  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.

Analysis of PDEs