Quasistatic Hypoplasticity at Large Strains Eulerian

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.

Automated summary

This study investigates the isothermal quasistatic hardening-free plasticity problem at large strains. The model is reformulated in terms of rates and the plastic distortion is completely eliminated. The existence and regularity of weak solutions are proved using a regularization combined with Galerkin approximation. The study also considers rate-dependent plasticity and includes the Jeffreys' viscoelastic rheology and Kelvin-Voigt rheology.