Mechanistic framework for reduced-order models in soft materials: Application to three-dimensional granular intrusion

Abstract

Granular intrusion is common in a range of processes including ballistic impact and penetration problems, and locomotion of humans, animals, and vehicles in natural terrains. The computational cost of full-scale numerical modeling is high, whereas a capability to model such scenarios in real-time is critical in applications such as path planning and efficient maneuvering of vehicles in sandy terrains and extraterrestrial environments. Existing reduced-order methods that model intrusion have limited capabilities due to their shape-and media-specific forms. This work formulates a reduced-order modeling technique, 3-dimensional Resistive Force Theory (3D-RFT), capable of accurately and quickly predicting the resistive force on arbitrary-shaped bodies moving in grains. Aided by a continuum mechanical description of the granular bed, a comprehensive set of symmetry constraints, and a large amount of reference data, we develop a self-consistent and accurate form for 3D-RFT. We verify the model capabilities in a wide range of cases and show it can be quickly recalibrated to different media and intruder surface types.

Mole crab-inspired vertical self-burrowing

“…While RFT is a tool utilized for over 50 years (Gray and Hancock, 1955), it was introduced as a viable tool for modeling granular materials in 2009, and several works have since demonstrated its applicability to various excavation and wheeled and legged locomotion tasks (Li et al, 2013;Zhang and Goldman, 2014;Shrivastava et al, 2020). Several recent works have expanded upon our understanding of RFT, including adding velocity dependence terms (Agarwal et al, 2021), and developing models for three dimensional intrusion scenarios (Treers et al, 2021;Agarwal et al, 2022;. Thus far, Granular RFT analyses primarily apply to dry, uniform granular media.…”