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

Soft materials often display complex behaviors that transition through apparent solid- and fluid-like regimes. While a growing number of microscale simulation methods exist for these materials, reduced-order models that encapsulate the global-scale physics are often desired to predict how external bodies interact with soft media, as occurs in diverse situations from impact and penetration problems to locomotion over natural terrains. This work proposes a systematic program to develop three-dimensional reduced-order models for soft materials from a fundamental basis using continuum symmetries and rheological principles. In particular, we derive a reduced-order technique for modeling intrusion in granular media which we term three-dimensional Resistive Force Theory (3D-RFT), which is capable of accurately and quickly predicting the resistive stress distribution on arbitrary-shaped intruding bodies. Aided by a continuum description of the granular medium, a comprehensive set of spatial symmetry constraints, and a limited amount of reference data, we develop a self-consistent and accurate 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. The premises leading to 3D-RFT anticipate application to other soft materials with strongly hyperlocalized intrusion behavior.