that navigate manipulate these highly complex materials. Granular Resistive Force Theory, or RFT, flexible, reduced-order model for predicting intrusion on media. 2D RFT describes plate whose velocity normal vectors lie same vertical plane. We introduce 3D method projects total vector two scenarios can already be described by which allows us to extend with minimal additional experimental characterization. then superimpose independently calculated forces, weighted experimentally fit scaling factors, determine force plate. When applied discretized convex hulls, this performs estimates arbitrary trajectories space. The proposed formulation predicts experienced oscillating circumnutating bodies, motions motivated mole crab burrowing plant root growth respectively. This well-suited complement more computational tools, such Discrete Element Method. By expanding application scenarios, broader set real-world applications now analyzed.