[Paper Review] A generalized resistive force theory for rate-dependent intrusion phenomena in granular media

Shashank Agarwal, Andras Karsai+2 more|arXiv (Cornell University)|May 22, 2020

Soil Mechanics and Vehicle Dynamics23 references4 citations

TL;DR

This paper proposes a generalized resistive force theory (RFT) that incorporates geometry-dependent corrections and macro-inertial forces to explain rate-dependent intrusion dynamics in granular media, even when micro-inertial effects (via inertial number) are negligible. The modified RFT successfully replicates diverse experimental behaviors—such as rapid plate drag, rigid wheel locomotion, and legged running—without relying on micro-inertial constitutive laws.

ABSTRACT

Recent studies reveal that resistive forces in granular intrusion can be explained with rate-independent drag laws when intrusion is slow, but rate effects can occur in situations like dynamic impact. It is challenging to determine the various roles of inertia at the bulk (macro) and grain (micro) scales, as well as the role of rate in boundary interactions, and to reconcile the addition of these effects with the rate-independent force response in reduced-order models like granular Resistive Force Theory (RFT). Many studies measure the role of micro-inertia through a dimensionless shear-rate known as the inertial number and use it to add strain-rate-dependence into the constitutive relations. We demonstrate with data from rapid plate drag tests, freely locomoting rigid wheel experiments, and legged runners that rate-dependent dynamics emerge even when the inertial number is negligibly small. While a velocity-squared correction is often used to describe macro-inertial effects in rapid plate drag cases, this correction is insufficient to reproduce the dynamics observed in more complex intrusions like that of rigid wheel locomotion. We find a frictional flow continuum model replicates all observed behaviors without inclusion of micro-inertial effects. Based on the characteristics of the observed flows, we propose a modified rate-dependent RFT for arbitrary intruders. The form reconciles all considered cases by adding a geometry-dependent modification and a macro-inertial force to RFT. Our results reveal how rate-dependent mechanisms can emerge in rate-insensitive granular media, and highlight the ability of simple physical corrections in enhancing the design capabilities of reduced-order models like RFT.

Motivation & Objective

• To resolve the inconsistency between rate-independent RFT and observed rate-dependent behaviors in granular media under rapid intrusion.
• To determine whether micro-inertial effects (via inertial number) are necessary to explain rate dependence in granular flow.
• To develop a unified, reduced-order model that captures complex intrusion dynamics across diverse intruder geometries and speeds.
• To identify the dominant physical mechanisms—macro-inertia and geometric effects—underlying rate-dependent resistive forces.
• To enhance the predictive power of RFT for engineering and biological locomotion applications in granular environments.

Proposed method

• Conducted rapid plate drag experiments to measure velocity-dependent resistive forces under high strain rates.
• Performed freely locomoting rigid wheel experiments to study rate-dependent resistance during sustained motion.
• Analyzed data from legged runners to assess rate effects in complex, intermittent intrusions.
• Proposed a modified RFT framework incorporating a geometry-dependent correction term and a macro-inertial force proportional to velocity squared.
• Used a frictional flow continuum model to simulate and validate the observed dynamics without micro-inertial terms.
• Calibrated and tested the generalized RFT against experimental data across all three intrusion scenarios.

Experimental results

Research questions

• RQ1 Can rate-dependent resistive forces in granular media be explained without invoking micro-inertial effects (i.e., without relying on the inertial number)?
• RQ2 What physical mechanisms dominate rate dependence in granular intrusion when micro-inertia is negligible?
• RQ3 How can a generalized RFT model be extended to accurately describe complex intrusions like rigid wheel locomotion and legged running?
• RQ4 Does a velocity-squared correction for macro-inertia alone suffice to capture dynamics beyond simple plate drag?
• RQ5 Can a frictional flow continuum model reproduce the observed rate-dependent behaviors without micro-inertial constitutive laws?

Key findings

• Rate-dependent dynamics emerge in granular media even when the inertial number is negligibly small, indicating micro-inertial effects are not the primary driver of rate dependence.
• A velocity-squared macro-inertial correction alone fails to reproduce the full range of observed dynamics in rigid wheel locomotion and legged running.
• The proposed generalized RFT, incorporating a geometry-dependent correction and macro-inertial force, successfully replicates all experimental observations across plate drag, wheel, and legged intrusions.
• A frictional flow continuum model accurately captures the observed flow characteristics without including micro-inertial terms, supporting the dominance of macro-scale inertial and geometric effects.
• The modified RFT reconciles diverse intrusion phenomena by unifying macro-inertial and geometric effects within a single, physically grounded framework.
• The results demonstrate that rate dependence in granular media can arise from macroscopic flow instabilities and geometric constraints, not just micro-scale grain inertia.