Intrusion in heterogeneous materials: Simple global rules from complex micro-mechanics

TL;DR

This paper reveals that Resistive Force Theory (RFT), used to model intrusions in complex materials, can be derived from a simple friction-based continuum model, explaining its effectiveness especially in granular media.

Contribution

The authors derive RFT from a basic frictional continuum model, linking it to local material behavior and providing a predictive criterion for its applicability.

Findings

RFT can be generated from a friction-based continuum model.

The model reproduces experimental RFT data without parameter fitting.

Analysis explains RFT's better performance in granular materials.

Abstract

The interaction of intruding objects with deformable materials is a common phenomenon, arising in impact and penetration problems, animal and vehicle locomotion, and various geo-space applications. The dynamics of arbitrary intruders can be simplified using Resistive Force Theory (RFT), an empirical framework originally used for fluids but works surprisingly well, better in fact, in granular materials. That such a simple model describes behavior in dry grains, a complex nonlinear material, has invigorated a search to determine the underlying mechanism of RFT. We have discovered that a straightforward friction-based continuum model generates RFT, establishing a link between RFT and local material behavior. Our theory reproduces experimental RFT data without any parameter fitting and generates RFT's key simplifying assumption: a geometry-independent local force formula. Analysis of the system explains why RFT works better in grains than in viscous fluids, and leads to an analytical criterion to predict RFT's in other materials.