Granular intrusions, such as dynamic impact or wheel locomotion, are complex multiphase phenomena where the grains exhibit solid-like and fluid-like characteristics together with an ejected gas-like phase. Despite decades of modeling efforts, a unified description of the physics in such intrusions is as yet unknown. Here, we show that a continuum model based on the simple notions of frictional flow and tension-free separation describes complex granular intrusions near free surfaces. This model captures dynamics in a variety of experiments including wheel locomotion, plate intrusions, and running legged robots. The model reveals that one static and two dynamic effects primarily give rise to intrusion forces in such scenarios. We merge these effects into a further reduced-order technique (dynamic resistive force theory) for rapid modeling of granular locomotion of arbitrarily shaped intruders. The continuum-motivated strategy we propose for identifying physical mechanisms and corresponding reduced-order relations has potential use for a variety of other materials.

While terrestrial locomotors often contend with permanently deformable substrates like sand, soil, and mud, principles of motion on such materials are lacking. We study the desert-specialist shovel-nosed snake traversing a model sand and find body inertia is negligible despite rapid transit and speed dependent granular reaction forces. New surface resistive force theory (RFT) calculation reveals how wave shape in these snakes minimizes material memory effects and optimizes escape performance given physiological power limitations. RFT explains the morphology and waveform-dependent performance of a diversity of non-sand-specialist snakes but overestimates the capability of those snakes which suffer high lateral slipping of the body. Robophysical experiments recapitulate aspects of these failure-prone snakes and elucidate how re-encountering previously deformed material hinders performance. This study reveals how memory effects stymied the locomotion of a diversity of snakes in our previous studies (Marvi et al., 2014) and indicates avenues to improve all-terrain robots.

We analyze the capabilities of various recently developed techniques, namely Resistive Force Theory (RFT) and continuum plasticity implemented with the Material Point Method (MPM), in capturing dynamics of wheeldry granular media interactions. We compare results to more conventionally accepted methods of modeling wheel locomotion. While RFT is an empirical force model for arbitrarily-shaped bodies moving through granular media, MPM-based continuum modeling allows the simulation of full granular flow and stress fields. RFT allows for rapid evaluation of interaction forces on arbitrary shaped intruders based on a local surface stress formulation depending on depth, orientation, and movement of surface elements. We perform forced-slip experiments for three different wheel types and three different granular materials, and results are compared with RFT, continuum modeling, and a traditional terramechanics semi-empirical method. Resultsshow that for the range of inputs considered, RFT can be reliably used to predict rigid wheel granular media interactions with accuracy exceeding 1 arXiv:1901.10667v1 [cond-mat.soft] 30 Jan 2019 that of traditional terramechanics methodology in several circumstances.Results also indicate that plasticity-based continuum modeling provides an accurate tool for wheel-soil interaction while providing more information to study the physical processes giving rise to resistive stresses in granular media.

Granular intrusion is commonly observed in natural and human-made settings. Unlike typical solids and fluids, granular media can simultaneously display fluid-like and solid-like characteristics in a variety of intrusion scenarios....