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Quasistatic Hypoplasticity at Large Strains Eulerian

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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.

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Acknowledgements

The author is very thankful for extremely valuable and inspiring discussions and comments to the manuscript to Giuseppe Tomassetti. Also valuable discussions about transport equations with Sebastian Schwarzacher and about hypoplasticity models with Yannis F. Dafalias are warmly acknowledged. Careful reading and many valuable suggestions by two anonymous referees are thankfully acknowledged, too. Also the supports from the MŠMT ČR (Ministry of Education of the Czech Republic) project CZ.02.1.01/0.0/0.0/15-003/0000493 and the institutional support RVO:61388998 (ČR) are acknowledged.

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  1. Mathematical Institute, Charles University, Sokolovská 83, CZ-186 75, Prague 8, Czech Republic

    Tomáš Roubíček

  2. Institute of Thermomechanics, Czech Academy of Sciences, Dolejškova 5, CZ-18200, Prague 8, Czech Republic

    Tomáš Roubíček

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  1. Tomáš Roubíček
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Roubíček, T. Quasistatic Hypoplasticity at Large Strains Eulerian. J Nonlinear Sci 32, 45 (2022). https://doi.org/10.1007/s00332-022-09785-x

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