Elastic Resistive Force Theory: Development and Applications to Flexible Intruders

Abstract

Dry granular intrusion and extraction occur commonly for off-road vehicles, foundation work, and plant uprooting. Although many models exist to describe such scenarios, reduced-order models such as granular resistive force theory (RFT), offer a good balance between accuracy and computational cost. RFT efficiently approximates the resistive force experienced by an intruder moving through a granular medium as a function of the intruder's velocity direction, geometry, and material parameters. However, due to the explicitly velocity-dependent nature of its formulation, it fails at modeling static conditions, the force build-up that occurs before flow, and stagnant points on moving intruders. We propose elastic RFT to remedy these shortcomings. Elastic RFT intrinsically models both granular elasticity and flow adjacent to intruders by splitting intruder motion into separate parts corresponding to elastic and plastic granular deformation. This allows force to build up elastically before flow and lets the plastic part of motion maintain RFT flow rules. We present the details of the underlying kinematic and constitutive assumptions for elastic RFT. Moreover, we also propose a procedure to couple RFT or elastic RFT to deformable intruders, which we demonstrate in applications of elastic RFT to sample plant uprooting problems treating the roots as nonlinear inextensible beams. We highlight potential application areas for elastic RFT coupled to deformable objects, including simulation of deformable wheel locomotion.