Objective Nontensor Rheology: Unique Flow Decompositions from Correlated Microscopic Motions

TL;DR

This paper introduces a novel approach to rheology based on microscopic motions, providing unique flow decompositions into rotation, shear, and extension, challenging traditional continuum mechanics methods.

Contribution

It presents a new set of equations for flow decomposition that depend on a single material parameter and are derived from microscopic motions, offering an alternative to invariant-based rheology.

Findings

Flow decompositions are uniquely determined by microscopic motions.

The equations depend on only one free material parameter.

Finite size effects and boundary conditions influence flow interpretation.

Abstract

The use of continuum mechanics and invariants built from the deviator as an adequate foundation for rheology has been recently disputed by this author. Here we give a specific example of the kind of parcel deformations that are uniquely decomposed by way of microscopic motions into a maximal rotation, a pure shear and an extension. The construction of these equations depends on only one free material parameter but they have no nice form in terms of the operations of vector and tensor calculus which may be why they were overlooked. Although the first order flow is often sufficient to give the rheological information, finite sized parcel deformations can give confusion because of boundary effects, the relevance of which are highly dependent on the global geometry of the experiment.