A note about hardening-free viscoelastic models in Maxwellian-type rheologies at large strains

TL;DR

This paper introduces a new viscoelastic model for large strain rheology that avoids spurious hardening effects by incorporating strain and strain rate gradients, supported by mathematical existence proofs.

Contribution

It proposes an alternative inelastic creep model using strain and strain rate gradients to prevent artificial hardening at large slips, advancing rheological modeling.

Findings

The new model prevents spurious hardening effects at large strains.

Existence of weak solutions is established through Faedo-Galerkin approximation.

Combines Kelvin-Voigt damping with Maxwellian creep for improved rheology.

Abstract

Maxwellian-type rheological models of inelastic effects of creep type at large strains are revisited in relation to inelastic-strain gradient theories. In particular, we observe that a dependence of the stored-energy density on inelastic-strain gradients may lead to spurious hardening effects, preventing the model from accommodating large inelastic slips. The main result of this paper is an alternative inelastic model of creep type, where higher-order energy-contribution is provided by the gradients of the elastic strain and of the plastic strain rate, thus preventing the onset of spurious hardening under large slips. The combination of Kelvin-Voigt damping and Maxwellian creep results in a Jeffreys-type rheological model. Existence of weak solutions is proved via a Faedo-Galerkin approximation.