  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.
