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

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 a 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. The existence of weak solutions is proved by way of a Faedo-Galerkin approximation.

Automated summary

In this paper, Maxwellian-type rheological models of inelastic effects at large strains are reexamined in relation to inelastic strain gradient theories. An alternative inelastic model of creep type is proposed to prevent spurious hardening effects under large slips, by introducing higher-order energy contribution from elastic strain and plastic strain rate gradients. The combination of Kelvin-Voigt damping and Maxwellian creep results in a Jeffreys-type rheological model, and weak solutions are proven to exist through a Faedo-Galerkin approximation.