A few notes about viscoplastic rheologies

TL;DR

This paper employs convex analysis to synthesize viscoplastic dissipation potentials from viscous and plastic elements, comparing rigorous models with empirical harmonic mean-based models for geomaterials.

Contribution

It introduces a convex analysis framework for combining viscous and plastic potentials into a unified viscoplastic model, bridging theoretical and empirical approaches.

Findings

Convex analysis effectively synthesizes viscoplastic dissipation potentials.

Rigorous models are compared with empirical harmonic mean models.

The approach enhances understanding of viscoplastic behavior in geomaterials.

Abstract

The rigorous tools of convex analysis are used to examine various serial and parallel combinations of linear viscosity and perfect plasticity. Nonlinear viscosities are also considered. The general aim is to synthesize a single convex ``viscoplastic'' dissipation potential from the potentials of particular viscous or plastic elements. Rigorous serial-viscosity models are then compared with empirical models based on harmonic means, which are commonly used for various geomaterials.