Linear theory of viscoelasticity in a generalized hydrodynamic framework

TL;DR

This paper reviews a linearized generalized hydrodynamic theory that unifies elasticity and viscoelasticity, highlighting its relation to classical models like Kelvin-Voigt and Maxwell, and emphasizing its systematic and adaptable framework.

Contribution

It provides a comprehensive overview of a generalized hydrodynamic formalism for viscoelasticity, connecting it to well-known models and illustrating its flexibility in representing different material behaviors.

Findings

Unified description of elasticity and viscoelasticity within a hydrodynamic framework

Relation of the formalism to Kelvin-Voigt and Maxwell models

Ability to interpolate between perfect elasticity and flow by adjusting a single parameter

Abstract

A generalized hydrodynamic theory that systematically incorporates elasticity and viscoelasticity had been derived about a quarter of a century ago. It is based on a strictly Euler point of view, as is natural for hydrodynamics. We used and adapted this theory particularly in a linear framework. There, it is straightforward to focus on what are the flow and displacement fields in linearized hydrodynamics and elasticity, which provides some advantages. Since this theoretical approach appears not to be as commonly widespread as it deserves to be, we here overview and review the formalism. Specific further focus is on pointing out relations to the commonly known Kelvin-Voigt model and Maxwell model. They are naturally contained within this description. The two limits of perfect long-term elasticity on one hand and long-term flow on the other hand can be represented by adjusting only one parameter.