# Similarities between GSH, Hypoplasticity and KCR

## TL;DR

This paper compares GSH, a physics-based hydrodynamic theory, with hypoplasticity and KCR, revealing their similarities in modeling elasto-plastic behavior in granular media and establishing a solid theoretical foundation for these models.

## Contribution

It demonstrates the deep connections between GSH, hypoplasticity, and KCR, providing a physics-based basis for constitutive relations used in granular media modeling.

## Key findings

- GSH and hypoplasticity show great similarity in uniform, slow elasto-plastic motion.
- Proportional paths and Goldscheider rule naturally emerge from GSH equations.
- GSH provides a robust physical foundation for KCR and related models.

## Abstract

Accounting for elasto-plastic motion in granular media, hypoplasticity is a state-of-the-art constitutive model derived from data accumulated over many decades. In contrast, GSH, a hydrodynamic theory, is derived from general principles of physics, with comparatively few inputs from experiments, yet sporting an applicability ranging from static stress distribution via elasto-plastic motion to fast dense flow, including non-uniform ones such as a shear band. Comparing both theories, we find great similarities for uniform, slow, elasto-plastic motion. We also find that proportional paths and the Goldscheider rule used to construct barodesy, another, more recent constitutive model, are natural results of GSH's equations. This is useful as it gives these constitutive relations a solid foundation in physics, and in reverse, GSH a robust connection to reality. The same symbiotic relation exists between GSH and KCR, or Kamrin's non-local constitutive relation, a model that was successfully employed to account for a wide shear band in split bottom cells.