Calculus of Variations and Geometric Measure Theory

E. Davoli - T. Roubicek - U. Stefanelli

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

created by davoli on 16 Dec 2020
modified on 05 Jan 2021


Accepted Paper

Inserted: 16 dec 2020
Last Updated: 5 jan 2021

Journal: Mathematics and Mechanics of Solids
Year: 2021


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.

Keywords: weak solutions, creep at large strains, spurious hardening, gradient of the elastic strain