Elastic Resistive Force Theory: Development and Application to Plant Uprooting

Granular Resistive Force Theory (RFT) is a reduced-order model that has been used as a successful tool to model the motion of rigid intruders in granular media, with reduced computational cost. RFT is based on a rate-independent theory that calculates the force experienced by an intruder moving through a granular medium using only a few material and kinematic parameters, including its direction of velocity. This makes it challenging to use RFT to model scenarios where the intruder is static, such as a stagnant plant being uprooted. To overcome this limitation, we introduce elastic RFT (eRFT) which employs a rate-independent plasticity flow-rule–like criterion. Below the yield threshold governing the flow of the grains, an elastic resistive force is defined, removing the inability of existing RFT to model static scenarios.

We demonstrate the applicability of eRFT by modeling uprooting processes which inherently have flexible intruders and are often dynamically controlled. By combining eRFT with a nonlinear beam theory to represent slender, inextensible roots we create a speedy computational tool. To explore anchoring mechanisms of different geometries, we simulate various uprooting experiments. We showcase the validity of eRFT results by comparing them to experimental data. To make eRFT a more accessible tool for wider engineering applications, we implement eRFT in ABAQUS, by making use of a user subroutine.