Quasistatic hypoplasticity at large strains Eulerian

TL;DR

This paper develops a quasistatic hypoplasticity model at large strains in an Eulerian framework, proving existence of solutions and incorporating gradient theories, with applications to rate-dependent plasticity and creep.

Contribution

It introduces a rate-dependent hypoplasticity formulation at large strains, eliminating plastic distortion and proving solution existence with gradient regularization.

Findings

Existence and regularity of weak solutions established.

Plasticity model includes gradient theories for dissipation.

Model covers creep and viscoelastic rheology in shear.

Abstract

The isothermal quasistatic (i.e.\ acceleration neglected) hardening-free plasticity at large strains is considered, based on the standard multiplicative decomposition of the total strain and the isochoric plastic distortion. The Eulerian velocity-strain formulation is used. The mass density evolves too, but acts only via the force term with a given external acceleration. This rather standard model is then re-formulated in terms of rates (so-called hypoplasticity) and the plastic distortion is completely eliminated, although it can be a-posteriori re-constructed. Involving gradient theories for dissipation, existence and regularity of weak solutions is proved rather constructively by a suitable regularization combined with a Galerkin approximation. The local non-interpenetration through a blowup of stored energy when elastic-strain determinant approaches zero is enforced and exploited. The plasticity is considered rate dependent and, as a special case, also creep in Jeffreys' viscoelastic rheology in the shear is covered while the volumetric response obeys the Kelvin-Voigt rheology.