Visco-elastodynamics at large strains Eulerian

0566120 - ÚT 2023 RIV CH eng J - Článek v odborném periodiku
Roubíček, Tomáš
Visco-elastodynamics at large strains Eulerian.
Zeitschrift für angewandte Mathematik und Physik. Roč. 73, č. 2 (2022), č. článku 80. ISSN 0044-2275. E-ISSN 1420-9039
Grant CEP: GA MŠMT(CZ) EF15_003/0000493
Institucionální podpora: RVO:61388998
Klíčová slova: elastodynamics * Kelvin–Voigt rheology * spatial coordinates * global weak solutions
Obor OECD: Applied mathematics
Impakt faktor: 2, rok: 2022
Způsob publikování: Open access
https://link.springer.com/content/pdf/10.1007/s00033-022-01686-z.pdf?pdf=button

Isothermal visco-elastodynamics in the Kelvin–Voigt rheology is formulated in the spatial Eulerian coordinates in terms of velocity and deformation gradient. A generally nonconvex (possibly also frame-indifferent) stored energy is admitted. The model involves a nonlinear 2nd-grade nonsimple (multipolar) viscosity so that the velocity field is well regular. To simplify analytical arguments, volume variations of the solid material are assumed to be only rather small so that the mass density is constant, exploiting the concept of semi-compressible materials. Existence of weak solutions is proved by using the Galerkin method combined with a suitable regularization, using nontrivial results about transport by smooth velocity fields.
Trvalý link: https://hdl.handle.net/11104/0337852