Quasistatic hypoplasticity at large strains Eulerian

0566139 - ÚT 2023 RIV US eng J - Článek v odborném periodiku
Roubíček, Tomáš
Quasistatic hypoplasticity at large strains Eulerian.
Journal of Nonlinear Science. Roč. 32, č. 4 (2022), č. článku 45. ISSN 0938-8974. E-ISSN 1432-1467
Grant CEP: GA MŠMT(CZ) EF15_003/0000493
Institucionální podpora: RVO:61388998
Klíčová slova: finitely strained plasticity * creep in Jeffreys’ rheology * multiplicative decomposition * rate formulation * quasistatic * galerkin approximation * weak solutions
Obor OECD: Applied mathematics
Impakt faktor: 3, rok: 2022
Způsob publikování: Open access
https://link.springer.com/content/pdf/10.1007/s00332-022-09785-x.pdf?pdf=button

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.
Trvalý link: https://hdl.handle.net/11104/0337835