Rover Mobility on Granular Soil: Marrying Multi-Scale Modeling and High Fidelity Experiments to Infer Soil Stresses under the Moving Wheel

In this work, we show how high resolution imaging coupled with a novel physics-based computational framework can provide a rich description of regolith-structure interactions, using the rover mobility in soft soil as a challenging canonical problem. The images of soil deformation under a rolling wheel were collected at 7 Hz resolution in time and 0.19 mm per pixel in space, with the camera approximately following the wheel motion. The soil under the wheel is a lunar simulant GRC-1. Image correlation (optical flow) was used to infer material velocities, i.e. regolith kinematics, at near-grain scale. From this data, strains can be calculated during post-processing, but stresses are beyond the reach of experimental measurements. Here we present a method to infer material stresses under the rolling wheel using a multiscale framework with a simple Drucker-Prager material description. From a purely computational standpoint, this mobility problem is extremely challenging involving wheel-regolith contact and interacting localization bands on the material scale, as indicated by the experiments. Capturing these features with the correct constitutive description is at the very cutting edge of computational research today. We bypass some of the aforementioned difficulties by inferring from experimental images a key plastic internal variable, the dilatancy, which is known to control strength and softening in dilative granular materials, and use its evolution directly in multi-scale computations. The method successfully marries experiments and computations in order to quantify material stresses under the wheel, which at present are beyond the reach of either method alone. From a practical standpoint, an understanding of the material stress state is helpful for several reasons, perhaps the chief of which is that stress distributions serve as input into reduced-order mobility models, e.g. Bekker-Wong terramechanics expressions.